Interpreting Model Coefficients When the True Model Form Is Unknown

In this paper, we critically examine mathematical modeling. We outline the major assumptions required by modeling methods used in epidemiology and discuss in detail one fundamental assumption that is usually violated in epidemiologic studies: the assumption that the structural model form is correctly specified. We apply concepts from the econometrics literature to examine how epidemiologic inference may be affected when the structural model form is incorrectly specified. Because the structural model is almost always misspecified in practice, tests and confidence intervals for model coefficients do not refer to "true population parameters" in the ordinary sense. Rather, these statistics concern parameters that depend on features of study design, as well as the effects under study. In cohort studies analyzed with multiplicative rate models, model parameters are interpretable as approximations to log standardized rate ratios; unfortunately, such interpretations are not as accurate for other models and designs. We therefore conclude that model coefficients can serve as reasonable effect summaries in some, but not all, situations.