Subnational old-age mortality modeling: Accounting for underreporting in a Bayesian framework

Qian Lu, Katja Hanewald, Andres M. Villegas and Xiaojun Wang

Abstract: Accurate old-age mortality projections for subnational areas are important for assessing health outcomes and valuing pension liabilities. However, subnational mortality data often face small sample sizes at older ages. In some countries, the underreporting of deaths and population num- bers poses additional problems. We propose a new Bayesian framework for old-age mortality that allows for death underreporting by introducing a reporting probability, which is defined as the ratio of reported deaths to real deaths and uses informative priors derived from demographic death distribution methods. We show that the proposed modeling framework works well for province-level old-age mortality data (ages 60–99) in China over 1982–2010. Compared to a more conventional framework that assumes the reported data are accurate and uses reported mortality data directly, the proposed framework provides a better fit, with a lower deviance information criterion. The proposed framework generates a reasonable mortality curvature and coherent forecasts for subpopulations with sparse or incomplete mortality data.

Keywords: Old-age mortality, Subnational modeling, Bayesian framework, Death underreporting