Behavioral Modeling in Weight Loss Interventions

Abstract

Designing systems with human agents is difficult because it often requires models that characterize agents' responses to changes in the system's states and inputs. An example of this scenario occurs when designing treatments for obesity. While weight loss interventions through increasing physical activity and modifying diet have found success in reducing individuals' weight, such programs are difficult to maintain over long periods of time due to lack of patient adherence. A promising approach to increase adherence is through the personalization of treatments to each patient. In this paper, we make a contribution towards treatment personalization by developing a framework for predictive modeling using utility functions that depend upon both time-varying system states and motivational states evolving according to some modeled process corresponding to qualitative social science models of behavior change. Computing the predictive model requires solving a bilevel program, which we reformulate as a mixed-integer linear program (MILP). This reformulation provides the first (to our knowledge) formulation for Bayesian inference that uses empirical histograms as prior distributions. We study the predictive ability of our framework using a data set from a weight loss intervention, and our predictive model is validated by comparison to standard machine learning approaches. We conclude by describing how our predictive model could be used for optimization, unlike standard machine learning approaches which cannot.

Keywords: OR in health services; inverse optimization; machine learning; predictive modeling; weight loss.

Figure 1:

Comparison of data (blue dots) with MLE estimates of weight, exercise, and caloric intake (red line).

Figure 2:

Posterior likelihood of final weight conditioned on 30 days of data (solid) compare to intial weight (dashed) and final weight corresponding to a 5% weight loss (dotted).

Figure 3:

Comparison of MAP estimates of weight, exercise, and caloric intake trajectories dark blue dots) with future data not used to computed estimates (light blue dots).

Figure 4:

ROC curves computed using leave-one-out cross-validation for our predictive model with an empirical Bayesian prior (blue solid), our predictive model without a Bayesian prior (red dashed), linear SVM model (purple dash dot), decision tree model (green dashed dot), and logistic regression (cyan dashed) are compared.

Figure 5:

Posterior likelihood of final weight of an individual conditioned on 50 days of data and conditioned on either having 12,000 steps/day goals after 50 days (dash dotted) or 8,000 steps/day goals after 50 days (solid), and compared to initial weight (dashed) and final weight corresponding to a 5% weight loss (dotted).

Figure 6:

Posterior likelihood of final weight of an individual conditioned on 50 days of data and conditioned on either having no office visits after 50 days (dash dotted) or having 4 office visits after 50 days (solid and final weight corresponding to a 5% weight loss (dotted).