ABSTRACT
In a randomized clinical trial the mean response difference between treatment groups is an unbiased estimate for the causal treatment effect, since potential confounding factors between the treatment and response are eliminated by randomization. However, it is more complex to determine exposure-response relationships since drug exposure, e.g., drug concentration, is generally not controlled even in a randomized clinical trial and is often affected by confounding factors. The Food and Drug Administration (FDA) has issued a technical document for exposure-response analysis (FDA, 2003), with an emphasis on the importance of dealing with confounding bias. The focus of causal effect determination is to eliminate or reduce the bias. Recent statistical developments in causal effect estimation make available several approaches for determining causal effects in exposure-response relationships. See, for example, Hernan and Robins (2015). This chapter introduces relevant current developments and discusses potential applications of classical approaches and recent technical advances in determining causal effects in exposure-response relationships. The scope of this chapter extends to ER modeling in a wide range of situations, in particular, the analysis of observational studies where the concept of exposure is very general and may refer to PK exposure, dose level, or different treatments. An attempt is also made to unify approaches in PKPD modeling and modeling of observational data. Simulated data are also used in examples, since one can assess the bias and performance of different procedures only when one knows the true data generating model. With the general definition of exposure, we will consider causal effect estimation in a general ER model. Our interest may be in parameter estimates in a marginal model that shows the average response for a given exposure level or a model including covariates to describe individual responses with certain covariates. Although in most cases one can reconstruct the former with the latter (Section 9.1), it may be more appropriate to estimate the former directly, especially in the presence of confounders. In this chapter we always assume the stable unit treatment value assumption (Hernan and Robins, 2015), that is, the exposure
ical exposures and denote it di, while for continuous one, we consider it as concentration and denote it ci.
