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., PHREG 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.
Highlights
Epidemiological and medical studies frequently use count data in which exposed and unexposed incidence rates are compared
∗, days outside of the risk windows represent the control window. ∗∗, −2 log P L or −2 log CL. +, Cox,s stratified partial likelihood method fitted in SAS for both parametric and semiparametric models. ++, conditional Poisson likelihood regression fitted in SAS for the parametric model and in STATA for the semi-parametric model
∗, −2 log P L or −2 log CL. +, Cox’s stratified partial likelihood method fitted in SAS. ++, conditional Poisson likelihood regression fitted in SAS
Summary
Epidemiological and medical studies frequently use count data in which exposed and unexposed incidence rates are compared. Intercept parameters explaining each subject’s individual baseline risk for the event count of interest is not present in the likelihood (Farrington, 1995; Roy, et al, 2006) This results in a de facto adjustment for all subject-level risk factors and potential confounders (measured and not measured), allowing only within-subject comparisons of incidence rates between exposed and unexposed time intervals. SCCS is useful for controlling for confounding by indication, wherein the probability of exposure to vaccine is related to the subject-level risk of the outcome (Whitaker, et al, 2006) Another example of dependent count data is the matched cohort method, in which exposed subjects are matched to unexposed subjects on certain characteristics to reduce confounding effects. We will give examples of each study design, and finish with a discussion of implications of our findings
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