In this work, we consider semiparametric estimation of quality adjusted lifetime (QAL) distribution using Cox proportional hazards model for the sojourn time in each health state. The regression coefficients are estimated by maximizing the corresponding partial likelihood and the baseline cumulative hazards are estimated by using the method of Breslow (Biometrics 30:89-99, 1974). The estimate of QAL distribution is obtained by using these estimates in the theoretical expression of QAL distribution. The asymptotic normality of the proposed estimator is established. The performance of the proposed estimator is studied using Monte Carlo simulation. Areal data example of the Stanford Heart Transplant Program is used to illustrate the proposed method. Extension to a general model is also discussed and illustrated with an analysis of International Breast Cancer Study Group (IBCSG) Trial V data.
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