Multivariate permutation test to compare survival curves for matched data

Background In the absence of randomization, the comparison of an experimental treatment with respect to the standard may be done based on a matched design. When there is a limited set of cases receiving the experimental treatment, matching of a proper set of controls in a non fixed proportion is convenient. Methods In order to deal with the highly stratified survival data generated by multiple matching, we extend the multivariate permutation testing approach, since standard nonparametric methods for the comparison of survival curves cannot be applied in this setting. Results We demonstrate the validity of the proposed method with simulations, and we illustrate its application to data from an observational study for the comparison of bone marrow transplantation and chemotherapy in the treatment of paediatric leukaemia. Conclusions The use of the multivariate permutation testing approach is recommended in the highly stratified context of survival matched data, especially when the proportional hazards assumption does not hold.