  We propose and study a fully efficient method to estimate associations of an
exposure with disease incidence when both, incident cases and prevalent cases,
i.e. individuals who were diagnosed with the disease at some prior time point
and are alive at the time of sampling, are included in a case-control study. We
extend the exponential tilting model for the relationship between exposure and
case status to accommodate two case groups, and correct for the survival bias
in the prevalent cases through a tilting term that depends on the parametric
distribution of the backward time, i.e. the time from disease diagnosis to
study enrollment. We construct an empirical likelihood that also incorporates
the observed backward times for prevalent cases, obtain efficient estimates of
odds ratio parameters that relate exposure to disease incidence and propose a
likelihood ratio test for model parameters that has a standard chi-squared
distribution. We quantify the changes in efficiency of association parameters
when incident cases are supplemented with, or replaced by, prevalent cases in
simulations. We illustrate our methods by estimating associations of single
nucleotide polymorphisms (SNPs) with breast cancer incidence in a sample of
controls and incident and prevalent cases from the U.S. Radiologic
Technologists Health Study.
