Detecting participant noncompliance across multiple time points by modeling a longitudinal biomarker

Introduction: Participant noncompliance, in which participants do not follow their assigned treatment protocol, has long complicated the interpretation of randomized clinical trials. No gold standard has been identified for detecting noncompliance, but in some trials participants’ biomarkers can provide objective information that suggests exposure to non-study treatments. However, existing methods are limited to retrospectively detecting noncompliance at a single time point based on a single biomarker measurement. We propose a novel method that can leverage participants’ full biomarker history to detect noncompliance across multiple time points. Conditional on longitudinal biomarker data, our method can estimate the probability of compliance at (1) a single time point of the trial, (2) all time points, and (3) a future time point. Methods: Across time points, we model the biomarker as a mixture density with (latent) components corresponding to longitudinal patterns of compliance. To estimate the mixture density, we fit mixed effects models for both compliance and the biomarker. We use the mixture density to derive compliance probabilities that condition on the longitudinal biomarker data. We evaluate our compliance probabilities by simulation and apply them to a trial in which current smokers were asked to only smoke low nicotine study cigarettes (Center for the Evaluation of Nicotine in Cigarettes Project 1 Study 2). In the simulation, we investigated three different effects of compliance on the biomarker, as well as the effect of misspecification of the covariance structures. We compared probability estimators (1) and (2) to those that ignore the longitudinal correlation in the data according to area under the receiver operating characteristic curve. We evaluated estimator (3) by plotting its calibration lines. For Center for the Evaluation of Nicotine in Cigarettes Project 1 Study 2, we compared estimators (1) and (3) to a probability estimator of compliance at the last time point that ignores the longitudinal correlation. Results: In the simulation, for both compliance at the last time point and at all time points, conditioning on the longitudinal biomarker data uniformly raised area under the receiver operating characteristic curve across all three compliance effect scenarios. The gains in area under the receiver operating characteristic curve were smaller under misspecification. The calibration lines for the prediction of compliance closely followed 45°, though with additional variability under misspecification. For compliance at the last time point of Center for the Evaluation of Nicotine in Cigarettes Project 1 Study 2, conditioning on participants’ full biomarker history boosted area under the receiver operating characteristic curve by three percentage points. The prediction probabilities somewhat accurately approximated the non-longitudinal compliance probabilities. Discussion: Compared to existing methods that only use a single biomarker measurement, our method can account for the longitudinal correlation in the biomarker and compliance to more accurately identify noncompliant participants. Our method can also use participants’ biomarker history to predict compliance at a future time point.