Statistical Methods for Estimating Within-Cluster Effects for Clustered Poisson Data

Clustered Poisson data frequently appear in medical research. Interest often focuses on examination of an exposure effect within clusters. The objective of this paper is to compare the performance of six methods for estimating the exposure effect for clustered Poisson data: 1) independent Poisson; 2) fixed cluster effects Poisson; 3) conditional likelihood Poisson estimation; 4) Generalized Estimating Equations (GEE); 5) random cluster effects Poisson; and 6) random cluster effects Poisson, with separate between- and within-cluster effects. Biases and standard errors of within- cluster exposure effects are compared across the six statistical methods considering constant or varying exposure ratio (number of exposed to unexposed subjects), constant or varying cluster sizes, different within-cluster exposure effect, different cluster variances, and number of clusters. Simulations and theoretical results show that exposure ratio is a key quantity. With constant exposure ratio designs, maximum likelihood estimates and asymptotic standard errors were obtained in closed form. All models, except GEE, give equivalent estimates and standard errors of the within-cluster  exposure effect. With varying exposure ratio designs, conditional likelihood and fixed cluster effects methods yield the same estimates and standard errors for the exposure effect. Results from the random cluster effects Poisson model with separate between- and within-cluster effects are very similar to those from fixed cluster effects Poisson and conditional Poisson methods. We applied the above approaches to birth cohort data, to analyze incidence of Respiratory Syncytial Virus (RSV) infection in young children in Indonesia.

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