Analysis of ordinal data in a study of endometrial cancer under a matched pairs case-control design

While estimating odds ratios (ORs) in the context of dose levels of conjugated oestrogen exposure and development of endometrial cancer, the categories formed by the levels of the exposure are ordinal in nature. In the literature, the binary logistic model is used for estimating OR for each category relative to the baseline category. We describe the use of two ordinal logistic models, the cumulative logit and continuation-ratio logit models, to estimate the ORs for the matched pairs case-control data set of the Los Angeles endometrial cancer study. A test for equality of the cumulative ORs across the exposure levels is proposed. The test statistic follows asymptotically the chi-square distribution.