Modelling covariate adjusted mortality relative to a standard population

A study of long term survival of 1487 patients given an allogeneic bone marrow transplant for acute myelogenous leukaemia and 729 patients given a transplant for severe aplastic anaemia was conducted by the International Bone Marrow Transplant Registry. One aim of this study is to determine if the mortality rates of these patients return after some period of time to the same mortality rate as in the general population. To examine this question a model for the relative mortality of a bone marrow transplant patient relative to a matched individual in the general population is presented. This model allows for different relative mortality rates depending on the risk factors the patient may have. We discuss an estimation procedure for this model and construct a test that the mortality rate in the transplanted population is the same as in the reference population over a given time interval.