A critique of recent economic evaluations of community water fluoridation

Background: Although community water fluoridation (CWF) results in a range of potential contaminant exposures, little attention has been given to many of the possible impacts. A central argument for CWF is its cost-effectiveness. The U.S. Government states that $1 spent on CWF saves $38 in dental treatment costs. Objective: To examine the reported cost-effectiveness of CWF. Methods: Methods and underlying data from the primary U.S. economic evaluation of CWF are analyzed and corrected calculations are described. Other recent economic evaluations are also examined. Results: Recent economic evaluations of CWF contain defective estimations of both costs and benefits. Incorrect handling of dental treatment costs and flawed estimates of effectiveness lead to overestimated benefits. The real-world costs to water treatment plants and communities are not reflected. Conclusions: Minimal correction reduced the savings to $3 per person per year (PPPY) for a best-case scenario, but this savings is eliminated by the estimated cost of treating dental fluorosis.


Introduction
The USA and several other countries practice community water fluoridation (CWF), which has been promoted as the preferred solution to reduce caries for over half a century. 1 Approximately twothirds of the U.S. population is treated in this manner according to the Centers for Disease Control and Prevention (CDC). 2 Community water fluoridation programs have increased water fluoride concentrations to 0.7-1.2 mg/l [0.7-1.2 parts per million (ppm)], although a 2011 proposed recommendation, if finalized, would decrease this to 0.7 mg/l. 3 Community water fluoridation is a unique delivery mode of public health care in that fluoride is administered to everyone who drinks the water, regardless of dental status or needs, and at an amount proportional to the water consumed from the fluoridated source, which can range from zero to several liters per day. 4 At the same time, because most community water is not consumed by people, CWF results in dispersion of a regulated contaminant, fluoride, to the greater environment via wastewater treatment plants, storm sewer systems, and use on lawns and gardens. Fluoridation chemicals typically contain other regulated contaminants (e.g. arsenic), extending the possibility of human exposures and environmental dispersal. [5][6][7][8] A central argument for using CWF to reduce tooth decay is the cost savings claimed by the CDC: 9 Every $1 invested in this preventive measure yields approximately $38 savings in dental treatment costs. This argument is repeated by the majority of state governments (Appendix 1) and is frequently cited by proponents to argue for initiating or maintaining CWF.
All $ signs in this paper refer to US$ unless otherwise indicated. However, statements such as $1 saves $38 are currency neutral.
The CDC's estimate is calculated from the per person per year (PPPY) savings reported by Griffin et al.: 10 With base-case assumptions, the annual per person cost savings resulting from fluoridation ranged from $15.95 in very small communities to $18.62 in large communities. 10i Table 1 summarizes Griffin et al.'s results by population size. The CDC derived the $1-saves-$38 claim by scaling the $0.50 cost and the $18.62 savings estimate for large systems (.20,000 people) to get $0.50 : $18.62 < $1 : $38. However, this derivation is not valid because it implies scalability where scalability does not apply: spending more on CWF does not increase caries aversion or caries to be averted.
Griffin et al. 10 is the prime example of a body of work that attempts to evaluate the economics of CWF. As the most comprehensive and most cited work, it will be our focus. We limit our analysis to the smallest and largest systems in keeping with the CDC's report. 9 We also examined and comment on additional CWF cost-benefit analyses (Appendix 2). ii Key steps in Griffin et al. 10 A 1989 workshop 12 at the University of Michigan discussed the cost-effectiveness of CWF and other caries prevention programs, with cost estimates based primarily on data from Garcia. 13 A 1992 paper by Ringelberg et al. 14 improved upon Garcia's cost estimates, and Griffin et al. 10 produced their cost estimates (Table 1) by applying minor adjustments to the results of Ringelberg et al., 14 as described later in this paper.
Griffin et al. 10 adopted a ''societal perspective'' and defined benefit as the cost of averted dental fees and associated productivity losses. They used a 4% discount rate for the main result of $19.12 gross savings. Griffin et al.'s stated assumptions and key intermediate results, organized into a set of key inputs, are provided in Table 2. Note that Input (c) differs from Assumption (3) in the timing of treatment -the authors' calculation was consistent with treatment in the same year. The following steps explain how Griffin et al. obtained their value: Step 1: From Input (d), restoring one decayed tooth surface costs $54z$185$72. Step 2: As described by Input (e) the lifetime costs of a decayed surface include future replacement fillings; the number of replacements depends on when the decay occurs. Future replacement costs are discounted to arrive at a present value. The first avertable filling is discounted 1 year because of Input (f) in Table 2; replacements take place every 12 years up to age 65 years, based on Input (e). iii For example, for a child age 12.5 years, the lifetime cost at a 4% discount rate was estimated to be $159.61 as shown in the following equation: ii These papers are technically cost-benefit analyses, 11 although the term cost-effectiveness is frequently used to refer to the degree that the value of benefit exceeds cost.   10 and key inputs of the calculation of benefits

Stated assumptions Key inputs
(1) The benefit is decay prevented and begins at age 6 years (a) Benefit is the number of decayed tooth surfaces that would otherwise have been treated (2) The benefit is constant over time (3) All decay is eventually treated (4) The adverse effects are negligible (5) Dental fees equal the cost of dental resources (6) A decayed tooth surface will always receive a one-surface restoration (b) Benefit in dollar amounts, or gross savings, is quantified in terms of averted dental fees for amalgam fillings and averted productivity losses due to a visit to a restorative dentist (c) Every decayed surface results in a 1-hour dental visit for a single-surface restoration in the same year it occurs (d) The dental fee for a single-surface filling is $54, and the productivity loss from the visit is $18 (the U.S. average hourly wage) (e) A single-surface filling is replaced every 12 years with another single-surface filling, up to age 65 years (f) It takes one year of exposure for CWF to begin to prevent tooth decay (g) CWF averts 0.19 decayed tooth surfaces per person per year (PPPY) on average (h) The same rate of caries aversion applies from age 6 to 64 years CWF: community water fluoridation.
iii While cutting off replacement at age 65 years may appear to underestimate the benefit (cost of fillings), Griffin et al. appear to have overestimated by incorrectly or inconsistently applying the factors in the numerator, e.g. the expected lifetime costs of a decayed surface for age groups 55-59 and 60-64 years are both $69.235$72/1.04 (Table 3), without the factor (which should be around 0.79) to account for fewer teeth at older ages. (Since Griffin et al. did not present these factors, except for the few that appear in the Equation (1) example, we are not able to recalculate and correct the numbers in Table 3.) Thus the last replacement takes place at age 12.5z1z(4612)561.5 in this example. The cost for each filling or replacement filling is adjusted by a factor (the numerator of the term) representing the probability that the tooth remains at the replacement age.
Step 3: Calculate the national average, using the population distribution in Table 3. Use the midpoint to represent the group in each bracket, e.g. Equation (1) gives the lifetime benefit of an averted decay surface for the 6-19 age group, based on the midpoint, age 12.5 years.
Step 4: The calculation is repeated for each age bracket, except the first and the last age brackets as described by Input (h) in Table 2. Summing the weighted costs gives $100.62 as the national average lifetime cost averted per decayed surface.

Costs
Griffin et al. 10 based their cost estimates for CWF on Ringelberg et al., 14 except that the numbers were adjusted to 1995 dollars, and a different grouping of community sizes was used. Griffin et al. devote one paragraph to their cost estimates. 10 Ringelberg et al. 14 Ringelberg et al. used data for 44 Florida communities to estimate CWF costs. (Florida's phosphate industry is the largest U.S. producer of fluoridation chemicals.) 15,16 Ringelberg et al.'s improved estimates included costs for bulk storage and containment, labor, and opportunity costs of capital investment, and were based on a larger number of communities than previous estimates. 13 The estimated average cost increased from $0.49 PPPY 13 to $1.25 PPPY. 14 With phrases such as ''allowable initial one-time costs … were documented by copies of actual invoices for equipment and services'' Ringelberg et al. 14 appears detailed and based on actual data. However, these invoices were obtained from the Florida public health dental program, which has the authority to approve costs for communities seeking state grants to implement CWF, 17 and thus reflect costs allowed by the state dental program rather than actual costs.
Ringelberg et al. 14 used a 15-year life, with no remaining value, for initial implementation costs, and used 2.4% of the initial costs to calculate the maintenance and repair costs. Labor costs provided by CDC's fluoridation engineer were based on 1 hour per day for all systems and rates of $7 per hour for small systems and $9 per hour for medium and large systems. (Note that, in contrast, Input (d) in Table 2 uses $18 per hour to calculate CWF benefit.) We will show that this is a simplistic and unrealistic view of what is involved in CWF operations.

Reality on the ground
In 2010, amid a budget crisis, the City of Sacramento, CA, instructed all departments to review programs and services. Mr. Marty Hanneman, then Director of the Department of Utilities, wrote in a memo to the City Council: 18 The City of Sacramento has been fluoridating its water supplies just over 10 years. Within that time, the actual cost of operating and maintaining the fluoridation systems has proven to be considerably more than the initial estimate. … The fluoridation infrastructure at the E.A. Fairbairn Water Treatment Plant is overdue for replacement and will be very expensive to replace. … Fluoridating water is a very costly and labor intensive process and requires constant monitoring of fluoride concentrations to ensure proper dosages. … The chemical is very corrosive, so all equipment that is used in the fluoridation process has a very short life expectancy and needs to be replaced frequently. … but also causes frequent and complex system failures.  All of our chemical feed systems require regular maintenance which is routine but fluoride feed equipment often requires replacement and more frequent attention. … I have toured plants and seen in trade publications deteriorating pipes, steel doors and casing, electrical components, etc. There are millions of dollars spent yearly on infrastructure damage caused by fluoride in our industry.
The realities expressed in these two quotes are not the exceptions. A water plant manager in Alberta, Canada, complained that the fumes from the acid etched the glass, paint, and computer screens of the water treatment plant. 19 Seven years after CWF began in 2001, Riverton, Utah, spent nearly $1.2 million for two new buildings ''to get fluoride out of electrical and pump area.'' 20 Several incidents of fluoride overfeeds at watertreatment plants have been investigated. Gessner et al. 21 described an accident that occurred in Hooper Bay, Alaska, in 1992, in which 296 residents suffered acute poisoning and a 41-year-old man died. Petersen et al. 22 reported on an overfeed incident in a residential Connecticut community in 1986. The fluoride caused gastroenteritis in 33% of those who drank the water and itching and skin rashes in those with dermal contact; the acidity leached copper from domestic plumbing. Penman et al. 23 investigated an outbreak of acute poisoning caused by a fluoride overfeed in a small rural community in Mississippi in 1993. Several people became ill and connected the onset of their illness to drinking tap water at the same restaurant. A community survey was performed, and the authors concluded that approximately one third of households in the town may have been affected, though the extent remains unknown.
Akiniwa 24 examined seven events of acute fluoride poisoning related to the fluoridation of drinking water that have been reported in the U.S. He estimated from these reports that acute fluoride poisonings have occurred at doses of 0.1-0.8 mg fluoride per kg of body weight. One fatal fluoride intoxication caused serious illness in 12 patients, 3 of whom died, in a hospital hemodialysis unit in Chicago in 1993. 25 Caused by failure of a widely used deionization system, this event would not have been catastrophic had the water not been fluoridated.
Other incidents reported in local media have included injuries to water plant workers, massive evacuation around an interstate highway, damages to water pipes or concrete floors, and environmental hazards to fish and ground. A number of these incidents are cited in Appendix 3.
An economic evaluation taking a societal perspective should have considered the societal costs from these inevitable consequences of CWF. However, comprehensive data needed to estimate such costs are lacking, because the government agencies that should track these incidents appear to have a conflict of interest in protecting and defending the CWF policy (e.g. Florida; 26 Layton; 27iv Appendix 1). Nevertheless, evidence presented here demonstrates that Ringelberg et al. 14 were unrealistic even considering only the direct costs of CWF to a water system.

Real-world estimates
In late 2010, Black and Veatch Corporation (Overland Park, KS USA) was retained through a competitive bid process to perform an objective evaluation of the fluoride program of the city of Sacramento, CA. After a comprehensive and detailed review, the study 28 observed that immediate and future upgrades would be needed to continue fluoridating and to achieve modest operational efficiency improvements. Noting that Sacramento's operational costs were within industry practice, the report developed detailed cost estimates and gave a different picture from Ringelberg et al., 14 e.g. the labor cost was set at a rate of $100 per hour, in contrast to the $7/$9 per hour labor rate from the CDC. The city's engineer, Mr. Brett Ewart, explained (Ewart, 2012, private communication): The 100/hr. is a hybrid rate used to represent the large variety of machinists, electrical staff, water quality staff, management, etc., that work on the program. The amount of staff time (and type of staff) dedicated to the fluoride program is flexible. Some maintenance activities are generally fixed, others are reactionary and difficult to predict in advance. The rate would include the employees' salary, benefits, and overhead to perform the work.
Sacramento's water system consisted of the following: One large treatment plant supplying 44% of the water, whose fluoridation system had already been updated in 2007; a second large treatment plant (Fairbairn WTP) supplying 42% of the water, whose fluoridation system was in need of replacement; and 27 wells supplying 14% of the water, and whose fluoridation systems also required updates. 29 The overall cost estimates provided by Black and Veatch for the needed replacement and updates, annualized using a 2.5% discount rate over a 20-year planning horizon, v were $1 million for the 27 wells and $464,000 for the Fairbairn WTP. 29 The cost projection for the Fairbairn WTP is applicable for large water treatment plants, while the cost projections for the well upgrades are applicable for small systems.
v First 5 Sacramento, the organization that funded the study, may fund the capital update cost with a condition that requires the city to commit to CWF for 20 years, regardless of the city's future fiscal conditions. 18 In July 2012, the city accepted a grant from First 5 Sacramento to continue fluoridation until June 30, 2015, even though the grant will provide less than 10% of the system costs over the next 3 years. 30 iv In a letter to Davis County Health Department and others, the Mayor of Layton, Utah strongly protested that the costs of fluoridation to the citizens of Layton and Davis County were far greater than the costs portrayed by the Department when it ''clearly knew better''. 27 To calculate the PPPY costs, we allocated the total population of Sacramento, 466,000 people (2010 U.S. Census), to the 27 wells and to the Fairbairn WTP using the percentages of total water supplied of 14% and 42%, respectively. The allocated populations are 65,000 and 196,000, respectively. Dividing the total costs by population and number of injection sites, we obtain a cost estimate of $15.38 and $2.37 PPPY for a singleinjection point water system serving 2,400 and 196,000 people, respectively. (Systems serving 2,400 people are not rare. Of the 44 systems in Ringelberg et al. 14 three systems had smaller populations and seven systems had smaller populations per injection site. ) We considered whether to adjust for the cost of living in Sacramento and determined that there was no need. The cost of living for Sacramento is 8% higher than the U.S. average. 31 This differential, however, is easily offset by other considerations, e.g. the use of a 2.5% instead of 4% discount rate. The cost projection also assumes that the Health Department continues to waive a requirement for certain standard equipment. In addition, actual bids for construction may turn out to be much higher than the engineer's estimates. 32,33 Finally, it was unknown whether implementing the recommendations would solve the city's fluoridation issues. 29 A small water system serving more than 2,400 people is expected to cost less than $15.38 PPPY. Similarly, many large systems serve less than 196,000 people and are expected to cost more than $2.37 PPPY. (Note that large water districts serving more than 196,000 people will not necessarily cost much less than $2.37 PPPY, because such water districts often have multiple treatment plants and/or auxiliary wells, which make them equivalent to a smaller single-injection point system). Therefore, reasonable cost estimates for the smallest (,5,000 people) and largest (.20,000) systems in Table 1 would be about $10 and $3 PPPY, respectively.
Strictly speaking the annual cost projections provided by Black and Veatch are 20-year financing costs.
At the end of the 20-year period, components such as new buildings may still have value. However, given the ability of the chemicals to degrade concrete (Appendix 3 items 17 and 19), significant annual maintenance and repair costs after the financing period are expected. In addition, circumstances could require a water system to implement major infrastructure changes to their fluoridation facilities. Sacramento is such an example. Despite implementing fluoridation comparatively late (around 2000), the city has already endured major infrastructure adjustments and is considering more, long before the 20-years projection period. Finally, it is possible that a system may discontinue CWF; in that case, buildings constructed specifically for CWF may hold little value.

Other estimates
The Black and Veatch report cited above is valuable in that it is recent, comprehensive, detailed, and authored by a firm that has consulted on other fluoridation programs. In general, reliable cost information for CWF programs is difficult to obtain, and information provided in response to a request is often limited to the cost of the fluoride chemicals. In Table 4, we present additional cost information and estimates collected from various sources. 20,[32][33][34][35][36][37][38][39][40] The majority of these are cost estimates prior to implementation; New York and some Utah figures show actual costs. Costs are reported either for implementation (I) or for annual operation and maintenance (O). For convenience, we calculate a PPPY cost by annualizing the implementation cost (I) using a 4% discount rate over 15 years vi (meaning $100 annualizes to $8.65) and normalizing the total, i.e., dividing the annualized I plus O, if available, by  Table 4 are incomplete or partial, or the values are underestimated. Several (denoted with {) do not include operation and maintenance (O&M) costs. The New York numbers consist of costs to rehabilitate CWF facilities in two plants, and only chemicals are included in O&M. The San Jose numbers provided in a Black and Veatch study were for wells that provide only half of the water for the city, which imports the other half. The preliminary estimates for Napa, CA are from about the time that Sacramento began its fluoridation program and probably suffer from similar underestimates of costs. 18 The estimates for Portland, OR were provided by the Water Bureau after a meeting with representatives from the CDC and the organizations pushing to fluoridate the city. The $575,000 O&M figure appears unrealistic -Sacramento already paid over $400,000 back in fiscal year 2008/2009 for hydrofluorosilicic acid (HFSA) to fluoridate 86% of their water; this translates to about $1 PPPY for the cost of HFSA alone. In addition, the O&M estimate excluded costs of additional caustic or other corrosion control chemicals to bring the pH back to an appropriate level, and the cost of additional capital improvements needed to mitigate water quality impacts were not included in the estimated capital costs. 37 Community water fluoridation proponents have a poor track record for cost estimates. For example, the county health board of Davis County, UT, provided a cost estimate of $1.38-$2 PPPY prior to a vote in 2000, but the true implementation cost was $4.29 PPPY. 41 This is also seen in the estimates/observed figures for the two Utah systems in Table 4. In 2001, Arkansas state legislators passed a state mandate to fluoridate community drinking water. They were partially motivated by an offer from Delta Dental of Arkansas to donate $500,000 total toward startup costs for the 32 water systems affected. 42 Later Delta Dental pledged $2 million for 34 systems and soon found itself needing to raise another $6-$10 million. 43 (State mandates in California and Arkansas both require the initial implementation costs be funded by outside sources.) Overall, reported costs of CWF are consistent with our real-world estimates and not with those estimates 10,14 commonly cited by fluoridation proponents.

Costs of dental fluorosis
Griffin et al.'s Assumption (4) in Table 2, that the adverse effects of CWF are negligible, 10 is common to most cost-benefit analyses of CWF. It is inexplicable that neither Griffin et al. 10 nor other similar studies (Appendix 2) mention dental fluorosis, defective enamel in permanent teeth due to childhood overexposure to fluoride. 44, 45 Community water fluoridation, in the absence of other fluoride sources, was expected to result in a prevalence of mild-to-verymild (cosmetic) dental fluorosis in about 10% of the population and almost no cases of moderate or severe dental fluorosis. 46 However, in the 1999-2004 NHANES survey, 41% of U.S. children ages 12-15 years were found to have dental fluorosis, including 3.6% with moderate or severe fluorosis. 47 As an increased prevalence of dental fluorosis became evident, there were attempts to shift attention to other sources of swallowed fluoride, such as toothpaste. 48 However, 1/4 liter (or about 8 oz) of fluoridated water at the ''optimal'' concentration of 1 mg/l contains the same amount of fluoride as a bead of toothpaste (0.15% w/v fluoride ion) 0.68 cm in diameter. Regarding other sources of ingested fluoride, Szpunar and Burt 49 state that the factor that differentiates the studied communities with respect to the prevalence of caries and fluorosis is the fluoride concentration in the community water supply.
Dental fluorosis had been dismissed as cosmetic by CWF promoters and government agencies in the U.S. until the National Research Council (NRC) concluded that ''severe dental fluorosis'' qualified as an adverse health effect due to increased risk of caries and loss of dental function. 44 When an economic evaluation is framed as having a societal perspective, it should include effects that result in social costs, regardless of whether the effects are cosmetic or systemically harmful. In a later paper, Griffin et al. indicated that some people may want ''esthetic restorative procedures'' to treat fluorosis, but treatment costs were not estimated. 50 We next provide a high level estimate of the minimal costs of treating dental fluorosis.
Dental fluorosis is classified by the severity of the discoloration, the presence of pitting, and the extent of the tooth surfaces affected. 44,45vii Although bleaching and microabrasion can be used to improve the appearance of milder cases of fluorosis, moderate and severe dental fluorosis can require extensive treatment to improve the cosmetic appearance and prevent further loss of enamel. 44,45 Treatment options include applications of veneers or crowns. Porcelain veneers may cost more than composite resin veneers ($800-$2,500 vs. $250-$1,500), but they require less frequent replacement (10-15 vs. 5-7 years). 52,53 vii Dean's classification for very mild, mild, moderate, severe and very severe dental fluorosis: at least two teeth contain mottled surface area covering less than 25%, between 25 and 50%, between 50 and 100%, 100% (with discrete pitting), and 100% (with confluent pitting) of the tooth surface, respectively 51 Crowns are ''usually used as a last resort because they can be a threat to tooth vitality. '' 44 For this analysis, we assume that each moderate or severe fluorosis tooth receives a porcelain veneer treatment. We further assume that a child with the condition gets the first treatment at age 13.5 years, and the veneers are replaced every 12 years. The lifetime cost of a veneer is calculated using equation (1), except the $72 is replaced by the cost of a veneer, for which we use a lower-end number of $1,000. This gives a lifetime cost of $2,217. Dean's Enamel Fluorosis Index, the most widely used classification of dental fluorosis, is assigned on the basis of the two most-affected teeth. 44 Thus, the lifetime cost of veneers for a child with moderate or severe fluorosis would be at least $4,434.
Beltrá n-Aguilar et al. 47 reported that 3.6% of U.S. children ages 12-15 years in 1999-2004 had moderate or severe dental fluorosis, but did not provide information on the fluoridation status of the affected children. At most about 60% of the U.S. population received fluoridated water during the time period when these children were susceptible to development of fluorosis. viii Both the prevalence and the severity of dental fluorosis are correlated with the fluoride concentration in drinking water. 45,49,55 If all of the cases of moderate and severe dental fluorosis occurred in fluoridated rather than nonfluoridated areas, then at least 6% of children in fluoridated areas would have moderate or severe fluorosis. ix For our calculations, we have assumed that 5% of children in fluoridated areas have moderate or severe fluorosis. From Table 3, the percentage of children at age 13.5 years is about 20.4% / 14 5 1.46%. Thus the minimum cost of treating dental fluorosis is estimated to be $4,43461.46%65% 5 $3.24 PPPY.

Other costs
There are other costs missing from the conventional cost-benefit analyses of CWF (Appendix 2). The NRC's 2006 report on fluoride exposures and toxicity found that the U.S. Environmental Protection Agency's (EPA) drinking water standard for fluoride was not protective of human health. 44 The NRC did not evaluate CWF for safety or efficacy, but the report showed that the average fluoride exposures associated with adverse health effects are within the expected range of fluoride intake for populations with fluoridated water, especially for infants, young children, and people with high water intake. 44,56x Peckham and Awofeso's recent review specifically concluded that fluoridation has ''significant costs'' in relation to adverse effects on human health, although these costs were not quantified. 57 Health risks to water plant operators are not included in most discussions of CWF, but these individuals may receive substantial occupational exposures to fluoride if the safety infrastructure or training is not adequate or if equipment malfunctions. 58,59 Most of the fluoridation chemicals used in the U.S. are byproducts of the phosphate fertilizer industry in North America or Asia. 15,16,60 Since only a small percentage of municipal water is actually consumed by people, the practice results in wide dispersion of a regulated pollutant into the environment via local water districts. Fluoride pollution may result in serious ecological risks to aquatic organisms. 61 Fluoride is regulated by the U.S. EPA as a contaminant in drinking water 62 and as an air pollutant. 63 A number of fluoride compounds are considered hazardous substances with assigned Reportable Quantities. 64 In addition, fluoridation chemicals often contain other regulated contaminants. [5][6][7][8] Hirzy et al. 65 estimated that the typical concentration of arsenic in the major fluoridation chemical (HFSA) could be responsible for several excess lung and bladder cancers per year in the U.S. and the consequent costs of treatment.
Political costs have at times been acknowledged but not included in CWF analysis. 10 This category goes beyond costs associated with fluoridation referenda to include government expenditures for promoting fluoridation programs, costs associated with lobbying elected officials on this issue, legal challenges to fluoridation programs, and possible personal injury litigation involving workers or members of the public. [66][67][68][69][70] There are also costs associated with avoiding fluoridated tap water, either by need or by choice. These are all societal costs of CWF that should not simply be excluded or assumed negligible without examination.

Benefits
The primary benefit attributed to CWF is prevention of caries, although a major review in the United Kingdom reported no relevant studies of ''evidence level A (high quality, bias unlikely)'' and expressed surprise that little high quality research had been undertaken. 71 Caries prevention is commonly assessed in terms of a reduction of decayed, missing, or filled ix 3.6 / 53% 5 6.8% and 3.6 / 60% 5 6%.
viii Infants and young children are most at risk for exposures leading to dental fluorosis. 45  x People with high water intake include athletes, outdoor workers, military personnel, and people with medical conditions such as diabetes insipidus or diabetes mellitus. 44 People with impaired kidney function may have high water intake and might also have reduced urinary excretion of fluoride. 44 teeth (DMFT), DMF tooth surfaces (DMFS), or their variations. xi Estimation of averted caries is obviously central to a cost-benefit analysis.
Griffin et al. 10 relied on the theory that caries averted by CWF can be considered in terms of two factors as shown in the following equation Averted caries~Incidence|Effectiveness (2) where Incidence is the per person annual caries increment without CWF, and Effectiveness is the percentage reduction in caries due to CWF. Before we explain and critique how Griffin et al. 10 derived their values for Incidence and Effectiveness, it is worthwhile to examine the concepts of incidence and effectiveness in the context of CWF.

Incidence
Griffin et al. 10 treat the reported caries incidence in selected nonfluoridated areas as the caries incidence in the absence of CWF. However, they have not accounted for the decline in caries rates over time apart from CWF or the variability in caries rates among various areas, independent of CWF.
It has been known for decades that tooth decay prevalence has been declining in developed countries regardless of CWF status, i.e., the ''secular decline''. 11 Diesendorf 72 listed over 20 studies which reported substantial temporal reductions in caries in unfluoridated areas. In many cases, the magnitudes of the reduction were comparable to those attributed to fluoridation in some fluoridated areas; it was also pointed out that fluoride toothpaste or supplement could not have accounted for many of the reductions.
That fluoride is not needed for dental health is not surprising. A 1952 NRC report 73 described studies reporting that the teeth of ancient peoples and modern primitive peoples were relatively free from dental caries, in a striking contrast to the teeth of modern people. However, primitive peoples had increased rates of caries when brought into contact with a modern diet. This is consistent with the fact that caries are rare in animals in the wild. Finn 73 also described the significant geographic and temporal variability of caries prevalence, citing Hagan 74 for demonstrating how caries prevalence may vary within narrow geographic limits, as well as fluctuating within the same area from time to time.
Hagan 74 studied 12 communities in Georgia, including 24,092 children, and reported the following by community: The average annual caries increments were 0.18-0.90 for children up to 16 years old; the DMFT ranged from 0.40-2.44 at age 7 years to 1.41-10.64 at age 16 years; the percentage of children with at least 1 DMFT ranged from 23-77% at age 7 years to 58-100% at age 16 years. The ranges of DMFT for a given age in these pre-CWF situations approach or exceed the differences reported between fluoridated and nonfluoridated locations in more recent years. For example, Heller et al. 55 reported mean DMFS values ranging from 2.53 (0.7-1.2 ppm F) to 3.08 (,0.3 ppm F), with a mean DMFS of 2.75 for the entire sample (18,755 U.S. schoolchildren ages 5-17 years with a history of a single residence). The percentage of cariesfree children ranged from 52.5% (.1.2 ppm F) to 57.1% (0.3-0.7 ppm F), averaging 54.6% for the entire sample. McDonagh et al. 71 reported that, among 15 studies analyzed, the mean differences in dmft or DMFT ranged from 0.5 to 4.4 (median 2.25).
Other historical data contradicting the idea that fluoride is needed for dental health have been reported. Using data from New Zealand Health Department records of 5-year-olds' tooth decay from 1930 to 1990, fluoridation coverage, and fluoride toothpaste sales, Colquhoun 75 showed that the dramatic decline in tooth decay started long before water fluoridation, fluoride toothpaste, or application of fluoride. Another paper noted that the DMF rate in children ages 12-15 years in Taiwan was as low as 1/3 to 1/6 of that in children of the Western countries where water fluoridation had been in effect for 8-11 years. 76 Studies that attributed differences in tooth decay rates between selected communities to CWF may have only observed these geographic or temporal variabilities, independent of any effect of CWF. Other studies (see Appendix 5) found that nonfluoridated cities also experienced rapid reductions in tooth decay rates without installing CWF, even though these cities had previously been compared with fluoridated cities as evidence that CWF reduces caries. Hence the concept of a no-fluoridation caries incidence rate has little meaning.

Effectiveness
Griffin et al. 10  Community water fluoridation effectiveness has been variously reported in the literature. The unit of measure can be variations of DMFT, DMFS for permanent teeth, the corresponding measures for deciduous teeth, or the percentage of children with no caries. They could be for a single age or for an age range. Information about length of exposure to CWF xi DMFS counts the number of decayed (untreated), missing, filled tooth surfaces and DMFT counts teeth instead of surfaces. (An adult without wisdom teeth has 28 permanent teeth and 128 tooth surfaces.) Capital letters refer to permanent teeth and lower case letters (dmfs, dmft) to deciduous teeth. may or may not be included. Study parameters are often poorly defined and confounding factors not typically examined.
Often a percentage value is produced from some relative differentials and referred to as CWF effectiveness, despite that the percentages come from different situations. Some may argue that since all the different kinds of studies point to similar ranges of effectiveness, it is proof that the effectiveness estimates are robust. However, the premise of this argument is false.
First: Units. Units of measures do affect the results. An independent investigation of the 1987 NIDR data using DMFT instead of DMFS led to the conclusion of no effectiveness. 78 When asked about results for teeth, Brunelle was quoted to have said that they ''are in a box somewhere'' and she ''could not remember what exactly the results were'' and that the decay rate for teeth ''is rather low so that there is very little difference in most anything.'' 79 Truman et al. 80 estimated effectiveness in units of teeth from data reported in a number of studies (Table 5) even if a study reported data in both teeth and surfaces.
Studies reporting results in teeth were more common in the past. The focus shifted toward surfaces as the prevalence of caries dropped and caries became concentrated in a small subset of the population. 81 Measuring caries in units of surfaces gives heavy weight to the small percentage of people with high levels of decay. xii Second: Lengths of exposure. There are two relevant exposures: exposure to carious influence and exposure to CWF.
Exposure to caries is determined in part by the time a tooth erupts. Usually age is used as a surrogate for the length of this exposure. If a study examines subjects of a range of ages and one effectiveness number is to be presented, which age is selected or how different age groups are weighted to calculate an average can produce different results. Appendix 4 provides examples of studies showing differences in caries experience that were attributed to CWF exposures, when the results may be better explained by differences in age distributions of the populations being compared.
Exposure to CWF is often handled by comparing only those with lifetime exposure to those with no exposure. However, if a result is contingent on excluding partial exposure it weakens the argument for CWF as a public policy. More importantly, this approach introduces a probable bias if the two exposures (to caries and to CWF) are not independent.
Evidence indicates that ingested fluoride may delay tooth eruption, 44,45,85 which would affect caries scoring by giving the appearance of less decay for a given age. 44,45 Komárek et al. 86 used data for actual tooth eruption time and found no convincing effect of fluoride intake on caries development. Weaver 87 indicated that ''the caries inhibitory property of fluorine seems to be of rather short duration,'' consistent with a delay in the exposure of permanent teeth to a cariogenic environment.
Third: Methods. The methods of determining an effectiveness value are even more problematic, especially in regard to policy references. This is best demonstrated by an examination of Truman et al., 80 which was co-authored by Griffin, other CDC personnel, and a Task Force appointed by the Director of the CDC. The Task Force was established by the U.S. Department of Health and Human Services (HHS) in 1996 to provide recommendations for community preventive services, programs, and policies. Reported in 2000, the findings of the Task Force's systematic review 88 became the main results of Truman et al. 80 on CWF effectiveness, as well as the basis for Healthy People xiii 2010's goal of increasing CWF in the U.S. to cover 75% of the population. 91 Healthy People 2020 92 continues with a goal of increasing coverage to 79.6%.
Truman et al. 80 based their conclusion on 14 studies in three groups (Table 5): 76,[93][94][95][96][97][98][99][100][101][102][103][104][105] N Studies starting or continuing CWF with before and after measurements (Group A-On) N Studies stopping CWF with before and after mea- N Studies starting or continuing CWF with only post measurements (Group B-On) They calculated a number of ''estimates of effectiveness'' from the studies using two formulas, one for Group A (before-and-after) and one for Group B (post measurements only). The measures were mostly DMFT or dft.
The median of estimates was taken to represent the CWF effectiveness for each study type; the results were 29.1% for Group A-On, 50.7% for Group B-On, and 17.9% for Group A-Off. (The 29.1% and 50.7% figures were presented by the Task Force.) 88 With these numbers the authors concluded ''strong evidence shows that CWF is effective.'' This conclusion is not valid. We describe three areas of problems below (details provided in Appendix 5).
xii Proponents often appeal to sympathy for young children with high levels of tooth decay to argue for CWF. 82 However, early childhood caries (ECC) is not prevented by fluoride. 83 Selection of studies: Studies of higher quality and relevance such as the NIDR surveys or other U.S. studies were not included. Many studies on the effect of cessation of CWF (Group A-Off) were omitted even though this group had only three studies. Not all included studies are relevant for CWF or meet the stated criteria.
Selection of estimates: The number of estimates selected from each study appears arbitrary. Fewer estimates were selected from large-scale studies reporting findings in detail than from small studies reporting few findings. Sometimes the selected estimate did not fit the group it was placed in. Selection of arbitrary numbers of estimates from an arbitrary set of studies does not lead to confidence in the reported median.
Selection of formula: Within the limited set of studies and estimates selected, the authors failed to apply their formula consistently. In addition, the results from the application of the formula can be misleading. Upon examination of the data, some purported positive outcomes are revealed as purely an artifact of the formula -the never-fluoridated communities had a dramatic reduction in caries without the help of CWF.
The incidence and effectiveness in Griffin et al. 10 Three estimates for Incidence were compiled from several unrelated sources while three estimates for Effectiveness were derived from a single source. They are paired by magnitude and substituted in Equation The base-case averted DMFS of 0.19 is the key input (g) in Table 2. (Note that not all studies cited by the authors measured DMFS, and the differences were not always pointed out.) We next examine how the numbers on the left-hand side were derived.

The Incidence
Griffin et al. 10 obtained three sets of annual caries increments in nonfluoridated communities as Incidence; they are reproduced in Table 6. The sources were, respectively, published studies cited in Garcia, 13 the National Survey of Oral Health (NSOH) in U.S. Schoolchildren and a separate NSOH in Employed Adults and Seniors, and the First and Third National Health and Nutrition Examination Survey (NHANES I, 1971-1974and NHANES III, 1989-1994. For the best case, the authors used the controls in Garcia's review 13 of published studies of clinical and community trials. For the base case, the incidence for children was imputed by dividing the difference in mean DMFS for 6-year-olds and 17-year-olds living in communities without fluoridation by 11. Unrelated to the children's survey, the adult NSOH survey was measured in DFS (without M, missing surface) and was not stratified by community fluoridation status. Hence, they imputed the incidences by using the least fluoridated region (Pacific). They scaled the mean DFS by the ratio of average numbers of teeth in the two age points to adjust for missing teeth. They also added root caries incidences from other studies. For the worst case, the authors imputed the incidence using data from two NHANES surveys, which did not report fluoridation status. A major difference from the base case was that they tried to use data on the same birth cohort over time. Additional adjustment was applied because earlier NHANES data measured DFT instead of DFS.
The source of the best case, Garcia, 13 was the basis for discussion of CWF in the 1989 Michigan Workshop. Workshop participants were critical of the numbers. ''Most work groups felt that the estimates of caries incidence in Garcia's report were generally too high and reduced them by several decimal points, though some reduced them further.'' 12 Griffin et al. 10 also stated in their discussion that the samples were probably not representative of the general population. Thus, the best case is invalid.
Griffin et al. 10 also admitted that the base case was overestimated. They remarked that, given the secular decline in caries, using cross-sectional data to impute  96 7-9 A-On/2 Evans et al. 97 5 A-On/3, B-On/1 Guo et al. 76 4-15 A-On/2, B-On/3 Kü nzel and Fischer 98 6-15 A-On/4, A-Off/2 Attwood and Blinkhorn 99 10 A-Off/1 Kalsbeek et al. 100 15 A-Off/2 Brown and Poplove 101 14-17 B-On/4 Fanning et al. 102 3-6 B-On/3 Hawew et al. 103 6,12 B-On/4 Provart and Carmichael 104 5 B-On/2 Rugg-Gunn and Nicholas 105 5 B-On/3 caries increment from the NSOH would overestimate current increment. Secular decline 11,72 refers to the widespread decline in caries observed in nonfluoridated areas. It means that when a 6-year old living in a nonfluoridated area today grows up to be 17 years old, he will likely have fewer caries than his 17-year old neighbor has today. Thus using the latter to represent the former (cross-sectional data) overstates the incidence of caries.

The Effectiveness
As with the Incidence, Griffin et al. 10 Table 12) and by region ( Table 7). The national averages from this subset of data showed a difference of 0.6 DMFS, or 18%, between the two exposure groups. By further restricting their sample to a subset of 5,954 children (reportedly by removing all data points with any supplemental fluoride exposure), the 18% difference was raised to 25%. No age or regional distribution was shown for this restricted set of data. Griffin et al. 10 took this 25% as the base-case Effectiveness. Brunelle and Carlos 77 ignored 58% of the total data (or 55% of those with complete residence histories), despite that partial exposure data from this national survey can be analyzed and are informative. 78 It is therefore questionable if the 18% reduction in DMFS represents the findings of the survey. Even more troublesome is the 25% adopted as the base-case Effectiveness, as it ignores 85% of the survey data.
The best-and worst-case Effectiveness, 29% and 12%, respectively, were supposed to be calculated from the best three and the worst four effective regions. However, the worst four regions (I, II, III, and V in Table 7) would average closer to 6% than 12% using regional population data found elsewhere. 106 It appears that Griffin et al. 10 may have removed Region III (Midwest) from the calculation given the comment: ''The negative effectiveness value in the Midwest may have been due to small sample size because few children living in this region actually received nonfluoridated water.'' This criticism would equally apply to the highest-effectiveness Region VII (Pacific), as few children in this region received fluoridated water, but it was not considered a problem.

Lack of evidence for adults
Assumption (2) and Input (h) in Table 2 assume the same CWF benefit to age 64 years, despite that estimates of Effectiveness were derived from a children's survey. Two adult studies 51,107 were cited to support this extrapolation. However, the data presented in Grembowski et al. 107 do not support its conclusion, and Eklund et al. 51 appear to be mis-cited in addition to the fact that the concentrations involved, 3.5 versus 0.7 mg/l, are irrelevant to an evaluation of CWF. We examine each of these studies below.
That few adult studies are available has been noted elsewhere. Garcia 13 stated that very limited information exists in the literature about caries incidence in adults, and Newbrun 108 identified only seven adult studies; he commented that very few acceptable data exist and that the comparison was either between those living in low-fluoridated and high-fluoridated (greater than optimal) communities or between those living in optimally fluoridated and high-fluoridated communities. Thus, it is not surprising that Truman et al. 80 included ''What is the effectiveness of CWF among adults aged § 18 years?'' among important unanswered questions.
More recently Slade et al. 109 presented an analysis of Australian data from a 2004-2006 survey, and Griffin et al. 110 did a meta-analysis of several earlier studies. We examine these papers in detail in Appendix 4. Among other problems, both articles (and several studies included in the latter) failed to properly account for different age distributions.
Grembowski et al. 107 This study examined Washington state employees and spouse-dependents aged 20-34 years living in Olympia, Seattle, or the Pullman, WA/Moscow, There are additional problems with Grembowski et al. 107 For example, it was stated that ''1,066 … formed the data base for this analysis''; but the paper shows results for only 595 participants, and makes no mention of the other 471 participants. In other words, 44% of the data are unaccounted for.
Grembowski et al. described calculating the years of fluoridation exposure for the age ranges: 0-5, 6-14, 15-19, and 20-34 years, to ''explore systemic and topical effects.'' However, Table 8 has a group described as having an exposure pattern, meaning exposure to CWF for the majority of time during the period of ''ages 0-5 only or ages 0-14 only'' -it appears to be a hastily created grouping to avoid showing results from the original design. Indeed only 40 adults were in this group, so that they had to qualify their conclusion that ''exposure to fluoridated water during childhood has lifetime benefits'' with ''These results are tentative, however, because the pre-eruptive sample size was small.'' The four groups differed in their education levels as well as their fluoride exposure (Table 8), with the noexposure group having the lowest percentage with a college degree. The CDC has reported that oral health disparities are associated with lower education level. 111xiv Although Grembowski et al. pointed out the difference in education level, they did not evaluate the possible impact of this difference on their findings. 107 Grembowski et al. revealed that people in the nonfluoridated sites had less untreated decay than in the fluoridated sites. They also pointed out that the filled component of DFS is influenced by dentists' treatment decisions. They noted that dentists in nonfluoridated areas may restore teeth in adults more frequently, and that use of identical treatment criteria would ''slightly reduce'' their estimates of fluoridation's benefits.
They claimed to offer evidence that exposure to fluoridated water during childhood has a lifetime benefit and concluded that their findings provide support for health officials to continue and expand this public health program. Their data do not support the conclusion.
Eklund et al. 51 This study examined the communities of Lordsburg and Deming, New Mexico, with fluoride concentrations of 3.5 and 0.7 mg/l in the drinking water supply, respectively. Subjects were approximately 30-60 years of age, had been born and lived at least the first 6 years of life in the city, and had an unequivocal water history. The main results were summarized in two tables, one for dental fluorosis and one for caries, reproduced in Tables 9 and 10, respectively.
Griffin et al. 10 wrote that this work found adults who received a high fluoride concentration experienced 20% fewer carious surfaces. The 20% number was an interpretation from two numbers, 7.0 and 8.7, found at the upper right corner of Table 10. (Note: the unit of measure was teeth, not surfaces.) The authors, however, were less inclined to draw the kind of conclusion that Griffin et al. 10 did. They wrote: The picture is less obvious for dental caries. … The assessment of dental caries in an adult population is difficult. … First, it is often difficult to determine why missing teeth were removed. … Second, it is not  possible to determine whether all filled teeth had a carious lesion as defined by the diagnostic criteria.
In contrast, they concluded that differences between the communities are ''obvious and unequivocal'' for dental fluorosis. Indeed, no one from Lordsburg escaped dental fluorosis and 76% of them were severe or very severe. At the lower concentration of 0.7 mg/l, Deming had 16% dental fluorosis, including some moderate cases. Table 10 shows that the higher DMFT in Deming was due to a much higher filled component across all age groups. As with Grembowski et al., 107 Eklund et al. 51 noted that the filled component is influenced by dentists' treatment decisions. On the other hand, the oldest age group in Lordsburg had many more missing teeth, similar to other studies that found a relationship between high fluoride exposure and tooth loss. 112,113 Costs of dental treatments Costs of dental treatments consist of dental fees and lost productivity. Griffin et al. 10 used survey data for the dental charge, 114 which may differ from the charge in a competitive market, and therefore not be representative of the resource costs. Assumption (6) holds that all fillings are single-surface fillings. This overestimates dental costs, since a three-surface cavity does not require three times more resources than a one-surface cavity requires, in terms of either time lost or dentist's effort. In fact, the fees in the survey were $53.60 and $83.27 for one-and threesurface amalgam fillings, respectively. 114 Griffin et al. used the U.S. average hourly wage for the productivity cost. Average hourly wage overestimates productivity cost, since another central argument for CWF is equity, i.e. it is supposed to be particularly beneficial to low-income people.

Minimal corrections
In this section, we show how the defects in the derivation of CWF benefits, or gross savings, discussed above can be corrected.

Costs of dental treatments
The resource value of a treatment is best represented by the allowable charge from a widely accepted insurance fee schedule. Fee schedules may vary for a number of reasons, but the relative values among closely related procedures tend to be stable. Table 11 shows the allowable charges for amalgam fillings from two large payers, one from a public payer 115 and one from the largest commercial payer (private communication). The payments are not proportional to the number of surfaces involved, and Assumption (6) in Table 2 clearly overestimates the dental charges. Using these relativities and two assumptions a new gross savings estimate will be provided.
Our first assumption is that the average number of decayed surfaces per filling is two and the average dental fee is about that of a two-surface filling. For example, a 40% : 30% : 20% : 10% distribution of one-, two-, three-, and four-or-more-surface fillings, respectively, produces such averages using the relativities in Table 11. Our second assumption is that each equivalent two-surface filling costs 1 hour in lost wages.
Brown and Lazar 114 reported that there were more two-surface fillings than one-surface fillings in the 1990 survey and that the number of one-surface fillings has been dropping faster despite a vastly increased number of examinations. Since the more the distribution is weighted toward more-surface decays the less gross savings there are, our first assumption likely overestimates gross savings. The $54 fee for a one-surface amalgam filling was based on a survey of about 5% of U.S. dentists in private practice. 114 We argue that the allowed charge from a major commercial dental insurer better represents the true cost of resources, and we have an actual allowable charge of $72 from the San Diego area ( Table 11). The cost of living in San Diego is 1.43 relative to the U.S. average. 31 Using that index would give a one-surface amalgam cost of $72/ 1.435$50.35 today. It is reasonable then to keep the national average assumption at $54, which is 38% higher than the current California Medicaid payment rate.
The $18 opportunity cost was a U.S. average hourly wage. The 2010 U.S. median and mean hourly wages are reported to be $12.68 and $19.21, respectively. 116 As equity is the other strongest appeal of CWF, the median wage is more appropriate than the mean wage for representing productivity loss. Substituting the $12.68 for the $18 in equation (4)  Averted caries -a consistent approach Calculating averted caries as a product of no-CWF Incidence and CWF Effectiveness is fundamentally unsound. Griffin et al. 10 could have derived a selfconsistent averted caries directly from Brunelle and Carlos, 77 the results from which are summarized in the first six columns in Table 12.
As it was assumed that CWF benefit begins at age 6 years and the caries aversion begins after 1 year of exposure [Inputs (f) and (h) in Table 2], the first annualized data point (difference in DMFS) is at age 7 years with 1 year of exposure. This procedure provides 11 data points, as illustrated in the last three columns in Table 12. Taking the mean of the 11 data points gives the average annual DMFS difference (0.11), which can be used as the averted tooth decay surfaces PPPY.

Lack of evidence for adults
Since there is no real evidence that CWF prevents caries in adults, we present hypothetical scenarios; each scenario assumes that the caries aversion rate extends to a given age.
To calculate the estimate for each scenario, Step 4 is modified by summing the weighted costs to the cutoff age. Thus, if CWF is effective to age 19, 29, 39, or 64 years, the national average lifetime cost averted per decayed surface becomes $32.56, $52.98, $74.48, or $100.62, respectively, prior to the corrections. The ratio of each of the lifetime costs to $100.62 is how the gross savings is reduced in each age scenario.

Corrected net savings
In the previous section, we showed how several defects in the derivation of the $19.12 PPPY estimate of CWF benefit can be corrected. The corrected gross savings estimate is $1.97, $3.20, $4.50, or $6.08, if the CWF benefit extends to age 19, 29, 39, or 64 years, respectively.
As described earlier, the cost estimates of $0.50 for large water systems and $3.17 for small systems 10 were not based on reality. We used a detailed engineering projection report prepared for a system that has a decade of CWF experience and has characteristics of both large and small systems to obtain a more reasonable estimate of $3 and $10 PPPY, respectively.
The net savings are summarized in Table 13. In short, there is minor savings only if the caries aversion attributed to CWF extends to old ages and only in large systems. Thus minimal correction to several methodological problems eliminates most of the savings. When we include the estimated cost of treatment of dental fluorosis of at least $3.24 PPPY, there are no savings left in any scenario in Table 13.

Topical effect
There is a question whether any savings for averted caries are real, because the mechanism by which fluoride is thought to help prevent caries is topical. Griffin et al. 10 explained that Assumption (1) in Table 2 was due to the benefit from water fluoridation being primarily ''topical and post-eruptive.'' The CDC 1 states that fluoride prevents dental caries predominantly after eruption of the tooth into the mouth, and its actions are primarily topical. Both articles referenced Featherstone, 117 who stated that the effect of ingested fluoride on caries is minimal.
Current official justification for continuing promotion of CWF is that fluoride in tap water provides teeth with continuous exposure from water, beverages, and foods prepared with tap water, and that a constant low concentration of fluoride is maintained in the dental plaque and saliva all day. 118 The first point can be left to common sense. The second point contradicts current oral hygiene recommendations concerning plaque and has been refuted concerning saliva. The concentrations of fluoride in ductal saliva, approximately 0.016 ppm in fluoridated areas and 0.006 ppm in nonfluoridated areas, are ''not likely to affect cariogenic activity.'' 119 In addition, fluoride, by ingestion or by contact, negatively affects enamel remineralization in individuals with low calcium and magnesium in teeth enamel (usually due to undernutrition). 57 Hence, CWF may increase caries in people with poor nutritional status.

Equitable?
That CWF particularly helps the poor at a very low average cost to all has been an integral argument for CWF. We briefly examine the equity aspect.
A major review of the effectiveness of CWF states ''There is some evidence [strength of evidence5C] that water fluoridation reduces inequality in dental health across social classes in 5-and 12-year-olds [in England] … The small quantity of studies, differences between these studies, and their low quality rating, suggest caution in interpreting these results.'' 71 In Appendix 5, we point out two studies missing from the review of Truman et al. 80 In the first study Szpunar and Burt 49 reported that a fluoride concentration of 1.0 or 1.2 mg/l prevented caries, but 0.8 mg/l did not. (The current CWF range is 0.7-1.2 mg/l, and HHS proposed to decrease it to 0.7 mg/l.) 3 This study chose a predominately white township bordering Detroit, instead of the largely black and long fluoridated Detroit, to represent a fluoridated community. Burt et al. 120 reported that only 0.2% of low-income adults in Detroit in the 14-35 age group (born after CWF started in 1967) were caries free (compared to 55% of children up to age 12z in the unfluoridated community in Szpunar and Burt). 49 In the second study, Shiboski et al. 121 found that the prevalence of early childhood caries was not affected by fluoridation status. Among Head Start (low income) children, the most fluoridated ethnic group (Asians, with 69% in fluoridated areas) had the worst tooth decay status. Among non-Head Start children, the most fluoridated ethnic group (Asians, with 81% in fluoridated areas) had tooth decay rates similar to those of white Head Start children, with 12% in fluoridated areas.
Truman et al. 80 stated: ''The current burden of poor oral health continues to disproportionately affect communities with large numbers of African Americans, American Indians, Hispanics, the poor, and the disabled of any race or ethnic group.'' (See also CDC.) 111 This was not the case historically. Citing many studies published between 1933 and 1947, Finn 73 stated that blacks had less caries than whites. On the other hand, recent data indicate that dental fluorosis is more prevalent among blacks and Hispanics, 47,111 suggesting that lack of fluoride is not an explanation for their poorer oral health.

Conclusion
For decades, the U.S. federal and state governments have promoted CWF to improve dental health of residents at low costs. Yet, in spite of the presumed savings in dental costs to Americans due to widespread use of CWF, employment of dentists is projected to grow by 16% between 2012 and 2022 (vs. 11% for all occupations), 122 and cosmetic dentistry in the U.S. has grown to be a multi-billion dollar industry. 123 We have shown that the promise of reduced dental costs was based on flawed analyses. In particular, the primary cost-benefit analysis used to support CWF in the U.S. assumes negligible adverse effects from CWF and omits the costs of treating dental fluorosis, of accidents and overfeeds, of occupational exposures to fluoride, of promoting CWF, and of avoiding fluoridated water. In assessing the benefits, it ignores important large data sets and assumes benefits to adults that are unsupported by data. Thus this analysis, as well as other economic analyses of CWF (Appendix 2), falls short of reasonable expectations for a cost-benefit analysis from a societal perspective. Minimal correction of methodological problems in this primary analysis of CWF gives results showing substantially lower benefits than typically claimed. Accounting for the expense of treating dental fluorosis eliminates any remaining benefit.

Disclaimer Statements
Contributors Both authors have contributed substantially to conception of the study, analysis and interpretation of data, drafting of the article, and critical revision of the article. Both authors have given final approval to the article as submitted.
Funding No outside funding was received for this project. Other studies examined dental insurance data and did not find CWF to be associated with lower utilization or costs of dental services. 126,127 In this appendix, we comment on several additional recent CWF cost-benefit studies: Campain et al. 128 assessed the impact of changing dental needs over time on the cost savings from CWF in Australia. O'Connell et al. 129 estimated the cost savings associated with CWF in Colorado and potential savings if the unfluoridated communities were to implement CWF. Wright et al. 130 investigated whether it would be costeffective to fluoridate water supplies that were not fluoridated in New Zealand. Kroon and van Wyk 131 examined whether water fluoridation is still a viable option to reduce dental caries in South Africa by addressing concerns about cost and effectiveness. Tchouaket et al. 132 estimate the cost savings in Quebec resulting from CWF; since this is a 2013 paper claiming to use an ''innovative approach'' we will comment on it separately.

Costs
As with Griffin et al., 10

Estimates of averted caries
O'Connell et al. 129 essentially used the base case from Griffin et al. 10 They used the 25% value for Effectiveness. For Incidence, they used the base case (middle row in Table 6 in the main text) with minor changes: They reduced the 0.77 and 1.09 values by 20.9% for the secular trend, but decided that the 0.43 value for age 45-65 years was too low; instead they used 1.08 and 1.31 for ages 45-64 years and ages 65 years and older, respectively, through consultation with Griffin. The resulting average averted caries is 0.2 DMFS, almost the same value (0.19 DMFS) as in Griffin et al., 10  Campain et al. 128 assumed uniform but changing effectiveness for all ages from age 6 years. They picked a value within the range of numbers reported from a set of references, including several discussed in this article. 77,107,108,133 Thus they assumed that CWF effectiveness was 50% in the 1970s, 30% in the 1980s, and 25% in the 1990s. For Incidence they constructed a matrix of year versus age range from their literature search and imputed values where information was missing.
Kroon and van Wyk 131 cited the 15% Effectiveness from Petersen et al., 134 and also modeled the benefit using 30% and 50%. This Effectiveness is applied to teeth, not surfaces as in the other studies. For Incidence they used local survey data by city. The method, according to Kroon and van Wyk,135 is to divide the DMFT survey of, say, 15-year-olds by 15-6 5 9 and assume it is the same for people of all ages, including those age 6 years and less. The authors noted that the mean DMFT for 12-year-old South African children decreased from 1.73 in 1988-1989 to 1.05 in 1999-2002 in this unfluoridated country.
Wright et al. 130 did not try to estimate a value for Effectiveness. For children aged 4-13 years, they compared treatment data for restorations and extractions for both deciduous and permanent teeth to calculate savings on dental fees. They used 1996 Wellington and Canterbury data without supporting the selection, since such data are available for all New Zealand and for all years. For ages 14-34 years, they used a 0.29 averted DFS number from Grembowski et al. 107 (but increased it to 0.59 surfaces for Maori) and assumed no effectiveness after age 34 years.

Costs of dental treatments
On productivity loss, Campain et al. 128 and O'Connell et al. 129 used approaches similar to Griffin et al. 10 Wright et al. 130 and Kroon and van Wyk 131 did not include productivity cost. Below, we note the variations in the methods of estimating dental fees in these studies.
Kroon and van Wyk 131 estimated caries in DMFT and used the average cost of two-surface fillings for the dental charge for each DMFT. Wright et al. 130 used the treatment database from Wellington and Canterbury for children ages 4-13 years and included both deciduous and permanent teeth. For those ages 14-34 years, they calculated the cost of a single-surface filling using an average dentist hourly rate (with inflation) and the 15 minutes time needed to put in the filling. They assumed that fillings are replaced every 8 years.
Campain et al. 128 and O'Connell et al. 129 attempted to include more-surface fillings, composite fillings, and crown or extraction costs. However, the calculations lack transparency, and there are questions as to whether the interaction between extractions and restorations is handled properly in the latter. The most serious problem with the two studies is that they calculated the dental fees plus productivity cost on a per visit or per service basis, rather than normalizing that cost to a per surface basis, because one visit or service may treat more than one surface. By multiplying the estimated averted DMFS by a cost per visit or service rather than a cost per surface, they overestimated the averted costs of dental services. In addition, crowns or extractions are not always due to caries, but may have other causes. Thus these approaches lead to a far worse overestimation than Assumption (6) in Griffin et al.'s analysis. 10 Tchouaket et al. 132 A paper by Tchouaket et al. claims to use an ''innovative approach'' to assess the economic value of water fluoridation for Quebec, in which only 2.7% of the population is fluoridated. 132 The presentation lacks critical information and contains fundamental errors. The authors claim that their analysis ''adopted a societal perspective that allowed us to track all the costs and effects of the intervention.'' However, they did not include or mention the costs of treating dental fluorosis or any of the costs we discussed under ''Other costs.'' All $ signs in this section are Canadian dollar, C$.
Tchouaket et al. produced $1.93, $2.05, or $2.25 PPPY as the costs of CWF, using information from the few fluoridated municipalities in Quebec. Supposedly, the three values correspond to using 3%, 5%, or 8% to amortize the subsidies received by these municipalities over 20 years. They listed several salary rates but provided no other quantitative information, thus readers are not able to repeat any calculations or confirm the numbers.
For CWF benefits, Tchouaket et al. did not try to estimate averted caries. Instead, they estimated the yearly costs associated with restorative dental treatments in Quebec to be $532.08, $532.87, or $534.05 PPPY, depending on discount rates. They compared these with the cost values above at various hypothetical values of CWF effectiveness, and claimed that CWF is cost-effective even at 1% effectiveness and that Quebec saves more than $560 million a year at an ''expected average effectiveness of 30%.'' It should be noted that the $532-$534 PPPY restorative expense exceeds the actual per capita spending on all dental services in Canada, which was reported to be $380. 83  The authors calculated the number of teeth restored in a year by multiplying the number of persons who used dental services within the past year, by age group, times the dmft/DMFT index for that age group. First, the average dmft/DMFT values given in the paper are clearly cumulative, not an annual increment. Only a small percentage of these would correspond to untreated decay that requires a restoration service. xv Second, Tchouaket et al. xv While the level of caries experience is very high in Quebec adults aged 35-44 years, only 1.8 out of 148 surfaces are decayed (in need of treatment), on the average, and more than half of the people (55.5%) have no decayed surfaces. 138 Ko and Thiessen Economic evaluations CWF apparently failed to recognize that routine dental cleaning and examinations are common in developed countries, thus having used dental services does not equate to having had a tooth restored. Data in the paper indicate that 25-61% of children (depending on age) were caries free, while 78-91% had visited a dentist in the past year; thus many of the children utilizing dental services had not had any restorations, that year or previously. Tchouaket et al. summarized fees for treatment of one cavity, including transportation costs and lost wages. A total fee for each of three categories (by type of tooth and age group) was not provided. The text and table in the paper disagree on the calculation of transportation costs, and some information in the summary table is not explained. The text indicates that those age 14 years or older require two separate trips, one for a complete examination and one for the restoration to treat one cavity. However, fees for routine dental exams should not be counted toward costs that can be saved by CWF.
The authors appear to have taken their calculated number of teeth restored for a given age group times the cost per restoration for that age group to obtain the total cost of restorations in one year for that age group. The combined total cost for the three age groups included in the analysis (5-8, 11-14, 35-44; 1.7 million people total) appears to have been averaged over the entire population of Quebec (7.9 million people) to obtain their final average of $532-$534 PPPY. This brings up the question of whether other age groups (9-10, 15-34, and 45z) were assumed to have no restorations. However, averaging (incorrectly) over the entire population rather than over the relevant age groups compensates partly for the great overestimation in the number of restorations per year.
The three values $532.08, $532.87, or $534.05 supposedly differ in the different discount rates (3%, 5% and 8%) used to calculate repeat treatment. Estimating the dental cost for replacement services is not new, but the scant description provided in two sentences does not show what the authors have done or allow readers to understand why the three results are so close.
Tchouaket et al. admitted that basing the 2010 economic value on caries prevalence data more than a decade old is a limitation. This is a legitimate concern due to the well known ''secular decline'' of caries in developed countries. 72 However, the authors argued that because the percentage of the Canadian population with at least one dental cavity has remained stable at 96%, the average DMFT in Quebec likely has remained the same or even increased. Actually, the 96% figure applies only to dentate adults aged 20-79 years. For children aged 6-11 years and adolescents aged 12-19 years, the corresponding national figures are less than 60%. 136 Factual error aside, this argument reflects their confusion with the differences between cumulative DMFT and new caries and with properly defined populations.

Appendix 3: Accidents, overfeeds and damages
A number of accidents, overfeeds, and damages caused by CWF are summarized in Table 14.  Fluorosilicic acid tank failure along with containment failure caused approximately 1,500 gallons of the acid to be released onto ground at the public utility. Approximately 1.5 acres were impacted. Workers cordoned off the area and placed berm along the west property line to prevent further runoff. The impacted area was to be excavated and soil properly disposed of.
CWF: community water fluoridation. Additional incidents of acute poisoning have been described elsewhere. 139,140 Below are the sources, which are mostly media reports, often reproduced in secondary sources, except for the following: Item 3 is a first-person account; Item 11 is an internal log of the water district obtained by request; Item 19 is a city council record; and Item 21 is a report in the National Response Center database. A compilation of other reports in this database up to February 2005 can be found in ActionPA. 141 All URLs for the sources were last accessed on August 20, 2013, except those in Item 4 that were accessed on April 10, 2014. and very different from CWF in many respects, e.g. the applications or dosages are controllable; it does not appear reasonable to combine them in a meta-analysis. They ''used a random-effects model, which assumes that each study was randomly selected from a hypothetical population of studies,'' without discussing the applicability of the model. We focus on the CWF-related studies. These authors concluded that the CWF effectiveness was a 27.2% reduction in caries. We are not able to reproduce this result, which was based on four studies reporting DMFT and one study reporting DMFS; there was no explanation how the different units were handled. As with Slade et al., 109 Griffin et al. 110 failed to adequately account for different age distributions.

Slade et al. 109
Thirty dentist-examiners conducted the oral examination in this national survey. For participants aged ,45 years, only teeth extracted because of dental caries or periodontitis were counted as missing, but all absent teeth for older people were counted. Fluoridation exposure was determined by residential history, and a value of 0, 0.5, or 1 was assigned if the fluoride concentration at the location was less than 0.3, between 0.3 and 0.7, or greater than 0.7 mg/l, respectively. A value of 0.5 was assigned to all localities in New Zealand, Canada, or the U.S. and 0 to all other foreign localities, without regard to the actual CWF status of the locality.
A significant portion of CWF exposure status was imputed: 3,779 people were considered to have valid exposure data (Complete case), meaning less than 50% of the person's residential data were missing; the missing years were assumed to be their average observed fluoridation exposure. The exposure status of the remaining 1,726 people with more than 50% missing residential data was imputed by substituting with the status of a random sample from the 3,779 people who belonged to the same geographical stratum and 10-year age group.
Slade et al. use unspecified linear regression models to ''age-adjust'' caries experience and fluoridation exposure. They draw the main conclusion of effectiveness by comparing the ''age-adjusted'' DMFT/ DFS scores of the ''prolonged'' and ''negligible'' groups for the cohorts born before 1960 and those born between 1960 and 1990, respectively. The observed DMFT/DFS scores are not provided. The ''age-adjusted'' DMFT/DFS scores are given by birth cohort and exposure group (Table 15).
The scores reported in Table 15 are not consistent with the conclusion that CWF exposure is effective. The scores for the two middle exposure levels were interpreted as ''suggested a dose-response relationship.'' This is an unreasonable explanation, as an apparent difference in DMFT/DFS is lacking among the first three exposure categories. In addition, exposure levels were defined by cumulative residential status relative to age. For example, a person who lived in places with a fluoride concentration of 1 mg/l for 50 years and 0.25 mg/l for 20 years (treated as 0 mg/l, as 0.25 is less than 0.3) would have been assigned to the 50 to ,75% exposure group, which, according to their results, gets no benefit relative to someone living all 70 years in nonfluoridated areas.
There are also questions regarding the validity of their use of linear regression models to ''age-adjust.'' Calculation from data provided by Slade et al. Table 16) reveals that some cells have few or no people. In particular, the category of §75% exposure level is clearly much younger than the other three exposure categories. Given the large difference in DMFT/DFS between the pre-1960 and 1960-1990 birth cohorts (Table 15), and the large difference in age distributions between the first three exposure categories and the fourth category (Table  16), it is not surprising that the §75% exposure category would have lower DMFT/DFS scores than the other exposure categories. Hence the differences in caries attributed to CWF between the ,25% and  There are other unexplained discrepancies. For example, the differences in DMFT or DFS between the ,25% and §75% exposure groups given in the text are not consistent with the numbers reproduced in Table 15. In particular, the DFS difference in the pre-1960 cohort was said to be 11.10 or 30%, but the numbers indicate 7.93 or 21%. Griffin et al. 110 This 2007 article included nine CWF studies (Table  17). 51,107,133,[142][143][144][145][146][147] Few, if any, of the studies can be considered high quality studies appropriate for examining the effects of CWF. Four studies involved concentrations greater than those used for CWF (0.7-1.2 mg/l). 51,133,143,145 In all, but one study, 146 the examiners were probably not blind to the location of a subject's residence. Eight studies were crosssectional, and the towns compared may have simply differed for reasons having nothing to do with CWF. The one study categorized as ''prospective'' is in essence a cross-sectional study that compares caries increment over an 18-month period, since no ''intervention'' was started or changed at the onset of the period. 143 Only four of the nine studies were conducted in the U.S. Of these, two were examined earlier in this paper. 51,107 Below we offer a few general remarks, followed by comments on the remaining studies, especially the other two U.S. studies. 142,143 As we discussed earlier, assessment of dental caries in adults is difficult. Wiktorsson et al. 144 described difficulties in judging caries prevalence based on fillings (due to practices such as preventive fillings for discolored fissures on occlusal surfaces) and in defining new caries incidence, since the majority of the primary caries lesions are only enamel lesions, possibly arrested caries in many cases.

(shown in
In some studies, 133,145,146 the reported age distributions suggest that the low fluoride groups were older than the fluoride groups. Griffin et al. 110 do not seem to have considered this difference in the age distributions in their analysis.
In the context of testing the hypothesis that adults benefit by continuing to drink fluoridated waters, the progression of the differences in caries is important. Englander and Wallace, 142 Murray, 133 and Stamm et al. 145 each reported narrowing of the differences in mean DMFT between the low fluoride and fluoride groups with increasing ages for lifetime residents. The logical conclusion is that drinking fluoridated water is not helpful beyond a certain age.
Englander and Wallace 142 examined 896 and 935 adults aged 18-59 years from two Illinois towns, Aurora (1.2 mg/l) and Rockford (0.1 mg/l, referred to as ''fluoride deficient''). All subjects were examined by the first author. The caries experience was found to be significantly less in the subjects from Aurora, which was attributed to the different fluoride levels in their drinking water. We offer some observations that disagree with that conclusion.
The differences in mean DMFT presented for the two towns were 5.22, 8.14, 6.62, 5.59, and 5.76 for the 18-19, 20-29, 30-39, 40-49, and 50-59 years old age groups, respectively. The mean years of consuming the respective waters in either city were increased by about 10 years for each additional 10 years age group. However, the difference in mean DMFT decreased for age groups above 29 years (for DMFS, the corresponding differences in the means decreased slightly for ages 30-39 years, but decreased substantially for ages .39 years). If the caries difference is to be attributed to fluoride, are we to conclude that after age 29 years, consuming water with 1.2 mg/l fluoride increases caries?
The study groups from the two cities were said to have similar socioeconomic structures, but there are questions as to how similar the two groups really were. Almost everyone in Aurora (pop. 65,000) and more than half the population of Rockford (pop. 130,000) were contacted. It was found that 2% of those in Aurora over 20 years old were toothless, yet the figure was 14% for Rockford. (Anyone with less than 10 teeth was not invited to participate. The percentages of people contacted who had 1-9 teeth were not given.) A sevenfold difference in the toothless population may indicate an economic difference. Even though the edentulous people were not included in the study, the authors appeared to consider the figures representative, as they tried to adjust the measurements by adding the  107 USA Cross-sectional Murray 133 Great Britain Cross-sectional 1.5-2.0 mg/l Englander and Wallace 142 USA Cross-sectional Hunt et al. 143 USA ''Prospective'' 0.7-1.5 mg/l Wiktorsson et al. 144 Sweden Cross-sectional Stamm et al. 145 Canada Cross-sectional 1.6 mg/l Thomas and Kassab 146 Great Britain Cross-sectional Morgan et al. 147 Australia Cross-sectional significant differences in age group structure of the samples from the two areas, the data show that Anglesey had more in the youngest (,20) age group, 24.1% versus 12.9% and fewer in the oldest (25-29 and 30-32) age groups, 30.0% and 5.9% versus 36.5% and 9.6%. The island of Anglesey was chosen for a demonstration fluoridation study in the 1950s. The experiment was terminated after only 5 years and the whole island was fluoridated based on the mean dmft index for 5-year-old children.
Morgan et al. 147 analyzed data for a group of Royal Australian Navy recruits, mostly males, ages 15-24 years, and with limited education. Griffin et al. 110 used only the results (mean DMFT scores by fluoride history) for 20-24 year olds (208 recruits). Morgan et al. indicated only that approximately 20% and 30% of the total sample (1,100 recruits) were considered ''fluoridated'' and ''nonfluoridated'' (determined by residential history), respectively, and included in the calculation of the mean DMFT scores. Griffin et al. used the percentages to impute the sizes of the ''fluoridated'' and ''nonfluoridated'' groups to be 42 and 62, respectively.
In contrast, four estimates were imputed from the much smaller Libyan study 103 -for each of the two ages reported, the public school data from the rural town were used twice to impute two estimates by comparing them with the public school data and, separately, with the private school data from Benghazi.
Selection of formula: Within the limited set of studies and estimates selected, the authors failed to apply their formula consistently. Two estimates for deciduous teeth from Guo et al. 76 were included in group A-On and two for permanent teeth in group B-On. The study clearly belongs to group A-On, as it reported before-and-after measurements for all ages and for both deciduous and permanent teeth. Instead of following their stated method and including the estimates of 300%, 211%, and 208% for the permanent teeth of the three selected age groups, they ignored the before measurements and treated them as if there were only post measurements for permanent teeth. Similarly, Evans et al. 97 reported measurements for 5-year-olds divided into three social classes. Truman et al. 80 included three Group A-On estimates, one for each social class; but the combined total for all social groups was treated as a post-only study and contributed another estimate in Group B-On.
The results from the application of the formula can be misleading. For example, the three positive estimates 99,100 in group A-Off are presented as estimates of how much CWF prevents caries. In fact, the data in these two studies, as well as other studies involving cessation of CWF, showed that there were no increases in caries after stopping fluoridation, aside from possibly a temporary and small increase shortly afterward, which could simply be reflecting the removal of the delayed eruption effect. (Within the 6-year period in Attwood and Blinkhorn, 99 the mean DMFT decreased by 0.54 in the neverfluoridated town and increased by 0.06 in the town that stopped fluoridation at the midpoint of the period. In the 9-year period that sandwiched the cessation of CWF in Kalsbeek et al., 100 the DMFT decreased by 3.7 in the never-fluoridated town and increased by 0.4 in the fluoridated town; 8 years later, it further decreased by 5.6 in the former and decreased by 2.3 in the latter town.) Thus the purported positive outcomes were purely an artifact of the formula -the never-fluoridated communities had a dramatic reduction in caries without the help of CWF.