Fitting Parametric and Semi-parametric Conditional Poisson Regression Models with Cox’s Partial Likelihood in Self-controlled Case Series and Matched Cohort Studies

Abstract

The self-controlled case series (SCCS) and the matched cohort are two frequently used study designs to adjust for known and unknown confounding effects in epidemiological studies. Count data arising from these two designs may not be independent. While conditional Poisson regression models have been used to take into account the dependence of such data, these models have not been available in some standard statistical software packages (e.g., SAS). This article demonstrates 1) the relationship of the likelihood function and parameter estimation between the conditional Poisson regression models and Cox's proportional hazard models in SCCS and matched cohort studies; 2) that it is possible to fit conditional Poisson regression models with procedures (e.g., \it {PHREG} \rm in SAS) using Cox's partial likelihood model. We tested both conditional Poisson likelihood and Cox's partial likelihood models on data from studies using either SCCS or a matched cohort design. For the SCCS study, we fitted both parametric and semi-parametric models to model age effects, and described a simple way to apply the parametric and complex semi-parametric analysis to case series data.