Estimating equations for fitting linear regression models describing the impact of partially-observed time-varying predictors on patterns of weight change among participants seeking to lose weight using ecological momentary assessment data
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People who attempt to lose weight and maintain weight loss often fail as a consequence of lapses in dietary and exercise protocols leading to weight regain. In the Ecological Momentary assessment via smart PhOne for WEight loss and Relapse prevention (EMPOWER) study, data are collected through Ecological Momentary Assessment (EMA), under which subjects were asked to record each temptation/urge to go off their healthy lifestyles, as well as dietary lapses using a cell-phone Application (APP). The APP prompted subjects to answer questions regarding their mood and environment at the times of each temptation/urge or lapse as well as at times generated from a known point process model. In addition, study participants were asked to weigh themselves daily using a blue-tooth enabled scale. One aim of the EMPOWER program is to identify what emotional and environmental factors lead to dietary lapse and quantify their impact on weight gain/loss during 6 month uniform intervention and 6-month followup period. Despite the observation that subjects tended to lose less weight or even gain weight in the follow-up period, subjects reported fewer lapses during follow-up suggesting that the lapse data were unreliable. Therefore, this dissertation focuses directly on the pattern of weight loss/gain over the 12 month of monitoring. We proposed linear regression model predicting instantaneous weight change and a function of time-varying covariates including two measures of self-efficacy, location, and environment. Under this model, the mean daily change in weight over any time interval is a linear function of the mean values of the time-varying predictors, values that could not be directly observed. Design-unbiased estimators for those mean levels can be obtained from the random assessments of the time-varying predictors. However, simply substituting these estimated means into the normal equations yields biased estimating equations and hence biased estimates of regression coefficients. We proposed unbiased estimating equations yielding consistent estimators for regression coefficients in two settings, linear fixed effects model for weight change in a single time interval for each subject, and mixed linear models for repeated disjoint intervals taking into account variation both within and between subjects and temporal correlations in patterns of weight change across weight change data. We demonstrate that the proposed estimating equations yield consistent and asymptotically normally distributed estimators with increasing numbers of study participants. We illustrate our approach using data from an EMA of weight loss program.