Properties of 2 Counterfactual Effect Definitions of a Point Exposure

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Abstract
As recognized for more than 2 decades, the way to define effects of an exposure may be unclear if the effects are conditional on occurrence of prior events. Since age-specific rates are inherently conditional on survival to the age for which rates are calculated, age-specific rate ratios may be misleading. We consider this problem in the context of a point exposure and an unmeasured risk factor that is independent of the exposure, together with potential outcome models and associated counterfactual effect definitions. The methods apply to a recurring exposure that "tracks" over time, as well as to more complicated situations (although additional issues may then arise). We identify and evaluate 2 seemingly-natural ways that the population effects of a point exposure might be defined. At least one definition of the population effects of a point exposure is identifiable, while another natural definition is not identifiable. We describe possible implications of these definitions for the distortion of time-specific rate ratios that can occur with passage of time. We discuss interpretation of effects for each definition, and how the definitions are related to selection bias as recently defined by Hernán et al (Epidemiology. 2004;15:615-625). We present implications for study design, and make several recommendations. Problems may be reduced or avoided by starting follow-up before onset of exposure and by using survival curves to compare exposed with unexposed.