Duration time models often should include correlated failure times, due to clustered data. These random effects hierarchical models sometimes are called "frailty models" when used for survival analyses. The data analyzed here involve such correlations because patient level outcomes (the times until graft failure following kidney transplantation) are observed, but patients are clustered in different transplant centers. We describe fitting such models by combining two kinds of software, one for parametric survival regression models, and the other for doing Poisson regression in a hierarchical setting. The latter is implemented by using PRIMM (Poisson Regression and Interactive Multilevel Modeling) methods and software (Christiansen & Morris, 1994a). An illustrative example for profiling data is included with k = 11 kidney transplant centers and N = 412 patients.