Nonparametric estimation of quality adjusted lifetime distribution in a simple illness-death model

Abstract

In this work, we consider the nonparametric estimation of quality adjusted lifetime (QAL) distribution in a simple illness-death model. We first derive the expression of QAL distribution in terms of the distribution of sojourn time in each health state. Next we substitute the estimate of sojourn time distributions in the expression of QAL distribution to obtain its estimate. Consistency and asymptotic normality of the proposed nonparametric estimator are established. Estimation in the presence of some missing data on the transition time to illness is also discussed. We conduct a simulation study to investigate the performance of the proposed estimator. For illustration, we analyse a data set of the Stanford Heart Transplant program. Extension to multistate progressive model is discussed along with an analysis of International Breast Cancer Study Group (IBCSG) Trial V data.

Keywords:

• consistency
• EM algorithm
• Gaussian process
• quality adjusted lifetime
• Illness-death model
• Kaplan–Meier estimate
• weak convergence

AMS Subject Classification (2000): :

• 62N02
• 62G05

Acknowledgements

The authors thank two anonymous referees for helpful comments. The authors would also like to thank the International Breast Cancer Study Group for providing the data used in Section 7.