Dunnett-type inference in the frailty Cox model with covariates

A frequent objective in medical research is the investigation of differences in patient survival between several experimental treatments and one standard treatment. In order to assess these differences statistically, we have to apply adjustments for multiple comparisons to prevent an increased number of false-positive findings. The most prominent procedure of this type is the Bonferroni correction, which maintains the error level but leads to conservative results. On the basis of a general statistical framework for simultaneous inference, we propose a new statistical procedure for many-to-one comparisons of treatments with adjustment for covariates for clustered survival data modeled by a frailty Cox model. In contrast to the Bonferroni method, dependencies between estimated effects are taken into account. The resulting simultaneous confidence intervals for the hazard ratios of the experimental treatments compared with a control can be interpreted in terms of both statistical significance and clinical importance. The quality of the new procedure is judged by the coverage probability for the simultaneous confidence intervals. Simulation results show an acceptable performance in balanced and various unbalanced designs. The practical merits are demonstrated by a reanalysis of a chronic myelogeneous leukemia clinical trial. The procedure presented here works well for multiple comparisons with a control with adjustment for covariates for survival data from multicenter clinical trials.