This was a monocentric retrospective study modeling the weight trajectories of patients having undergone gastric bypass surgery.

All procedures performed in this study involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and the 1964 Declaration of Helsinki and its later amendments or comparable ethical standards.

Group 1 comprised 795 patients who had gastric bypass surgery between 2003 and 2012 with at least 2 years of follow-up in the same reference center, performed by two surgeons (GB and PT). They were included for modeling their weight trajectories. They were within the Haute Autorité de Santé criteria for obesity surgery [12]. The patients analyzed represented 63.00% (795/1262) of the initial patients. A total of 11.01% (139/1262) were excluded for redo surgery; 28.62% (320/1118) were excluded because they were lost to follow-up within the 2 years after surgery.

Group 2 comprised 381 patients with a follow-up of 5 years after gastric bypass. They were classified according to the Reinhold criteria and allowed us to assess predictive capability of the model when applied within the first 18 months to predict later weight.

Weight was measured with patients wearing undergarments during postsurgery follow-up visits (1, 3, 6, 9, 12, and 18 months). The reference weight was that of the day before surgery. Certain data were missing. The EWL was calculated based on a body mass index (BMI) of 25 kg/m², with equation EWL = (initial weight – actual weight)/(initial weight – 25* height²); weight in kg and height in meters. The Reinhold [10] criteria were used to define failure (EWL after 18 months of less than 25%), success (EWL after 18 months exceeding 50%), and an intermediate result (EWL between 25% and 50%).

Calculations were performed using R version 3.0.2 (R Foundation for Statistical Computing) and MATLAB version 2010a (The MathWorks, Inc).

A total of 795 patients were included in this study (141 men and 654 women). The variability of data did not allow us to summarize the information in a single representative trajectory (Figure 3). Homogeneous groups of trajectories were necessary to summarize the entirety of the information. A total of 56 classes of representative trajectories came from the first HCA. After two successive HCA, the number of representative trajectories was reduced to 14 classes. Figure 4 shows the trajectories of the representative curve of each class.

Several of these representative trajectories had the same behavior (Figure 5):

Preoperative factors (age, sex, presence of diabetes) did not modify the trajectory predictions.

The Reinhold classification applied to weight observed at 18 months identified 87.4% (333/381) of patients in the category EWL >50% and 12.6% (78/411) of patients in the category EWL between 25% and 50%. There were no patients in the category EWL <25%.

The Reinhold classification was applied to the estimated weight at 18 months based on representative trajectories. Only one trajectory (7.1%) was classified EWL <25%. Six trajectories (42.9%) were classified EWL between 25% and 50%. Seven trajectories (50%) were classified EWL >50%.

The match between the Reinhold classification [10] based on observed or predicted weight is shown in Table 1. Classification with reference trajectories produced an overall rate of correct classification of more than 93%. It allowed correct classification of 97.6% (325/333) of persons with EWL >50% and more than 59% (46/78) of persons with EWL between 25% and 50%.

Table 2 shows the influence of the number of early weight values used in the prediction on the results at 5 years. The more the number of points increased, the more precise was the classification of the different profiles (best mean and lowest variability). For the persons who would be in the category EWL >50% at 18 months, the match rates increased with the number of values over time, but as of 6 months postsurgery, 91.6% (305/333) were well classified.

For the persons who would be in the category EWL between 25% and 50%, the match rate showed little increase over time (going from 47% to 56%). Therefore, between 44% and 53% of patients were poorly classified by the trajectories.

This study shows that it is possible to model weight loss over the 18-month period after a gastric bypass in representative trajectories. Applied to a group of patients at 5 years postsurgery, the representative trajectories correctly predicted more than 93% of the values. Postoperative data available for 1 to 6 months are sufficient to provide a satisfactory prediction of EWL >50%.

Unsupervised classification methods like the HCA that we used here makes it possible to define families of trajectories without a priori on the number of classes to obtain. This is a very commonly used method. In this study, it allowed us to determine families of weight trajectories only from their general appearance and without using additional variables, like in the research of Wise [11]. One of the advantages is that the classification can be updated as new weight data are added to the previous one. Also, we chose to use weight and not EWL (or the percentage of weight loss) to develop the trajectories because they are accompanied by arithmetic biases. For example, for a very high initial BMI, EWL will be less than for a lower BMI, despite an equivalent weight loss. We only used EWL to compare the value predicted by the trajectory to the observed value in group 2. The concept of predicting later weight is therefore valid from this data. The use of weight trajectories rather than trajectories of EWL or of percentages of weight loss was also preferred for conserving the maximum of behaviors within the trajectories.

The cohort came from the same center with two surgeons and a formalized protocol for the preparation and follow-up of patients. However, that limits the variability introduced by multiple teams using different preparation and follow-up protocols. This study did not analyze known factors of failure or of inadequate weight result like those identified by other authors [11]. The prediction is better for the patients who lose a lot of weight. This is explained by the initial imbalance between the three classes based on EWL in the database. Further analyses on more balanced bases are needed.

An early prediction of weight trajectory is clinically useful. A success prediction may empower postsurgical patients to carry on and reassure them, as many are anxious about regaining weight because of their past history of weight loss failures. This does not mean that weight will no longer be monitored. This also suggests that if a person is not classified as a later success, every effort should be made to understand the reasons and implement early corrective strategies. In that sense, the factors classically associated with less than optimal weight loss can be used not as predictors (with little efficiency) but as targets for an early additive strategy. Despite the low power to predict future results in this category, the idea of an early alert is clinically useful. Validation studies on other cohorts are needed. We should also point out that the validation database was very imbalanced (87.4% of EWL >50% vs 12.6% with EWL between 25% and 50% and no patient in weight loss failure). It is possible that the classification of patients with average weight loss will improve with better-balanced validation database. A machine learning process added to the application would provide evolutive classifications as the amount of data increases [17-19].

This study shows that a hierarchical cluster analysis allowed us to identify 4 profiles of weight trajectories associated with clinical expertise. The patients who were the most successful were those who lost weight regularly. The persons who lost the least had difficulties in the initial phase or had a secondary weight regain.

None of the preoperative parameters differed between the families of curves. This agrees with other published studies [8]. It seems difficult to predict weight loss after surgery with factors that do not consider the capacity for personal, psychological, or metabolic adaptation during the postsurgery period. The factors classically associated with poor weight loss results are postoperative (recurrence of depression, eating disorders, lack of follow-up, lack of arrangements for changes of eating habits, and physical activity) and usually occur late after surgery (24 months). The early identification of a trajectory is therefore an interesting feature of this model. Applied to a population of persons having undergone surgery and at 18 months after this surgery, this classification correctly identified more than 97% of EWL >50% and more than 58% of EWL between 25% and 50%.

Wise et al [11] recently published a comparable study. In a retrospective analysis of a cohort of gastric bypassed patients followed for 3 years, the authors demonstrated the exponential nature of the decrease of EWL and analyzed the factors influencing the trajectory, such as age. Our study used an original mathematical approach and adds to the study of Wise et al [11] because it validates the concept of trajectories in an independent population at 5 years. Like Wise et al [11], we conducted the analysis using EWL without showing better results than with weight only.

Given the prevalence of weight regain after obesity surgery, early identification of a nonoptimal weight trajectory would help to strengthen the second lines of treatment by reinforcing measures for behavioral change (self-care, physical activity, nutrition). This study proves the concept that a simple application could allow surgical patients to enter weight data themselves, evaluate the result, and eventually alert the health care provider.