<p>This thesis examines causal inference related topics involving intermediate variables, and uses Bayesian methodologies to advance analysis capabilities in these areas. First, joint modeling of outcome variables with intermediate variables is considered in the context of birthweight and censored gestational age analyses. The proposed methodology provides improved inference capabilities for birthweight and gestational age, avoids post-treatment selection bias problems associated with conditional on gestational age analyses, and appropriately assesses the uncertainty associated with censored gestational age. Second, principal stratification methodology for settings where causal inference analysis requires appropriate adjustment of intermediate variables is extended to observational settings with binary treatments and binary intermediate variables. This is done by uncovering the structural pathways of unmeasured confounding affecting principal stratification analysis and directly incorporating them into a model based sensitivity analysis methodology. Demonstration focuses on a study of the efficacy of influenza vaccination in elderly populations. Third, flexibility, interpretability, and capability of principal stratification analyses for continuous intermediate variables are improved by replacing the current fully parametric methodologies with semiparametric Bayesian alternatives. This presentation is one of the first uses of nonparametric techniques in causal inference analysis,</p><p>and opens a connection between these two fields. Demonstration focuses on two studies, one involving a cholesterol reduction drug, and one examine the effect of physical activity on cardiovascular disease as it relates to body mass index.</p> / Dissertation

In clinical trials, placebo response is considered a beneficial effect arising from multiple factors, including the patient’s expectations for the treatment. Due to the presence of placebo response, the classical parallel design often fails to declare an efficacious treatment. The Sequential Parallel Comparison Design (SPCD), a two-stage design where the first stage is a classical parallel trial, followed by another parallel trial among placebo patients from the first stage, was proposed to mitigate the placebo response. In SPCD, in lieu of treatment effect, a weighted average of the mean treatment difference in Stage I among all randomized patients and the mean treatment difference in Stage II among placebo non-responders was proposed as the efficacy measure. However, by mixing two possibly different populations, this weighted average lacks interpretability, the choice of weight remains controversial, and the classification of patients into placebo responders and non-responders via hard criterion-based rule warrants careful consideration. In this work, we first elaborate and study the shortcomings surrounding this efficacy measure, which motivates us to propose causal estimands for clinically meaningful principal strata under the principal stratification framework. To make the estimands identifiable, we invoke a set of assumptions and introduce two sensitivity parameters. Meanwhile, in the absence of a clinically proven criterion for classifying responders and non-responders, we additionally suggest estimating the response status and sensitivity parameters via the Expectation-Maximization (EM) algorithm by treating the principal strata as full latent characteristics. Next, we further refine and alternatively propose a more consistent and sophisticated EM procedure for classification, point estimation, and hypothesis testing. Finally, we evaluate our methods with extensive simulation studies and apply them to an actual SPCD study of antidepressant therapy to assess the benefit of low-dose aripiprazole adjunctive to antidepressant therapy treatment, the ADAPT-A trial. In conclusion, we believe this is an important step toward a more rigorous and transparent approach to evaluating the treatment benefit in the presence of placebo response. / 2025-09-18T00:00:00Z

Randomized clinical trials (RCTs) are considered to be the "gold standard" in order to demonstrate a causal relationship between a treatment and an outcome because complete randomization ensures that the only difference between the two units being compared is the treatment. The intention-to-treat (ITT) comparison has long been regarded as the preferred analytic approach for RCTs. However, if there exists an “intermediate” variable between the treatment and outcome, and the analysis conditions on this intermediate, randomization will break down, and the ITT approach does not account properly for the intermediate. In this dissertation, we explore the principal stratification approach for dealing with intermediate variables, illustrate its applications in two different clinical trial settings, and extend the existing analytic approaches with respect to specific challenges in these settings. The first part of our work focuses on clinical endpoint bioequivalence (BE) studies with noncompliance and missing data. In clinical endpoint BE studies, the primary analysis for assessing equivalence between a generic and an innovator product is usually based on the observed per-protocol (PP) population (usually completers and compliers). The FDA Missing Data Working Group recently recommended using “causal estimands of primary interest.” This PP analysis, however, is not generally causal because the observed PP is post-treatment, and conditioning on it may introduce selection bias. To date, no causal estimand has been proposed for equivalence assessment. We propose co-primary causal estimands to test equivalence by applying the principal stratification approach. We discuss and verify by simulation the causal assumptions under which the current PP estimator is unbiased for the primary principal stratum causal estimand – the "Survivor Average Causal Effect" (SACE). We also propose tipping point sensitivity analysis methods to assess the robustness of the current PP estimator from the SACE estimand when these causal assumptions are not met. Data from a clinical endpoint BE study is used to illustrate the proposed co-primary causal estimands and sensitivity analysis methods. Our work introduces a causal framework for equivalence assessment in clinical endpoint BE studies with noncompliance and missing data. The second part of this dissertation targets the use of principal stratification analysis approaches in a pragmatic randomized clinical trial -- the Patient Activation after DXA Result Notification (PAADRN) study. PAADRN is a multi-center, pragmatic randomized clinical trial that was designed to improve bone health. Participants were randomly assigned to either intervention group with usual care augmented by a tailored patient-activation Dual-energy X-ray absorptiometry (DXA) results letter accompanied by an educational brochure, or control group with usual care only. The primary analyses followed the standard ITT principle, which provided a valid estimate for the intervention assignment. However, findings might underestimate the effect of intervention because PAADRN might not have an effect if the patient did not read, remember and act on the letter. We apply principal stratification to evaluate the effectiveness of PAADRN for subgroups, defined by patient's recall of having received a DXA result letter, which is an intermediate outcome that's post-treatment. We perform simulation studies to compare the principal score weighting methods with the instrumental variable (IV) methods. We examine principal strata causal effects on three outcome measures regarding pharmacological treatment and bone health behaviors. Finally, we conduct sensitivity analyses to assess the effect of potential violations of relevant causal assumptions. Our work is an important addition to the primary findings based on ITT. It provides a profound understanding of why the PAADRN intervention does (or does not) work for patients with different letter recall statuses, and sheds light on the improvement of the intervention.

Noncompliance to treatment allocation is likely to complicate estimation of causal effects in clinical trials. The ubiquitous nonrandom phenomenon of noncompliance renders per-protocol and as- treated analyses or even simple regression adjustments for noncompliance inadequate for causal inference. For survival data, several specialist methods have been developed when noncompliance is related to risk. The Causal Accelerated Life Model (CALM) allows time-dependent departures from randomized treatment in either arm and relates each observed event time to a potential event time that would have been observed if the control treatment had been given throughout the trial. Alternatively, the structural Proportional Hazards (C-Prophet) model accounts for all-or-nothing noncompliance in the treatment arm only while the CHARM estimator allows time-dependent departures from randomized treatment by considering survival outcome as a sequence of binary outcomes to provide an 'approximate' overall hazard ratio estimate which is adjusted for compliance. The problem of efficacy estimation is compounded for two-active treatment trials (additional noncompliance) where the ITT estimate provides a biased estimator for the true hazard ratio even under homogeneous treatment effects assumption. Using plausible arm-specific predictors of compliance, principal stratification methods can be applied to obtain principal effects for each stratum. The present work applies the above methods to data from the Esprit trials study which was conducted to ascertain whether or not unopposed oestrogen (hormone replacement therapy - HRT) reduced the risk of further cardiac events in postmenopausal women who survive a first myocardial infarction. We use statistically designed simulation studies to evaluate the performance of these methods in terms of bias and 95% confidence interval coverage. We also apply a principal stratification method to adjust for noncompliance in two treatment arms trial originally developed for binary data for survival analysis in terms of causal risk ratio. In a Bayesian framework, we apply the method to Esprit data to account for noncompliance in both treatment arms and estimate principal effects. We apply statistically designed simulation studies to evaluate the performance of the method in terms of bias in the causal effect estimates for each stratum. ITT analysis of the Esprit data showed the effects of taking HRT tablets was not statistically significantly different from placebo for both all cause mortality and myocardial reinfarction outcomes. Average compliance rate for HRT treatment was 43% and compliance rate decreased as the study progressed. CHARM and C-Prophet methods produced similar results but CALM performed best for Esprit: suggesting HRT would reduce risk of death by 50%. Simulation studies comparing the methods suggested that while both C-Prophet and CHARM methods performed equally well in terms of bias, the CALM method performed best in terms of both bias and 95% confidence interval coverage albeit with the largest RMSE. The principal stratification method failed for the Esprit study possibly due to the strong distribution assumption implicit in the method and lack of adequate compliance information in the data which produced large 95% credible intervals for the principal effect estimates. For moderate value of sensitivity parameter, principal stratification results suggested compliance with HRT tablets relative to placebo would reduce risk of mortality by 43% among the most compliant. Simulation studies on performance of this method showed narrower corresponding mean 95% credible intervals corresponding to the the causal risk ratio estimates for this subgroup compared to other strata. However, the results were sensitive to the unknown sensitivity parameter.