3. A New Approach to Estimating Life Tables with Covariates and Constructing Interval Estimates of Life Table Quantities

Abstract

Extant approaches to constructing life tables generally rely on the use of population data, and differences between groups defined by discrete characteristics are examined by disaggregating the data before estimation. When sample data are used, few researchers have attempted to include covariates directly in the process of estimation, and fewer still have attempted to construct interval estimates for state expectancies when covariates are used. In this paper, we present a Bayesian approach that is useful for producing interval estimates for single-decrement, multiple-decrement, and multistate life tables. The method involves (1) estimating a hazard or survival model using Bayesian Markov chain Monte Carlo (MCMC) methods to produce a sample from the posterior distribution for the parameters of the model; (2) generating distributions of transition probabilities for selected values of covariates using the sample of model parameters; (3) using these distributions of transition probabilities as inputs for life table construction; and (4) summarizing the distribution of life table quantities. We illustrate the method on data simulated from the Berkeley Mortality Database, data from the National Health and Nutrition Examination Survey (and follow-ups), and data from the National Long Term Care Survey, and we show how the results can be used for hypothesis testing.

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