A Pairwise Likelihood Procedure for Analyzing Exchangeable Binary Data with Random Cluster Sizes

Abstract

For the exchangeable binary data with random cluster sizes, we use a pairwise likelihood procedure to give a set of approximately optimal unbiased estimating equations for estimating the mean and variance parameters. Theoretical results are obtained establishing the large sample properties of the solutions to the estimating equations. An application to a developmental toxicity study is given. Simulation results show that the pairwise likelihood procedure is valid and performs better than the GEE procedure for the exchangeable binary data.

Keywords:

• Exchangeable binary data
• Generalized estimating equation
• Pairwise likelihood

Mathematics Subject Classification:

• Primary 62H12
• Secondary 62P10

Acknowledgment

This research is supported in part by the National Natural Science Foundation of China (Grant Number 10701022).

Notes

GEE ⁽¹⁾: with Gaussian working matrices for higher moments and logistic models for mean and correlation.

 = ( ₁, ₂, ₁, ₂) ^T : the average of the 1,000 estimates ^p . T _p : times for which ^p  ≠ inΘ₀ based on all the 1,000 replications. T _i : times for which ⁽ⁱ⁾ ≠ inΘ₀ based on all the 1,000 replications, i = 1,2.

See Table 2 for the explanations of _i , _i , T _p , and T _i , i = 1, 2.