Towards assessing time-varying causal effect moderation in experimental and observational studies.

This dissertation considers statistical methodology for causal effect moderation in both experimental and observational studies, in both the point-treatment and time-varying treatments setting. We define causal effect moderation as the study of how the effects of treatment on an outcome of interest vary within levels of a covariate that is measured prior to treatment. In the first part of this thesis we treat the topic of causal effect moderation in one time point. The main purpose of this dissertation, however, is to work towards a framework for causal effect moderation in the time-varying setting, in which treatment is time-varying and so are the covariates said to moderate its effect. This topic constitutes the second part of this thesis, and it builds upon the ideas introduced in the first part. In the time-varying setting we define conditional intermediate causal effects that isolate the average effects of treatment at each time point on an end-of-study out-come, as a function of moderators available prior to that time point. We discuss and study extensively Robins' Structural Nested Mean Model (SNMM), a class of causal models for the conditional mean of the outcome given time-varying moderators and indexed by time-varying treatment. The SNMM includes a causal portion relating to the intermediate causal effects over time; it also includes a nuisance portion relating to non-causal associational effects of the moderators over time. We discuss two estimators of the causal effects in the SNMM. The first is a proposed 2-Stage Regression Estimator that requires properly specified models for the nuisance functions. The second is Robins' Semi-parametric G-Estimator that does not require correctly specified models for the nuisance functions. We discuss the assumptions under which we can make proper causal inference with each estimator. We present the results of a preliminary simulation study to understand the bias-variance trade-off between the two estimators. The methodology is illustrated using mental health data in which we seek to understand how the effects of time-varying treatments for depression are moderated by time-varying suicidal ideation.PhDPure SciencesStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/126620/2/3276092.pd