Predictive Modeling in Long-Term Care Insurance

Abstract

The accurate prediction of long-term care insurance (LTCI) mortality, lapse, and claim rates is essential when making informed pricing and risk management decisions. Unfortunately, academic literature on the subject is sparse and industry practice is limited by software and time constraints. In this article, we review current LTCI industry modeling methodology, which is typically Poisson regression with covariate banding/modification and stepwise variable selection. We test the claim that covariate banding improves predictive accuracy, examine the potential downfalls of stepwise selection, and contend that the assumptions required for Poisson regression are not appropriate for LTCI data. We propose several alternative models specifically tailored toward count responses with an excess of zeros and overdispersion. Using data from a large LTCI provider, we evaluate the predictive capacity of random forests and generalized linear and additive models with zero-inflated Poisson, negative binomial, and Tweedie errors. These alternatives are compared to previously developed Poisson regression models.Our study confirms that variable modification is unnecessary at best and automatic stepwise model selection is dangerous. After demonstrating severe overprediction of LTCI mortality and lapse rates under the Poisson assumption, we show that a Tweedie GLM enables much more accurate predictions. Our Tweedie regression models improve average predictive accuracy (measured by several prediction error statistics) over Poisson regression models by as much as four times for mortality rates and 17 times for lapse rates.

Application of Markov Model in Long-Term Care Insurance

“…There still have other methods to construct models for prediction in Long-term care insurance, such as Lally and Hartman [10] used data from a large LTCI provider, they constructed random forest models, GLM models, an additive model with zero-inflated Poisson, negative binomial, and Tweedie errors, and compared the predictive capacity.…”

Health Transition Probability and Long-Term Care Cost Estimation

“…Generalized regression uses multiple population characteristics and different models to fit transition probability, which is flexible in form and can better fit and smooth the solution process. In fact, there may be problems of inconsistency and subjectivity in variable selection and model setting, such as the Tweedie model [18], Gaussian model [19], and ordinal multicategorical model [20,21]. More importantly, due to the limited and detailed individual information available, the regression model has commonly been used to estimate one-period transition probability, assuming that the health states are unchanged to obtain the LTC cost.…”

The actuarial science editorship of the Accounting & Finance Review: some general considerations

“…Cyber risk (Egan et al, 2019;Eling, 2018) and the internet of things (with its major impact on the area of health) (Spender et al, 2019) can both be mentioned here. Similarly, not so recent techniques, such as predictive modeling, are being used more and more (again particularly in health) (Duncan, Loginov & Ludkovski, 2016;Lally & Hartman, 2016). Techniques such as machine learning have been used for quite traditional (and ever more relevant) topics, such as mortality forecasting models (Deprez, Shevchenko & Wüthrich, 2017).…”