Analysis Of A Case-Control Data With Two-Stage Cluster Sampling Of Controls

This paper discusses the analysis of case-control data which comes from a com-piex sampling. We employ Logistic regression model in the analysis and get the estimator of the relative risks.Firstly, we give an effective sampling design: a simple random case sample with replacement is drawn out of all cases; the control sample is drawn out of all controls with two-stage cluster sampling.The sampling design of controls is complicated: in the first stage, all controls are divided into M clusters and a sample of size m is drawn; in the second stage, each selected cluster is stratified by the confounding factors, then we give the sample of size in each stratum to make sure a frequence matching of case to control.Secondly, we give the likelihood function based on the proposed sampling design and a statistical inference method of the obtained case-control data. The MLE of regression parameter and a test of the model's significance are given.