Variance estimation for complex surveys using replication techniques

A simple method for comparing independent groups of clustered binary data with group-specific covariates is proposed. It is based on the concepts of design effect and effective sample size widely used in sample surveys, and assumes no specific models for the intracluster correlations. It can be implemented using any standard computer program for the analysis of independent binary data after a small amount of preprocessing. The method is applied to a variety of problems involving clustered binary data: testing homogeneity of proportions, estimating dose-response models and testing for trend in proportions, and performing the Mantel-Haenszel chi-squared test for independence in a series of 2 x 2 tables and estimating the common odds ratio and its variance. Illustrative applications of the method are also presented.

Missing data occur in survey research because an element in the target population is not included on the survey's sampling frame (noncoverage), because a sampled element does not participate in the survey (total nonresponse) and because a responding sampled element fails to provide acceptable responses to one or more of the survey items (item nonresponse). A variety of methods have been developed to attempt to compensate for missing survey data in a general purpose way that enables the survey's data file to be analysed without regard for the missing data. Weighting adjustments are often used to compensate for noncoverage and total nonresponse. Imputation methods that assign values for missing responses are used to compensate for item nonresponses. This paper describes the various weighting and imputation methods that have been developed, and discusses their benefits and limitations.