Marginal Models in Analysis of Correlated Binary Data with Time Dependent Covariates

Abstract

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A two-stage Generalized Method of Moments model for feedback with time-dependent covariates

“…The time-dependent covariate is BMI, with gender and age as covariates in the model. The questions of interest are: (1) are children who presently have lower BMI more likely to be sick now; (2) are children who had lower BMI in the past four and eight months more likely to be sick now; and (3) did BMI go down for children who were sick four and eight months ago. Thus, in Stage 1, we model the impact of past and present BMI on child’s likelihood of being sick (child’s morbidity).…”

“…(2) what risk factors in the past are associated with obesity status in the present (lag 1, lag 2, and lag 3)? ; and (3) does obesity increase the risk of depression and decrease physical activity levels in the future?…”

“…2 The partitioned GMM model addresses the first two questions of interest when analyzing longitudinal data. 3 In health-related data, there are situations where responses associate with future values of the time-dependent covariates (a feedback effect is present). Such is the case of the Add Health survey data, where an interesting issue is to investigate whether there is a feedback mechanism between depression scores and obesity and between physical activity levels and obesity.…”

“…An expansion of the partitioned GMM model that allows the responses measured presently to impact future covariates has been developed. 3 This is a two-stage population-averaged (PA) model that allows researchers to answer the three questions simultaneously. The first stage consists of a partitioned GMM model that answers the first two questions.…”

“…2 The partitioned GMM model addresses the first two questions of interest when analyzing longitudinal data. 3…”