Chapter 1: Since the early 2000s, evidence has accumulated for a significant differential effect of first-line antiretroviral therapy (ART) regimens on human immunodeficiency virus (HIV) treatment outcomes, such as CD4 response and viral load suppression. This finding was replicated in our data from the Harvard President's Emergency Plan for AIDS Relief (PEPFAR) program in Nigeria. Investigators were interested in finding the source of these differences, i.e., understanding the mechanisms through which one regimen outperforms another, particularly via adherence. This amounts to a mediation question with adherence playing the role of mediator. Existing mediation analysis results, however, have relied on an assumption of no exposure-induced confounding of the intermediate variable, and generally require an assumption of no unmeasured confounding for nonparametric identification. Both assumptions are violated by the presence of drug toxicity. In this paper, we relax these assumptions and show that certain path-specific effects remain identified under weaker conditions. We focus on the path-specific effect solely mediated by adherence and not by toxicity and propose a suite of estimators for this effect, including a semiparametric-efficient, multiply-robust estimator. We illustrate with simulations and present results from a study applying the methodology to the Harvard PEPFAR data.
Chapter 2: In causal mediation analysis, nonparametric identification of the pure (natural) direct effect typically relies on fundamental assumptions of (i) so-called ``cross-world-counterfactuals" independence and (ii) no exposure-induced confounding. When the mediator is binary, bounds for partial identification have been given when neither assumption is made, or alternatively when assuming only (ii). We extend these bounds to the case of a polytomous mediator, and provide bounds for the case assuming only (i). We apply these bounds to data from the Harvard PEPFAR program in Nigeria, where we evaluate the extent to which the effects of antiretroviral therapy on virological failure are mediated by a patient's adherence, and show that inference on this effect is somewhat sensitive to model assumptions.
Chapter 3: When assessing the presence of an exposure causal effect on a given outcome, it is well known that classical measurement error of the exposure can seriously reduce the power of a test of the null hypothesis in question, although its type I error rate will generally remain controlled at the nominal level. In contrast, classical measurement error of a confounder can have disastrous consequences on the type I error rate of a test of treatment effect. In this paper, we develop a large class of semiparametric test statistics of an exposure causal effect, which are completely robust to classical measurement error of a subset of confounders. A unique and appealing feature of our proposed methods is that they require no external information such as validation data or replicates of error-prone confounders. The approach relies on the observation that under the sharp null hypothesis of no exposure causal effect, the standard assumption of no unmeasured confounding implies that the outcome is in fact a valid instrumental variable for the association between the error-prone confounder and the exposure. We present a doubly-robust form of this test that requires only one of two models -- an outcome-regression and a propensity-score model -- to be correctly specified for the resulting test statistic to have correct type I error rate. Validity and power within our class of test statistics is demonstrated via multiple simulation studies. We apply the methods to a multi-U.S.-city, time-series data set to test for an effect of temperature on mortality while adjusting for atmospheric particulate matter with diameter of 2.5 micrometres or less (PM2.5), which is well known to be measured with error.Biostatistic
