Time to pregnancy, the number of menstrual cycles it takes a couple to conceive, and various covariates have been collected among couples ultimately achieving conception. To assess the influence of the covariates, we constructed a discrete survival model that allows time-dependent covariates. A random effect was included to account for unobserved heterogeneity. The collected waiting times are obtained through retrospective ascertainment and are analyzed as truncated data. Maximum likelihood estimation was implemented by Fisher scoring through iteratively reweighted least squares.