Dose as instrumental variable in exposure-safety analysis using count models

Confounding bias often occurs in the analysis of the exposure-safety relationship due to confounding factors that have impacts on both drug exposure and safety outcomes. Instrumental variable (IV) methods have been widely used to eliminate or to reduce the bias in observational studies in, for example, epidemiology. Recently applications of IV methods can also be found in clinical trials to deal with problems such as treatment non-compliance. IV methods have rarely been used in pharmacokinetic/pharmacodynamic analyses in clinical trials, although in a randomized trial with multiple dose levels dose may be a powerful IV. We consider modeling the relationship between pharmacokinetics as a measure of drug exposure and risk of adverse events with Poisson regression models and dose as an IV. We show that although IV methods for nonlinear models are in general complex, simple approaches are available for the combination of Poisson regression models and routinely used dose-exposure models. We propose two simple methods that are intuitive and easy to implement. Both methods consist of two stages with the first stage fitting the dose-exposure model; then the fitted model is used in fitting the Poisson regression model in two different ways. The properties of the two methods are compared under several practical scenarios with simulation. A numerical example is used to illustrate an application of the methods.