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The shape of the relationship between a continuous exposure variable and abinary disease variable is often central to epidemiologic investigations. Thispaper investigates a number of issues surrounding inference and the shape ofthe relationship. Presuming that the relationship can be expressed in terms ofregression coefficients and a shape parameter, we investigate how well theshape can be inferred in settings which might typify epidemiologicinvestigations and risk assessment. We also consider a suitable definition ofthe median effect of exposure, and investigate how precisely this can beinferred. This is done both in the case of using a model acknowledginguncertainty about the shape parameter and in the case of ignoring thisuncertainty and using a two-step method, where in step one we transform thepredictor and in step two we fit a simple linear model with transformedpredictor. All these investigations require a family of exposure-diseaserelationships indexed by a shape parameter. For this purpose, we employ afamily based on the Box-Cox transformation.

Logistic Box-Cox Regression to Assess the Shape and Median Effect under Uncertainty about Model Specification