Forecasting Hospitalization Trends in Europe

This presentation explores an application of the Lee-Carter model, originally developed for mortality projections, to analyze and forecast hospitalization trends relevant to hospital cash insurance products in Europe.

Hospital cash insurance provides policyholders with a fixed cash benefit for each day of hospitalization. Accurate projections of hospitalization incidence and average length of stay are therefore essential for pricing and risk assessment. Using publicly available European hospitalization data, we demonstrate how the Lee-Carter model can be adapted to capture patterns in hospitalization data.

The rationale for employing Lee-Carter lies in similarities between hospitalization rates and mortality patterns: both exhibit strong age dependencies and temporal trends, which can be effectively decomposed into age and period effects. Hospitalization data in Europe shows distinct age-related phenomena, including elevated rates among newborns, temporary increases related to childbirth, and a general rise with advancing age.

The model’s bilinear structure enables decomposition of hospitalization rates into age-specific and time-specific components, mirroring established mortality analysis techniques. Its flexibility and compatibility with time-series forecasting methods (e.g., ARIMA models) make it particularly suitable for this purpose.

Our study focuses on 11 European countries, with Italy as an illustrative example. Data are split into training and test periods, with separate models estimated by gender. The performance of multiple Lee-Carter model variants (Poisson, Negative Binomial, and the original specification) is evaluated under two approaches: direct modelling of hospital days and a decomposed approach using separate models for incidence rates and length of stay. The results indicate a strong fit and low, randomly scattered forecast errors, confirming robustness and practical applicability. Estimated and projected time trends and their associated uncertainty are presented for 11 European countries.

In conclusion, the Lee-Carter model offers actuaries a powerful, data-driven framework for projecting hospitalization risk in hospital cash portfolios. The approach is readily extendable to other datasets, providing a solid foundation for designing and managing hospital cash products across life and health insurers.