A semi-Markov model with pathologies for Long-Term Care Insurance

Guillaume Biessy (1, 2)

1 SCOR Global Life SE
2 LaMME - Laboratoire de Mathématiques et Modélisation d'Evry

Most Long-Term Care (LTC) Insurance products rely on definitions for functional disability based on the Activities of Daily Living (ADL). While functional disability may reflect the level of care required by the insured life, it is not on its own a good predictor of lifespan in LTC, which strongly depends on the underlying pathology responsible for disability. Indeed, cancer and respiratory diseases are associated with extremely short lifespan while dementia and neurological diseases make for much longer claims. Pathologies are therefore responsible for heterogeneity in the data, which makes estimation of mortality in LTC a difficult issue. As a consequence the associated literature is still scarce. In this paper, we study the mortality in LTC associated with 4 different groups of pathologies: cancer, dementia, neurological diseases and other causes based on data from a French LTC portfolio. We consider a semi-Markov framework, where mortality in LTC depends on both age at claim inception and time already spent in LTC. We first derive the incidence rate in LTC and mortality rate associated with each group of pathologies and for both males and females. To do so, we rely on local likelihood methods that we apply directly to transition intensities of the model. We then combine those transition intensities to get a second-step estimator of the overall mortality in LTC, which proves more accurate than a direct estimate regardless of the pathology. Finally our results indicates that the peak of mortality following entry in LTC observed in the data is mostly due to the cancer group.

Keywords: Long-Term Care Insurance; continuous time semi-Markov process; competing risks; local likelihood

Domains: Applications [stat.AP]; Santé publique et épidémiologie

Guillaume Biessy. A semi-Markov model with pathologies for Long-Term Care Insurance. 2016. ⟨hal-01356063⟩