Modelling Income Protection Claim Termination Rates by Cause of Sickness I: Recoveries

Abstract

In this paper we present methods and results for the estimation and modelling of the recovery intensity for Income Protection (IP) insurance claims, allowing for different causes of claim. We use UK data supplied by the Continuous Mortality Investigation relating to claims paid in the years 1975 to 2002, inclusive. Each claim is classified by one of 70 possible causes according to ICD8.We group causes where appropriate, and then use the Cox model and generalised linear models to model the recovery intensity.In two subsequent papers we complete our modelling of IP claim termination rates by discussing the modelling of the mortality of IP claimants.There are two main reasons why it is useful to incorporate cause of sickness in the modelling of IP claim terminations:(i) The cause of sickness will be known to the insurer for a claim in the course of payment. A reserve can be set more accurately for such a claim if a model of the termination rates appropriate for this cause is available.(ii) Different causes of claim will become more or less significant over time. For example, tuberculosis may have been an important cause of sickness in the past, but is likely to be far less significant now; the swine flu pandemic starting in 2009 is likely to have a significant effect on observed aggregate claim termination rates, skewing them towards higher rates at shorter durations. Information about trends in morbidity, together with a model of termination rates by cause of claim, allows future aggregate claim termination rates to be predicted more accurately, reserves to be set at more appropriate levels and policies to be priced more accurately.One of the covariates included in our models for recovery intensities is Calendar Year. Aggregate recovery intensities have been decreasing over the period considered, 1975 to 2002, and this is generally reflected in the models for recovery intensities by cause of sickness. However, when these intensities are projected for years beyond 2002, the results are not always plausible.

Survival Analysis of Left Truncated Income Protection Insurance Data

“…This IPI data comprise 70 different causes of sickness. Ling et al (2010) have previously conducted some analysis on the recovery intensities using this same data set and pointed out that cause of sickness is an important source of heterogeneity among IPI claimants, and so suggested estimating the recovery intensities by cause of sickness. We have chosen cause of claim 21 (benign neoplasms and neoplasms of unspecified nature) because of its high claim volume relative to other causes as an illustration to demonstrate the impact of ignoring the left truncation in the data when modelling, and to report our conditional mixture model based survival analyses.…”

“…This model assumed that there was only one sick state to represent all causes of sickness, which means all the claims in the same portfolio will be subject to the same termination assumption regardless of their different causes of sickness. Ling et al (2010) extended the model from CMI 12 and estimated recovery intensities by cause of sickness using IPI data provided by the CMI. The recovery intensities for each cause of sickness were estimated using the Cox proportional hazards regression model (Cox, 1972) and generalised linear models.…”

“…The recovery intensities for each cause of sickness were estimated using the Cox proportional hazards regression model (Cox, 1972) and generalised linear models. The graduation formulae for the recovery intensity presented in Ling et al (2010) modelled the impact of age at the date of falling sick, duration of disability and the deferred period on the recovery intensity.…”

On the prediction of claim duration for income protection insurance policyholders

“…While we have some understanding of the level of claim termination rates from existing industry tables and other industry level studies (e.g. CMI 12 1991 andLing et al 2010), this paper will provide a new outlook on IPI data classifications formulated using modern statistical methods that have not previously been used to advance our understanding of this area in Australia. We hope that this paper will appeal not just to researchers but also to actuarial practitioners in the insurance industry.…”

Modelling income protection claim termination rates by cause of sickness, Parts I and II – CORRIGENDUM

“…In a series of three papers, Ling et al . (2009a, 2009b & 2009c), the authors set out formulae for the calculation of the recovery and mortality intensities for Income Protection Insurance (IPI) claimants. These formulae, which allow for duration of sickness, age, cause of claim and other factors, are, unsurprisingly, complex.…”