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Abstract
In assessing the efficacy of a time-varying treatment Marginal Structural Models (MSMs) and Structural Nested Mean Models (SNMMs) are useful in dealing with confounding by variables affected by earlier treatments. MSMs model the joint effect of treatments on the marginal mean of the potential outcome, whereas SNMMs model the joint effect of treatments on the mean of the potential outcome conditional on the treatment and covariate history. These models often consider independent subjects with noninformative time of observation.
The first two chapters extend the two classes of models to clustered observations with time-varying treatments in the presence of time-varying confounding. We formulate models with both cluster- and unit-level treatments and derive semiparametric estimators of parameters in such models. For unit-level treatments, we consider both the presence and absence of interference, namely the effect of treatment on outcomes in other units of the same cluster. For MSMs, we show that the use of unit-specific inverse probability weights and certain working correlation structures can improve the efficiency of estimators under specified conditions. The properties of the estimators are evaluated through simulations and compared with the conventional GEE regression method for clustered outcomes. To illustrate our methods, we use data from the treatment arm of a glaucoma clinical trial to compare the effectiveness of two commonly used ocular hypertension medications.
The third chapter extends SNMMs to situations with intermittent missing observations. In observational longitudinal studies, subjects often miss prescheduled visits intermittently. Previous literature has mainly focused on dealing with monotone censoring due to early dropout. Here we focus on intermittent missingness that can depend on the subjects' covariate and treatment history. We show that under certain assumptions the standard SNMMs can be used for situations where non-outcome covariates are missing intermittently. In situations where outcomes are also missing intermittently, we use a method that does not require artificially censoring the data, but requires a strict missing at random assumption. The estimators are shown to be consistent and achieve reasonable efficiency. We illustrate the method by estimating the effect of non-steroidal anti-inflammatory drugs (NSAIDs) on genitourinary pain using data from a study of chronic pelvic pain.
