Estimating cohort health expectancies from cross-sectional surveys of disability

A life history can be regarded as a random process that evolves with age through various states of health before terminating with absorption into the state of death. Health expectancies are the occupation times of the non-absorbing states and their estimation is of interest. A continuing major problem has been the lack of satisfactory longitudinal data on which to base estimates and as a result standard inferential techniques may not be relevant. Supposing only cross-sectional data available, we propose a method that is generally applicable and first estimates a logistic parametrization of the probabilities of the various states. A large sample approximation is obtained for the distribution of age specific log (odds). Parameters are estimated by weighted least squares, and this in turn leads to estimates of cohort health expectancies. A result of Liang and Zeger is used to find standard errors. The method is illustrated by application to Australian data from the health surveys of 1981, 1988 and 1993.