Quantifying and correcting bias due to outcome dependent self-reported weights in longitudinal study of weight loss interventions

In response to the escalating global obesity crisis and its associated health and financial burdens, this paper presents a novel methodology for analyzing longitudinal weight loss data and assessing the effectiveness of financial incentives. Drawing from the Keep It Off trial—a three-arm randomized controlled study with 189 participants—we examined the potential impact of financial incentives on weight loss maintenance. Given that some participants choose not to weigh themselves because of small weight change or weight gains, which is a common phenomenon in many weight-loss studies, traditional methods, for example, the Generalized Estimating Equations (GEE) method tends to overestimate the effect size due to the assumption that data are missing completely at random. To address this challenge, we proposed a framework which can identify evidence of missing not at random and conduct bias correction using the estimating equation derived from pairwise composite likelihood. By analyzing the Keep It Off data, we found that the data in this trial are most likely characterized by non-random missingness. Notably, we also found that the enrollment time (i.e., duration time) would be positively associated with the weight loss maintenance after adjusting for the baseline participant characteristics (e.g., age, sex). Moreover, the lottery-based intervention was found to be more effective in weight loss maintenance compared with the direct payment intervention, though the difference was non-statistically significant. This framework's significance extends beyond weight loss research, offering a semi-parametric approach to assess missing data mechanisms and robustly explore associations between exposures (e.g., financial incentives) and key outcomes (e.g., weight loss maintenance). In essence, the proposed methodology provides a powerful toolkit for analyzing real-world longitudinal data, particularly in scenarios with data missing not at random, enriching comprehension of intricate dataset dynamics.