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The current body of research on developing optimal treatment strategies often places emphasis on intention-to-treat analyses, which fail to take into account the compliance behavior of individuals. Methods based on instrumental variables have been developed to determine optimal treatment strategies in the presence of endogeneity. However, these existing methods are not applicable when there are two active treatment options and the average causal effects of the treatments cannot be identified using a binary instrument. In order to address this limitation, we present a procedure that can identify an optimal treatment strategy and the corresponding value function as a function of a vector of sensitivity parameters. Additionally, we derive the canonical gradient of the target parameter and propose a multiply robust classification-based estimator for the optimal treatment strategy. Through simulations, we demonstrate the practical need for and usefulness of our proposed method. We apply our method to a randomized trial on Adaptive Treatment for Alcohol and Cocaine Dependence.

Existing methods in estimating the mean outcome under a given dynamic treatment regime rely on intention-to-treat analyses which estimate the effect of following a certain dynamic treatment regime regardless of compliance behavior of patients. There are two major concerns with intention-to-treat analyses: (1) the estimated effects are often biased toward the null effect; (2) the results are not generalizable and reproducible due to the potential differential compliance behavior. These are particularly problematic in settings with high level of non-compliance such as substance use disorder treatments. Our work is motivated by the Adaptive Treatment for Alcohol and Cocaine Dependence study (ENGAGE), which is a multi-stage trial that aimed to construct optimal treatment strategies to engage patients in therapy. Due to the relatively low level of compliance in this trial, intention-to-treat analyses essentially estimate the effect of being randomized to a certain treatment sequence which is not of interest. We fill this important gap by defining the target parameter as the mean outcome under a dynamic treatment regime given potential compliance strata. We propose a flexible non-parametric Bayesian approach, which consists of a Gaussian copula model for the potential compliances, and a Dirichlet process mixture model for the potential outcomes. Our simulations highlight the need for and usefulness of this approach in practice and illustrate the robustness of our estimator in non-linear and non-Gaussian settings.

Dynamic treatment regimens (DTRs), also known as treatment algorithms or adaptive interventions, play an increasingly important role in many health domains. DTRs are motivated to address the unique and changing needs of individuals by delivering the type of treatment needed, when needed, while minimizing unnecessary treatment. Practically, a DTR is a sequence of decision rules that specify, for each of several points in time, how available information about the individual's status and progress should be used in practice to decide which treatment (e.g., type or intensity) to deliver. The sequential multiple assignment randomized trial (SMART) is an experimental design widely used to empirically inform the development of DTRs. Sample size planning resources for SMARTs have been developed for continuous, binary, and survival outcomes. However, an important gap exists in sample size estimation methodology for SMARTs with longitudinal count outcomes. Further, in many health domains, count data are overdispersed - having variance greater than their mean. We propose a Monte Carlo-based approach to sample size estimation applicable to many types of longitudinal outcomes and provide a case study with longitudinal overdispersed count outcomes. A SMART for engaging alcohol and cocaine-dependent patients in treatment is used as motivation., Comment: Key words: dynamic treatment regimen (DTR); longitudinal outcome; overdispersed count; sample size estimation; sequential multiple assignment randomized trial (SMART)

One of the main goals of sequential, multiple assignment, randomized trials (SMART) is to find the most efficacious design embedded dynamic treatment regimes. The analysis method known as multiple comparisons with the best (MCB) allows comparison between dynamic treatment regimes and identification of a set of optimal regimes in the frequentist setting for continuous outcomes, thereby, directly addressing the main goal of a SMART. In this paper, we develop a Bayesian generalization to MCB for SMARTs with binary outcomes. Furthermore, we show how to choose the sample size so that the inferior embedded DTRs are screened out with a specified power. We compare log-odds between different DTRs using their exact distribution without relying on asymptotic normality in either the analysis or the power calculation. We conduct extensive simulation studies under two SMART designs and illustrate our method's application to the Adaptive Treatment for Alcohol and Cocaine Dependence (ENGAGE) trial., Comment: 20 pages, 5 figures, 3 tables

The cyclical and heterogeneous nature of many substance use disorders highlights the need to adapt the type or the dose of treatment to accommodate the specific and changing needs of individuals. The Adaptive Treatment for Alcohol and Cocaine Dependence study (ENGAGE) is a multi-stage randomized trial that aimed to provide longitudinal data for constructing treatment strategies to improve patients' engagement in therapy. However, the high rate of noncompliance and lack of analytic tools to account for noncompliance have impeded researchers from using the data to achieve the main goal of the trial. We overcome this issue by defining our target parameter as the mean outcome under different treatment strategies for given potential compliance strata and propose a Bayesian semiparametric model to estimate this quantity. While it adds substantial complexities to the analysis, one important feature of our work is that we consider partial rather than binary compliance classes which is more relevant in longitudinal studies. We assess the performance of our method through comprehensive simulation studies. We illustrate its application on the ENGAGE study and demonstrate that the optimal treatment strategy depends on compliance strata., Comment: 31 pages, 8 figures, 13 tables

In a clinical trial of a treatment for alcoholism, a common response variable of interest is the number of alcoholic drinks consumed by each subject each day, or an ordinal version of this response, with levels corresponding to abstinence, light drinking and heavy drinking. In these trials, within-subject drinking patterns are often characterized by alternating periods of heavy drinking and abstinence. For this reason, many statistical models for time series that assume steady behavior over time and white noise errors do not fit alcohol data well. In this paper we propose to describe subjects' drinking behavior using Markov models and hidden Markov models (HMMs), which are better suited to describe processes that make sudden, rather than gradual, changes over time. We incorporate random effects into these models using a hierarchical Bayes structure to account for correlated responses within subjects over time, and we estimate the effects of covariates, including a randomized treatment, on the outcome in a novel way. We illustrate the models by fitting them to a large data set from a clinical trial of the drug Naltrexone. The HMM, in particular, fits this data well and also contains unique features that allow for useful clinical interpretations of alcohol consumption behavior., Comment: Published in at http://dx.doi.org/10.1214/09-AOAS282 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)