Pricing for life insurers is undergoing a period of great change, with increasing numbers of insurers moving to an approach combining better risk modelling (often involving Generalised Linear Models) and models of customer demand and retention. This approach, often referred to as price optimisation, is facilitated by our Radar software.

A key part of this approach for mortality or longevity-focused products is correct modelling of the underlying mortality risk. Assumption-setting for health-related products, whether critical illness, enhanced annuities or long-term care, has always been difficult and most insurers have found the problem insurmountable without technical support from reinsurers. 

For simple products such as term insurance, the relative mortality impacts of policyholder characteristics such as smoking status and body-mass index (BMI) can have a significant effect on premium rates, but reliable and consistent information on the effect of such rating factors across a full range of diseases is hard to obtain.

Setting longevity improvement assumptions is problematic, with many firms doing little more than joining the output from extrapolative models to somewhat arbitrary long-term improvement endpoints. Stresses to the improvement assumptions may be even less meaningful, with extensive stochastic ‘number crunching’ of the last 40-50 years’ population data providing results which, while mathematically interesting, may bear no relation to the biological or medical plausibility of mortality variation in the near future.

PulseModel is a multi-state disease-based morbidity and mortality model that Willis Towers Watson has developed to assist firms with these challenges. It models mortality in a ‘bottom-up’ way according to the passage from a starting state (healthy or otherwise) through one of a number of disease groups, then through possible comorbidities, to eventual death. The transition probabilities between these states are modified by risk factors such as duration since diagnosis, BMI and socio-economic status as well as various medical markers (where available in policy data). A panel of medical experts provide the parameterisation in respect of improvements relating to their specialist fields.

Business applications: How PulseModel can be used in practice

PulseModel is ideally suited to help businesses across a range of areas:

Segmentation – The risk factor information inherent in the model’s parameters allows firms to consider greater segmentation on standard (non-medical) business – for instance, regarding the mortality effect of BMI, smoking status and socio-economic level. Evidence shows that firms who introduce segmentation can generally reap material ‘first mover’ benefits. Introducing segmentation in respect of major risk factors such as BMI could increase the value of new business by of the order of 1%. 

Medical underwriting – PulseModel provides pricing assumptions for any business with benefits or premium payment contingent on specific medical events. There should also be scope to reduce the cost of medical underwriting (to reduce the involvement of medical professionals). A particular advantage of our approach is that results are provided as a bespoke mortality curve for the policyholder in question, avoiding the problem of underwriters providing a broad ‘+50%’ recommendation leaving the level and shape of the mortality curve to which it should apply completely unresolved. 

As an example of the mortality impact of allowing properly for segmentation via improved medical underwriting, Figure 1 below shows the effects on life expectancy of varying sample policyholder characteristics. Starting from the base case of a healthy 50-year-old male non-smoker, we can model the mortality of his ‘twin’ who is identical in all respects but is a regular smoker. Just the change in smoking characteristics reduces life expectancy by 4.9 years. We can then model the effect if this 50-year-old smoker had type II diabetes: this represents a further reduction of 4.0 years, a total of 8.9 years compared with the healthy non-smoker. Finally, we can see the effect of high blood sugar, which implies a further 2.2 years reduction in life expectancy. 

Figure 1. Effects on life expectancy of varying sample policyholder characteristics

Effects on life expectancy of varying sample policyholder characteristics
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Risk management

 The model can help in various ways:

  • Are premiums too low for particular segments?  The model can help a firm’s second line of defence establish whether the lack of segmentation may lead to a new business mix risk. 
  • With changing levels of medical underwriting in a market, what is the anti-selection risk?
  • Analysis of longevity scenarios to allow improved understanding of longevity risk. For instance we can use PulseModel to examine the effects of a ‘diabetes explosion’, with diabetes incidence rates worsening at twice the best estimate rate. If we take a population of healthy 50-year-old males as our base population (as per the previous example), the diabetes scenario reduces life expectancy by 1.2 years. We can also explore the effects of major medical advances, for instance a ‘cure for cancer’. If we halve cancer mortality rates over the next 10 years, we increase life expectancy by 1.4 years.

These applications support both a firm’s ‘first line of defence’ and the risk management activities of its second line by providing methodological independence and ensuring full independence from the techniques used by the first line both for pricing and the setting of longevity stresses. 

These are just some examples of business applications; others include product innovation, reinsurance management, more robust improvement assumptions in the face of internal and regulatory challenge, and improved consistency of mortality modelling in groups and between different types of assumption (in particular, best estimate and stress). 

Since its release earlier in 2016, PulseModel has been used on longevity risk projects and advising on the expected age and gender structure of longevity improvements, in addition to more direct support on a more robust assumption-setting process for mortality improvements.

Parameterisation

The UK version of PulseModel is parameterised from a large database of around six million UK primary care records (we are working on parallel versions of PulseModel using data sources specific to major insurance markets).

This database provides the transition probabilities for movements from one state in the model to another – for instance, the probability of moving from healthy to diabetes, or from lung cancer to death. These ‘raw’ transition probabilities are then modelled using generalised linear models to smooth out random noise (in particular, in the age and duration curves), and to properly quantify the effect of the various risk factors.

The risk factors include obvious aspects such as age, sex, and duration since diagnosis, but also smoker status, BMI and socio-economic quintile. There are also a number of more specific medical markers used for some of the transitions – for instance, for transitions involving diabetes, measures of blood glucose (via glycosylated haemoglobin HbA1c) are very predictive.

Figure 2 provides some typical results relating to the effect of risk factors on some of the transitions modelled.

Figure 2. Examples of parameter effects

Examples of parameter effects
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Model structure

Figure 3 shows the structure of the multi-state model, with simplification for clarity (the diagram omits comorbidities).

Lives start either as healthy, or with a known major disease. In any year, lives can progress towards the right: a healthy life may pass into one of the disease states, or a diseased life may die. Note that lives may also progress directly from healthy to death in a year (this is common in particular for cardiovascular events), although this step is not shown in the diagram for the sake of simplicity.

Although there is no explicit passage from right to left, so a life with a disease cannot revert to fully healthy, the idea of healing over time is allowed for in the model via a duration factor. This measures duration since diagnosis and, for most diseases, the probability of death decreases materially over the first few years since diagnosis. 

The model runs a large number of simulations through all possible paths, applying a Monte Carlo process rather than trying to force a mathematical solution. The mean of the simulations gives a bespoke mortality projection for each policyholder. 

Figure 3. Multi-state model structure

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Improvements

Medical experts provide advice on the future improvement rates applying to the transitions that are reasonable to assume in their specialist fields, as well as feasible stresses to those improvements. These improvement rates cover both changes in disease incidence (that is, the trend moving from healthy to the disease group in question) and changes in mortality given a particular disease.

Figure 4 gives an example of how the various possible inputs regarding expected annual morbidity and mortality improvements can be combined in the modelling framework (the numbers shown are illustrative only). The parameterisation of ‘base’ morbidity and mortality provides a valid structure to weight these improvement assumptions (and this weighting can be portfolio-specific, allowing the quantification of bespoke portfolio improvement assumptions).

Figure 4. Annual mortality and morbidity improvements by disease (illustrative)

Annual mortality and morbidity improvements by disease (illustrative)
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As an example of the thought process being applied here, let’s consider stroke. Our stroke expert (a professor of stroke medicine) has quantified recent changes in stroke mortality and identified the underlying drivers behind those improvements. Most improvements have related to organisational changes such as the establishment of dedicated stroke units in many hospitals, with some improvement contributed by treatments such as thrombolysis and thrombectomies. Consideration of what’s happening within the health service, the impact of any emerging medical treatments and pharmaceutical developments, and the effect of smoking and other lifestyle trends, leads to a sensible medically-reasoned estimate of how stroke mortality will move over the next 10 years or so.

Our advisors also provide opinions on biologically and medically plausible stresses to these improvements, allowing the model to provide meaningful longevity improvement stresses that reflect current reality. The nature of the model also means these stresses can be clearly communicated to senior life insurance managers.

Conclusion

Despite the fundamental importance of mortality to many insurance products, there has been relatively little effort to model the underlying biological process. Most of the mortality modelling advances of the last 10 years have involved either multifactorial analysis of mortality at a best estimate level, allowing a better understanding of the effect of factors such as socio-economic status on the mortality ‘end result’, or complex stochastic modelling of mortality, allowing better understanding of the variability of historical mortality rates.

PulseModel enables an entirely different approach: to explicitly model the underlying process of mortality, which is a disease-based process, doing so through the use of medical data for the historical parameterisation and the incorporation of medical experts’ views for the ‘future’ parameterisation of improvements. This type of modelling has a number of uses across pricing, risk management and product design, and is a valuable adjunct to other types of mortality model.