Estimation of Drug Effectiveness by Modeling Three Time-dependent Covariates: An Application to Data on Cardioprotective Medications in the Chronic Dialysis Population

In a population of chronic dialysis patients with an extensive burden of cardiovascular disease, estimation of the effectiveness of cardioprotective medication in literature is based on calculation of a hazard ratio comparing hazard of mortality for two groups (with or without drug exposure) measured at a single point in time or through the cumulative metric of proportion of days covered (PDC) on medication. Though both approaches can be modeled in a time-dependent manner using a Cox regression model, we propose a more complete time-dependent metric for evaluating cardioprotective medication efficacy. We consider that drug effectiveness is potentially the result of interactions between three time-dependent covariate measures, current drug usage status (ON versus OFF), proportion of cumulative exposure to drug at a given point in time, and the patient's switching behavior between taking and not taking the medication. We show that modeling of all three of these time-dependent measures illustrates more clearly how varying patterns of drug exposure affect drug effectiveness, which could remain obscured when modeled by the more standard single time-dependent covariate approaches. We propose that understanding the nature and directionality of these interactions will help the biopharmaceutical industry in better estimating drug efficacy.