Maximum likelihood estimation of the structural nested mean model using SAS PROC NLP: With application to the study of time-varying moderators of the effect of weight change on quality of life

This chapter reviews Robins’ Structural Nested Mean Model (SNMM) for assessing the effect of predictors that vary over time. The SNMM is used to study the effects of time-varying predictors (or treatments) in the presence of time-varying covariates that are moderators of these effects. We describe a SAS implementation of a maximum likelihood (ML) estimator of the parameters of a SNMM using SAS PROC NLP. The proposed ML estimator requires correct model specification of the distribution of the primary outcome given the history of time-varying moderators and predictors, including proper specification of both the causal and non-causal portions of the SNMM. The estimator also relies on correct model specification of the observed data distribution of the putative timevarying moderators given the past. We illustrate the methodology and SAS implementation using data from a weight loss study. In the empirical example, we assess the impact of early versus later weight loss (or gain) on endof-study health-related quality of life as a function of prior weight loss and time-varying covariates thought to be moderators of these effects.

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