Restricted Mean Life with Adjustment for Covariates

Abstract Although the mean is the most widely used measure of location in comparing two distributions, its use is essentially precluded in the presence of substantial censoring, typical in survival analysis of medical therapies. To accommodate censoring, Irwin (1949) proposed estimation of the expectation of life restricted to a time T, using the actuarial estimator of the survival function. In this article we examine the restricted mean as an index for comparing survival in two groups and then extend the method to incorporate covariates into the analysis. For this purpose it is convenient to depart slightly from the actuarial approach and to consider piecewise exponential models. Asymptotic properties are explored, and the assumption of piecewise exponentiality is shown to be rather mild, as departures from the model have a relatively small effect on estimation of the restricted mean. The methodology is illustrated using published data from a study conducted by the Radiation Therapy Oncology Group (RTOG) in cancer of the mouth and throat, and the results are compared with those obtained from analysis based on the Cox (1972) regression model.