Estimation and Bias Adjustment of Regional Mortality Rates with Incomplete Information—The Case of German Federal States

Source abstract

Reliable regional mortality rates are crucial for public health monitoring and planning. However, their estimation is often complicated by data limitations, with data being published only in broad age groups or affected by systematic errors. This is particularly relevant in intercensal periods, when population estimates may increasingly diverge from the true population structure. Using the German federal states as a case study, we develop and evaluate models for estimating and nowcasting age-, sex-, and nationality-specific rates under the outlined data issues. The analysis covers 1995–2023 and accounts for heterogeneous data availability, changing age groups, missing regional information on sex and nationality in recent years, and census-related revisions of population estimates. We first compare negative binomial regression models of increasing complexity. We then propose a state-specific generalized additive model based on a penalized splines framework, using national mortality schedules as a reference and explicitly modeling deviations associated with sex, nationality, calendar time, and time since the last population revision. The final model substantially outperforms the directly specified regression models based on in-sample, semi- and full-out-of-sample prediction compared with unadjusted regional estimates and national reference rates. The approach produces plausible, bias-adjusted mortality schedules despite limited regional data and can be used both to revise historical estimates and to nowcast mortality during intercensal periods. Although developed for Germany, the framework is applicable to other countries and small-area settings with incomplete or error-prone demographic data.