Here, a weight trajectory is the evolution of patient weight after bariatric surgery. In the present analysis, good weight trajectories are taken as those that demonstrate considerable early weight loss that is maintained in the mid- to long-term, while poorer trajectories show lesser initial weight gain and either greater weight regain after a nadir, or sustained low weight loss. A recent study by Courcoulas et al[10] (1,738 patients who underwent RYGB, 7 years follow-up) determined 6 trajectories into which the patients’ post-surgical weight loss outcomes could be grouped. Data were further presented regarding the evolution of the patients’ co-morbidities stratified by weight loss trajectory group, thereby providing a first detailed assessment of the association between separate weight loss outcomes and co-morbidity burden within the same surgical cohort. Applying these data in the present study, the prevalence of three co-morbidities (T2D, HTN, and DLP as high low density lipoprotein as reported by Courcoulas et al) could be estimated as a function of post-RYGB weight trajectory by considering both resolution in patients with the co-morbidity at baseline and new onset among those without. Models were employed, informed by available data, to extrapolate reported outcome results to a 10-year window. The analysis scheme is depicted in Figure 1.
Study cohort
The main analyses in the present study consider a cohort of 100 patients who have undergone RYGB surgery and who then follow one of the 6 post-surgical trajectories. Baseline demographic characteristics are taken from a Canadian study of wait-listed, medically-managed and bariatric surgical patients in Alberta.[14] Using the data of the surgical cohort, the hypothetical patients considered here were 87% female, 43.5 ± 9.5 years of age with body mass index (BMI) of 46.2 ± 7.2 kg/m2. Baseline co-morbidities were 45%, 61% and 60% for T2D, HTN and DLP respectively (Table 1).
Outcomes of weight loss trajectory
Non-linear regression models were investigated for fitting to the observed patient trajectory group data of Courcoulas et al.[10] Group labels in the present study correspond to those reported there, with broadly increasing weight loss from the poorest in group 1 (G1) to the best outcomes in group 6 (G6) over the post-RYGB period. Model fits were determined separately for each trajectory group using CurveExpert Professional version 2.6 and the best model for each was selected based on a score derived in part from the Akaike Information Coefficient adjusted for small sample sizes (AICC). Yield density models were found to be the most suitable for the extremes (G1 and G6) while the intermediate weight loss trajectories were best fit with reciprocal quadratic models (G2 to G5). The modelled total weight loss (TWL) percentage was applied to the hypothetical cohort baseline demographics to calculate BMI over the 10 years post-RYGB.
Co-morbidity evolution
After bariatric surgery, many factors may contribute to the resolution of co-morbidities in patients with the disease at baseline or development of new onset disease in patients without. In the absence of detailed data, the present study estimated co-morbidity evolution by correlating the trajectory group outcomes reported by Courcoulas et al[10] with the available, reported group demographic data over time post-surgery (age and BMI). Resolution data for each co-morbidity were reported for each trajectory group at time points of 6 months, and years 1, 2, 3, 4, 5 and 7 post-surgery. Linear regression models were fit to associate patient post-surgical age and BMI with expected resolution; more complex models were not used to reduce the risk of over fitting. Models for each co-morbidity were determined to estimate resolution as a function of post-RYGB age and BMI in patients of the hypothetical cohort who had the disease at baseline.
Incident disease after RYGB has been reported to be low.[10, 15] The incident data of Courcoulas et al[10] were not stratified by trajectory group, meaning only total numbers of new cases by post-surgical timepoint were available for modelling. As above, in the absence of further data, a parsimonious approach was used with linear models to predict new onset cases in patients of the hypothetical cohort who did not have disease at baseline as a function of the overall cohort BMI at each post-surgical timepoint.
For both the remission and new onset groups, patients are assumed to remain within their respective groups over the time horizon. Patients with the co-morbidity at baseline who achieve remission therefore remain in that group and are not added to the group at risk for new onset. Similarly, new onset cases cannot achieve remission, as there were no data to inform accurate estimates of this movement.
Cost analysis
The overall prevalence of each co-morbidity at 1-year intervals post-RYGB was calculated as the sum of non-resolved and new onset cases. Total patient-years of treatment of co-morbidities were determined over the 10-year time horizon for each co-morbidity using annual treatment costs in the Canadian public health care system (Table 1). A study from Canada has suggested that patient treatment costs may increase according to overweight and obesity (relative to normal weight) independently of presence of co-morbidities.[16] Since the present analysis calculates BMI over time after surgery for each trajectory group, a scaling factor was calculated for cost increase as a function of BMI. Curve-fitting (including linear regression) was performed yielding a reciprocal linear relationship as the most suitable to model the annual cost-scaling factor as a function of BMI.
Input costs are shown in Table 1. All costs are for public payers in the Canadian context. Costs for T2D and HTN thus include physician and hospital treatments, while those for DLP are the public costs of additional lab work for patients receiving statins. An annual discount rate of 1.5% was applied across the 10-year time horizon.
Table 1 Model parameters
Parameter
|
Reference
|
Base case
|
Notes
|
Age
|
Padwal et al 2014[10]
|
43.5 ± 9.5 years
|
Use population demographics of a Canadian surgical cohort (150 patients, Alberta)
|
BMI
|
46.2 ± 7.4 kg/m2
|
Female
|
87.3 % ± 2.7 %
|
T2D baseline
|
44.7 % ± 4.1 %
|
HTN baseline
|
61.3 % ± 4.0 %
|
DLP baseline
|
60.0 % ± 4.0 %
|
Cohort size
|
N/A
|
100 patients
|
Example cohort
|
Provincial RYGB surgical volume
|
CIHI report[4]
|
Ontario 2,380
Quebec 310
Alberta 260
|
Most recent data available for the provinces with top 3 RYGB volumes in year ending 2014
|
Discount rate
|
CADTH guidelines[17]
|
1.5 %
|
4th edition guidelines
|
Cost T2D, year 1
|
Rosella et al 2016[18]
|
Male: $4,061 ± $609
Female: $4,017 ± $603
|
Ontario
Base value uncertainty taken as ±15%
|
Cost T2D, year 2+
|
Rosella et al 2016[18]
|
Male: $828 ± $123
Female: $1,023 ± $124
|
Ontario
Base value average costs years 2-8 in study
|
Cost HTN
|
Weaver et al 2015[19]
|
$2,163 ± $227
|
Canada wide
|
Cost DLP
|
Conly et al 2011[20]
|
$79 ± $8
|
Alberta
Final value includes only laboratory costs for patients on statins minus costs for patient time and travel
|
Costs from reported currency year were inflated to 2018 Canadian dollars using Statistics Canada consumer price index data for health services and products. CADTH, Canadian Agency for Drugs and Technologies in Health; CIHI, Canadian Institute for Health Information; DLP, dyslipidaemia; HTN, hypertension; NA, not applicable; RYGB, Roux-en-Y gastric bypass; T2D, type 2 diabetes mellitus.
Sensitivity analysis
The robustness of the base case cohort was assessed through probabilistic sensitivity analysis with 10,000 iterations. For each iteration, parameters were sampled using the normal distribution (age, initial BMI, proportion of female patients, the proportion of patients at baseline with T2D, HTN or DLP, and all cost parameters) according to the mean and standard deviation for each. The 10-year total patient-years of treatment and costs were calculated, from which 95% credibility intervals (95% CrIs) were determined. Calculations were performed using the R statistical programming language version 3.6 (R Project for Statistical Computing).
Scenario analyses
The primary analysis considered a hypothetical group of 100 patients following each of the 6 separate trajectories. It is expected that in real world practice, there will be a distribution of patients among different weight loss trajectories. To estimate outcomes in co-morbidity burden and corresponding costs in a more representative cohort, scenario analyses were generated of 100 patient cohorts in which different proportions of patients follow the different trajectories (Table 2). In the base case scenario, taken as standard care, patients are distributed according to the proportions reported in Courcoulas et al[10] with, for example, 13.3% of patients in the best (G6) post-RYGB weight loss trajectory and 4.8% in the lowest (G1). The first improvement scenario considers a case where all patients are improved to the next best trajectory according to area under the curve for 10-year weight loss. Patients in the poorest G1 therefore are moved to G2, G2 to G3 and so on. Patients in the best (G6) trajectory remain there and are not considered to improve further. In the second improvement scenario, patients are redistributed among the top 3 trajectories (G4, G5 and G6). Co-morbidity patient-years of treatment and associated costs were calculated for the entire 100-patient cohort according to each scenario. Differences between the improved and standard care scenarios were further assessed in the context of reported RYGB surgical volume for the top 3 Canadian provinces performing the procedure in 2014.
Table 2 Patient distribution by weight loss trajectory for scenario analyses
Group
|
Standard Care
|
Broad Improvement
|
Top 3 Trajectories
|
G6
|
13.3%
|
39.6%
|
29.2%
|
G4
|
26.3%
|
6.1%
|
57.7%
|
G5
|
6.1%
|
27.8%
|
13.4%
|
G3
|
27.8%
|
21.6%
|
0.0%
|
G2
|
21.6%
|
4.8%
|
0.0%
|
G1
|
4.8%
|
0.0%
|
0.0%
|
Post-gastric bypass weight loss trajectories (G1 to G6 as defined in reference[10]) are shown ordered from greatest to lowest 10-year total weight loss, and percentages indicate the distribution of patients according to scenario. The standard care represents the base case; in broad improvement, all patients are shifted up to the next best trajectory (those in the best trajectory, group 6, remain there); in the final scenario, all patients are redistributed among the top 3 trajectories by total 10-year weight loss.
Statistical analysis
Values are reported as medians and 95% CrIs determined from the 10,000 replicates. Differences may be considered significant for 95% CrIs that do not include zero (which would indicate that 95% of simulation results include both positive and negative differences). However, intervals are presented to allow readers individually to determine the relevance of the reported estimates according to local context, independently of statistical determination of significance