Sequential, multiple assignment, randomized trial (SMART) designs have become increasingly popular in the field of precision medicine by providing a means for comparing sequences of treatments tailored to the individual patient, i.e., dynamic treatment regime (DTR). The construction of evidence-based DTRs promises a replacement to adhoc one-size-fits-all decisions pervasive in patient care. However, there are substantial statistical challenges in sizing SMART designs due to the complex correlation structure between the DTRs embedded in the design. Since the primary goal of SMARTs is the construction of an optimal DTR, investigators are interested in sizing SMARTs based on the ability to screen out DTRs inferior to the optimal DTR by a given amount which cannot be done using existing methods. In this paper, we fill this gap by developing a rigorous power analysis framework that leverages multiple comparisons with the best methodology. Our method employs Monte Carlo simulation in order to compute the minimum number of individuals to enroll in an arbitrary SMART. We will evaluate our method through extensive simulation studies. We will illustrate our method by retrospectively computing the power in the Extending Treatment Effectiveness of Naltrexone SMART study.

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.

Sequential, multiple assignment, randomized trials (SMARTs) compare sequences of treatment decision rules called dynamic treatment regimes (DTRs). In particular, the Adaptive Treatment for Alcohol and Cocaine Dependence (ENGAGE) SMART aimed to determine the best DTRs for patients with a substance use disorder. While many authors have focused on a single pairwise comparison, addressing the main goal involves comparisons of >2 DTRs. For complex comparisons, there is a paucity of methods for binary outcomes. We fill this gap by extending the multiple comparisons with the best (MCB) methodology to the Bayesian binary outcome setting. The set of best is constructed based on simultaneous credible intervals. A substantial challenge for power analysis is the correlation between outcome estimators for distinct DTRs embedded in SMARTs due to overlapping subjects. We address this using Robins' G‐computation formula to take a weighted average of parameter draws obtained via simulation from the parameter posteriors. We use non‐informative priors and work with the exact distribution of parameters avoiding unnecessary normality assumptions and specification of the correlation matrix of DTR outcome summary statistics. We conduct simulation studies for both the construction of a set of optimal DTRs using the Bayesian MCB procedure and the sample size calculation for two common SMART designs. We illustrate our method on the ENGAGE SMART. The R package SMARTbayesR for power calculations is freely available on the Comprehensive R Archive Network (CRAN) repository. An RShiny app is available at https://wilart.shinyapps.io/shinysmartbayesr/.

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.

Existing methods for estimating the mean outcome under a given sequential treatment rule often rely on intention‐to‐treat analyses, which estimate the effect of following a certain treatment rule 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 potentially differential compliance behavior. These are particularly problematic in settings with a high level of non‐compliance, such as substance use disorder studies. 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, instead of the actual effect of the treatment. We obviate this challenge by defining the target parameter as the mean outcome under a dynamic treatment regime conditional on a potential compliance stratum. We propose a flexible non‐parametric Bayesian approach based on principal stratification, which consists of a Gaussian copula model for the joint distribution of the potential compliances, and a Dirichlet process mixture model for the treatment sequence specific outcomes. We conduct extensive simulation studies which highlight the utility of our approach in the context of multi‐stage randomized trials. We show robustness of our estimator to non‐linear and non‐Gaussian settings as well.