Computational modelling of self-reported dietary carbohydrate intake on glucose concentrations in patients undergoing Roux-en-Y gastric bypass versus one-anastomosis gastric bypass

Abstract Objectives Our aim was to investigate in a real-life setting the use of machine learning for modelling the postprandial glucose concentrations in morbidly obese patients undergoing Roux-en-Y gastric bypass (RYGB) or one-anastomosis gastric bypass (OAGB). Methods As part of the prospective randomized open-label trial (RYSA), data from obese (BMI ≥35 kg/m2) non-diabetic adult participants were included. Glucose concentrations, measured with FreeStyle Libre, were recorded over 14 preoperative and 14 postoperative days. During these periods, 3-day food intake was self-reported. A machine learning model was applied to estimate glycaemic responses to the reported carbohydrate intakes before and after the bariatric surgeries. Results Altogether, 10 participants underwent RYGB and 7 participants OAGB surgeries. The glucose concentrations and carbohydrate intakes were reduced postoperatively in both groups. The relative time spent in hypoglycaemia increased regardless of the operation (RYGB, from 9.2 to 28.2%; OAGB, from 1.8 to 37.7%). Postoperatively, we observed an increase in the height of the fitted response curve and a reduction in its width, suggesting that the same amount of carbohydrates caused a larger increase in the postprandial glucose response and that the clearance of the meal-derived blood glucose was faster, with no clinically meaningful differences between the surgeries. Conclusions A detailed analysis of the glycaemic responses using food diaries has previously been difficult because of the noisy meal data. The utilized machine learning model resolved this by modelling the uncertainty in meal times. Such an approach is likely also applicable in other applications involving dietary data. A marked reduction in overall glycaemia, increase in postprandial glucose response, and rapid glucose clearance from the circulation immediately after surgery are evident after both RYGB and OAGB. Whether nondiabetic individuals would benefit from monitoring the post-surgery hypoglycaemias and the potential to prevent them by dietary means should be investigated. KEY MESSAGES The use of a novel machine learning model was applicable for combining patient-reported data and time-series data in this clinical study. Marked increase in postprandial glucose concentrations and rapid glucose clearance were observed after both Roux-en-Y gastric bypass and one-anastomosis gastric bypass surgeries. Whether nondiabetic individuals would benefit from monitoring the post-surgery hypoglycaemias and the potential to prevent them by dietary means should be investigated.


Detailed description of the statistical methods
In Bayesian inference parameters of interest are considered as random variables instead of unknown constants, and thus any prior knowledge can be incorporated in inferring the distribution of the parameters of interest through utilization of the Bayes' theorem to compute the posterior distribution. Therefore, Bayesian statistics provides more intuitive, meaningful, and interpretable inferences on complex problems through utilization of all available information. The method is designed as follows.
Collected glucose concentration data of the pth patient ∈ 1,2, … , , where P is the total number of patients, is a time series vector of length i.e.,

= , … ,
Furthermore, each patient has recorded meals, indexed by ∈ 1,2, … , Here, is the amount of carbohydrates in grams in the mth meal of the pth patient, calculated as the sum of sugar and starch. We assumed that the glucose curve of an individual p, , is given by where ∈ ℝ is a constant baseline which we set to the median of the observations, ∈ ℝ is the additive glucose response to the mth meal, and = , … , is a vector of Gaussian observation errors. In words, the glucose curve equals the sum of the trend and meal-specific response curves, plus noise.
The response function specifies the impact a meal has on the glucose curve over the time. Here we assume a symmetric bell-shaped curve as the response function, which is expressed by two parameters, patient and meal-specific ℎ and patient-specific . Here, ℎ describes the height of the glucose response, while is the length-scale, and therefore proportionally represents the duration of the glucose peak. The total duration of the response is approximately 5 .
To estimate how the glucose response depends on the amount of carbohydrates in a meal, we allowed the height of the response, ℎ , to depend on the amount of carbohydrates: In the above equation, the coefficient β represents the personalized impact of the carbohydrate intake on the height of the response for the pth individual. In other words, β shows the amount of glucose response peak, if one gram of carbohydrate is consumed. To efficiently perform the statistical inference with the limited data available, we introduced a Bayesian hierarchical prior, 1 which enables information to be shared across individuals. Further details of the method and of the prior distribution are given in the original article. 2 Statistical inference was done using Markov chain Monte Carlo (MCMC) algorithm implemented in software STAN. 3 We also rely on a Bayesian t-test, 4 when assessing the significance of a difference between estimated posterior distributions, i.e. estimated distribution of preoperative and postoperative average height parameter β and length-scale parameter . It generates the posterior distribution of the difference between the means of the two groups and is considered significant with 5% level of significance if the 95% highest density interval (HDI) does not contain the value zero, in which case the null hypothesis is rejected. Data are presented as mean ± standard deviation. Within-group comparisons before and after the operation were done with the Bayesian t-test. , height parameter of the glucose response; α, width parameter of the glucose response; PreOP, prior to the operation; PostOP, after the operation; Difference, the 95% CI for the difference between parameters after and before the surgery; RYGB, roux-en-Y gastric bypass; OAGB, one-anastomosis gastric bypass.