We propose a joint model for binary and continuous responses using a latent variable for the binary response. The observed continuous response and the latent response are treated as correlated normals obeying a bivariate regression model. We develop an EM algorithm to find maximum likelihood estimates for the parameters. We perform the E-step analytically and use an iterative algorithm for the M-step.

The algorithm is applied to a prostate cancer clinical trial whose goal was to assess therapeutic effects of diethylstilbestrol (DES) in advanced cancer patients and to assess possible excess cardiovascular mortality. Therapeutic effects were measured as prostatic acid phosphatase (PAP) levels follow-up and whether the patient progressed to stage IV or died of cancer. The treatment reduced PAP levels but not the incidence of cancer mortality within a six-month time frame. Higher doses of DES were associated with increased risk of cardiovascular-related death.