Modeling Nonlinear Dose-Response Functions: Regression, Simulation, and Causal Networks

Cox Jr., Louis Anthony

Recent advances in understanding of biological mechanisms and adverse outcome pathways for many exposure-related diseases show that certain common mechanisms involve thresholds and nonlinearities in biological exposure concentration-response (C-R) functions. These range from ultrasensitive molecular switches in signaling pathways, to assembly and activation of inflammasomes, to rupture of lysosomes and pyroptosis of cells. Realistic dose-response modeling and risk analysis must confront the reality of nonlinear C-R functions. This chapter reviews several challenges for traditional statistical regression modeling of C-R functions with thresholds and nonlinearities, together with methods for overcoming them. As mentioned in Chap. 10.1007/978-3-030-57358-4_1, statistically significantly positive exposure-response regression coefficients can arise from many non-causal sources such as model specification errors, incompletely controlled confounding, exposure estimation errors, attribution of interactions to factors, associations among explanatory variables, or coincident historical trends. This chapter discusses and illustrates these sources of positive C-R regression coefficients, explaining why the unadjusted regression coefficients do not necessarily predict how or whether reducing exposure would reduce risk. It discusses statistical options for controlling for such threats, and proposes that causal Bayesian networks and dynamic simulation models can be valuable complements to nonparametric regression modeling for assessing causally interpretable nonlinear C-R functions and understanding how time patterns of exposures affect risk. These approaches are promising for extending the great advances made in statistical C-R modeling methods in recent decades to clarify how to design regulations that are more causally effective in protecting human health.