The analysis of stratified multiple responses

Surveys often contain qualitative variables for which respondents may select any number of the outcome categories. For instance, for the question "What type of contraception have you used?" with possible responses (oral, condom, lubricated condom, spermicide, and diaphragm), respondents would be instructed to select as many of the outcomes that apply. This situation is known as multiple responses. When the data includes stratification variables, we discuss two approaches: (1) the "GEE" approach which uses logit models directly applying the generalized estimating equations (GEE) method (Liang and Zeger, 1986); and (2) the "GMH" approach which extends the generalized Mantel-Haenszel type estimators (Greenland, 1989) to make inferences across multiple responses. These approaches can also be used for data with dependent observations across strata.