Analyzing multiply matched cohort studies with two different comparison groups: application to pregnancy rates among HIV+ women

We develop a new statistical method to analyze multiply matched cohort studies with two different comparison groups. We employ a linear-logistic model to describe the underlying log-odds ratios and use a conditional likelihood approach to conduct inference. Under the assumption of homogeneous log-odds ratios, we provide methods to construct both asymptotic and exact confidence regions of the two log-odds ratios in a simple case. We propose a score test to evaluate the assumption of homogeneous log-odds ratios across strata. While our methods are general, we develop them around a specific application, namely, the study of pregnancy rates in HIV-infected women. Our analyses suggest that HIV infection is associated with a decrease in pregnancy rates and that this decrease in fertility becomes significant after accounting for illicit drug use.