A fully Bayesian mixture model approach for identifying noncompliance in a regulatory tobacco clinical trial

Identifying noncompliance in a randomized trial is challenging, but could be improved by leveraging biomarker data to identify participants that did not comply with their assigned treatment. For randomized trials of very low nicotine content (VLNC) cigarettes, the biomarker of total nicotine equivalents (TNE) could be used to identify noncompliance. Compliant participants should have lower levels of TNEs than participants that did not comply and smoked normal nicotine content cigarettes, resulting in a mixture of compliant and noncompliant participants at each dose level. Thresholds of TNE could then be identified from the compliant groups at each dose level and used to determine which study participants were compliant. Furthermore, proposed biological relationships of TNE with nicotine dose could be incorporated into improve the efficiency of estimation, but may introduce bias if misspecified. To account for multiple modeling assumptions across dose levels, we explore model averaging via reversible jump markov chain monte carlo (MCMC) within each dose level to take advantage of improvements in efficiency when the proposed relationship is true and to downweight the biological model when it is misspecified. In simulation studies, we demonstrate that model averaging in the presence of a correct biological relationship results in a decrease in the mean square error (MSE) of up to 85%, but downweights the model in dose levels where the relationship is not appropriate. We apply our approach to data from a randomized trial of VLNC cigarettes to estimate TNE thresholds and probability of compliance curves as a function of TNEs for each nicotine dose used in the trial.