Statistical Methods for Addressing Missing Data and Evaluating Treatment Effect Heterogeneity in Randomized Clinical Trials

Abstract

Randomized clinical trials are the gold standard for evaluating the efficacy and safety of new treatments, but analyses of clinical trials can be complicated by missing data and treatment effect heterogeneity. First, when patients drop out of the study or miss visits, many commonly held statistical methods are not suitable to analyze response for interventions due to missing data, which limits investigators to draw robust inference from the study sample. Second, the standard statistical paradigm in clinical trials often lies in estimating or testing the treatment effect for the overall population. However, patients can have heterogeneous responses to treatment, for which the treatment of interest might be beneficial for a specific patient subgroup but could be neutral or harmful to others. This dissertation discusses considerations for these challenges and proposes novel approaches to improve the validity and robustness of statistical inference in randomized clinical trials. In Chapter 1, we address the issue of conducting covariate adjustment in clinical trials in the presence of missing data. Covariate adjustment is a commonly used statistical approach to account for chance imbalance in baseline covariates and to increase precision of the treatment effect estimate. In the light of recent theoretical advancement, we first review several covariate adjustment methods with incomplete covariate data. We investigate the implications of the missing data mechanism on estimating the average treatment effect in randomized clinical trials with continuous or binary outcomes. In parallel, we consider settings where the outcome data are fully observed or are missing at random; in the latter setting, we propose a full weighting approach that combines inverse probability weighting for adjusting missing outcomes and overlap weighting for covariate adjustment. We conduct comprehensive simulation studies to examine the finite sample performance of the proposed methods and compare with a range of common alternatives. We apply the proposed methods to the Childhood Adenotonsillectomy Trial to assess the effect of adenotonsillectomy on neurocognitive functioning scores. In Chapter 2 and 3, we focus on statistical challenges for the analyses of cluster-randomized trial (CRT), an alternative trial design which randomizes all individuals in the same cluster to receive the same intervention condition. In Chapter 2, we propose new estimators for estimating the marginal treatment effect in CRTs with multi-level missing outcomes. When outcomes are missing at random (MAR), methods such as inverse probability weighted generalized estimating equations have been proposed to account for informative missingness by weighting the observed individual outcome data in each cluster. These existing methods have focused on settings where missingness occurs at the individual level and each cluster has partially or fully observed individual outcomes. In the presence of missing clusters, e.g., all outcomes from a cluster are missing due to drop-out of the cluster, these approaches effectively ignore this cluster-level missingness and can lead to biased inference if the cluster-level missingness is informative. Informative missingness at multiple levels can also occur in CRTs with a multi-level structure where study participants are nested in subclusters such as health care providers, and the subclusters are nested in clusters such as clinics. To address informative missing outcomes at multiple levels, we propose the multi-level multiply robust estimator based on weighted generalized estimating equations. We show that the proposed estimator is consistent and asymptotically normally distributed provided that one set of the propensity score models is correctly specified. We evaluate the performance of the proposed method through extensive simulations and illustrate its use with a CRT evaluating a Malaria risk-reduction intervention in rural Madagascar. In Chapter 3, we turn into the topic of treatment effect heterogeneity in CRTs. Investigation of treatment effect heterogeneity in contemporary clinical research and practice holds promises to inform tailored healthcare services and improve patient outcomes, but current methods for identifying patient subgroups with differential treatment effects for CRTs are limited. To address the methodological gap, we propose a testing procedure to detect the existence of a patient subgroup with an enhanced treatment effect in CRTs. We consider a semi-parametric change-plane model based on the generalized estimating equations approach, which includes an unspecified baseline function for the covariate effects and a subgroup-treatment interaction defined by the change-plane. A score-type test statistic is then formulated based on this model, and the asymptotic distributions of the test statistic are established. When the null hypothesis of no subgroup with an enhanced treatment effect is rejected, the enhanced treatment effect characterized by the change-plane parameters can be estimated. Through extensive simulations, we empirically assess the performance of the proposed method in finite samples. Then, we apply the proposed testing procedure to a CRT evaluating a behavioral intervention program for treating chronic pain among patients receiving long-term opioid therapy.