Cox proportional hazards models with frailty for negatively correlated employment processes

In promotion discrimination cases, individuals affected by discrimination may decide to retire earlier than otherwise. Two Cox proportional hazards models are used to describe the promotion process from non-retired employees and the retirement process, respectively. To account for a potential negative correlation between the two outcomes, promotion and retirement, frailty terms are introduced. Model diagnoses in the presence of unobserved frailty terms are difficult. Therefore, the robustness of the parameter estimates to the fitting of an unnecessary frailty or a frailty distribution or form different from the underlying one is examined. The data from a reverse discrimination case, Alexanderv.Milwaukee, are analyzed. The original finding of liability relying on a statistically significant coefficient for membership in the legally protected group (White-male) is shown to be robust to several choices of the frailty model. This provides further support for the court’s decision.