Semiparametric analysis of case series data

The case series model for estimating the association between an age-dependent exposure and an outcome event requires information only on cases and implicitly adjusts for all age-independent multiplicative confounders, while allowing for an age-dependent base-line incidence. In the paper the model is presented in greater generality than hitherto, including more general discussion of its derivation, underlying assumptions, applicability, limitations and efficiency. A semiparametric version of the model is developed, in which the age-specific relative incidence is left unspecified. Modelling covariate effects and testing assumptions are discussed. The small sample performance of this model is studied in simulations. The methods are illustrated with several examples from epidemiology.