Analysis of failure times for multiple infections following bone marrow transplantation: An application of the multiple failure time proportional hazards model

We report an application of the proportional hazards model for multiple failure times in a study arising from the Bone Marrow Transplant Database at the University of Minnesota. The study compared the risk of infections after transplantation for patients who received allogeneic bone marrow transplants from unrelated donors (URD) versus related donors (RD). In 249 patients there was a total of 365 infections in 2.5 years of follow-up. The multiple failure time model uses all the data and provides empirical estimates of standard errors that incorporate the within-person dependencies in the data. The estimate of relative risk associated with URD was 1.4 (naive 95 per cent confidence interval 1.14 to 1.73, empirical 1.08 to 1.79), compared to the estimate 1.6 (naive or empirical, 1.1 to 2.1) from the proportional hazards model on 165 first infections only. The multivariate model gives great flexibility in modelling, for example, in accommodating a separate base hazard function for each type of failure and in allowing analysis of intervals between infections as an alternative to analysis of time from a marker event, here transplantation.