The randomization process in clinical trials is disrupted with the existence of post-randomization events or intercurrent events. The "gold-standard" intention-to-treat (ITT) estimand therefore loses its clinical relevance because it compares treatment assignments instead of actual received treatments. Alternative estimands need to be defined and identified to quantify the causal effect of treatments. In this dissertation, we focus on the intercurrent event of treatment nonadherence and identify the causal estimands in clinical trials with two active treatments. We work under the Neyman-Rubin causal framework and the principal stratification framework. First, we propose a nonparametric approach which identifies the complier average causal effect (CACE) as the ratio of the ITT effect of treatment assignment on the outcome to the ITT effect of treatment assignment on the treatment received under the exclusion restriction, monotonicity, and no partial-compliers assumptions. We discuss violation of the identification assumptions and derive the corresponding bias formulas. Simulations with various degrees of assumption violations are conducted to evaluate the performance and sensitivity of the approach. The results show that the nonparametric approach can yield an unbiased estimator for CACE when sample size is 500 or above and the percentage of compliers is above or equal to 70%. In addition, increasing the number of compliers has the potential to reduce the bias to as close as zero. Second, we propose a multisite design approach which identifies the CACE under the zero correlation assumption. We derive the bias formula when measurement errors and omitted variables exist. Simulations across various scenarios are conducted for the oracle, naive, and bootstrap estimators. The results show that multisite design approach can yield an unbiased estimator if there are no measurement errors and omitted variables. Increasing the number of people in each site can reduce the bias because it reduces the variation of the measurement errors. Increasing the number of sites, on the other hand, does not make a significant impact on the bias. We apply the two proposed approaches to the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) data to identify the causal effects of the medication augmentation and the causal effects of the medication switching. We show that augmenting citalopram with sustained-release bupropion is no better than augmenting citalopram with buspiron in terms of remission but has a higher response rate. Augmenting citalopram with sustained-release bupropion also reduces the 17-item Hamilton Rating Scale for Depression (HAM-D17) score greater than augmenting citalopram with buspiron. We also show that switching to extended-release venlafaxine has a slightly better performance compared switching to sustained-release bupropion in terms of remission, HAM-D17 scores at the end of the study, and reduction of HAM-D17 scores.
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