Addressing Causality and Homogeneity Assumptions in Exposure-Response Analyses

Exposure-response, or pharmacokinetic-pharmacodynamic (PKPD), analyses support many drug development decisions. It is typically applied without assessment of causality and homogeneity, where the latter refers to the assumption that the reason for variability in exposure is unimportant for the impact on response. Randomized dose is the ideal variable for instrumental variable (IV) analysis that can help determine causal effects. In this work, we present adaptations of two standard IV models, predictor substitution (PS) and control function (CF), to repeated-measures analyses. We compare these to PKPD (PKPDC) models, without (with) correlations between PK and PD random effects, and to a new, partitioned effects (PE), model that allows separate PD relations for dose, covariate, and random effect-driven variability in exposure. Six scenarios simulate situations: (i) without any confounding, (ii) with three different types of confounding, generated through shared underlying variables (protein binding, disease severity, or renal function) between PK and PD, (iii) of an unmeasured active metabolite responsible for driving the response, and (iv) reversed causality. In all but the base case, the PKPD model provided biased parameter estimates that led to inappropriate dose adjustments for response-, concentrations-, or covariate-based dosing. The other models provided adequate estimates for a majority of the scenarios, but only the PE model provided for all scenarios. The PE model also formed the basis for adequate individualization based on concentration or response and can, like CF and PS, be used based on both single and repeated measures.