Angus Smith Macdonald

Longevity in the 21st Century

The main objective of this paper is to offer a detailed analysis of mortality change in the United Kingdom at the beginning the 21st century. Starting from an exploration of 20th century mortality trends, focusing in particular on the 1990s, underlying forces driving trends in longevity are discussed. These include the ‘cohort effect’ and the ‘ageing of mortality improvement’. International mortality statistics and trends are also analysed. The pace of medical advances is discussed, with specific focus on research into the ageing process and a potential treatment for cardiovascular disease. The paper also discusses the potential threat from infectious diseases.

Sensitivity of the impact of geological uncertainty on production from faulted and unfaulted shallow-marine oil reservoirs: objectives and methods

Estimates of recovery from oil fields are often found to be significantly in error, and the multidisciplinary SAIGUP modelling project has focused on the problem by assessing the influence of geological factors on production in a large suite of synthetic shallow-marine reservoir models. Over 400 progradational shallow-marine reservoirs, ranging from comparatively simple, parallel, wave-dominated shorelines through to laterally heterogeneous, lobate, river-dominated systems with abundant low-angle clinoforms, were generated as a function of sedimentological input conditioned to natural data. These sedimentological models were combined with structural models sharing a common overall form but consisting of three different fault systems with variable fault density and fault permeability characteristics and a common unfaulted end-member. Different sets of relative permeability functions applied on a facies-by-facies basis were calculated as a function of different lamina-scale properties and upscaling algorithms to establish the uncertainty in production introduced through the upscaling process. Different fault-related upscaling assumptions were also included in some models. A waterflood production mechanism was simulated using up to five different sets of well locations, resulting in simulated production behaviour for over 35 000 full-field reservoir models. The model reservoirs are typical of many North Sea examples, with total production ranging from c. 15×106 m3 to 35×106 m3, and recovery factors of between 30% and 55%. A variety of analytical methods were applied. Formal statistical methods quantified the relative influences of individual input parameters and parameter combinations on production measures. Various measures of reservoir heterogeneity were tested for their ability to discriminate reservoir performance. This paper gives a summary of the modelling and analyses described in more detail in the remainder of this thematic set of papers.

Modeling the Impact of Genetics on Insurance

Abstract The role of probabilistic models in the debate over genetics and insurance is discussed. A Markov model is used to show that, under quite extreme assumptions, adverse selection in life insurance ought to be controllable. The statistical problems of estimating small differences in mortality are discussed; these might limit the use of many genetic disorders as rating factors. The influence of the insurance industry on policy-making, especially through its support of research, is discussed. It is suggested that participating contracts are suitable and simple vehicles to carry the genetic risks in life insurance.

The Genetics of Breast and Ovarian Cancer I: A Model of Family History

We present a Markov model of breast cancer (BC) and ovarian cancer (OC) and estimate its transition intensities, mainly using United Kingdom population data. In the case of BC and OC, we estimate intensities according to BRCA1 and BRCA2 genotype. We use this to estimate the probabilities that an applicant for insurance has a BRCA1 or BRCA2 mutation, given complete or incomplete knowledge of her family history of BC and OC. Life (and other) insurance underwriters typically have incomplete knowledge of family history, for example no information on the number of healthy relatives. We show how these probabilities depend strongly on estimates of the mutation frequencies and penetrances, and conclude that it may not be appropriate to apply risk estimates based on studies of high-risk families to other groups.

A mathematical model of Alzheimer's disease and the ApoE gene

Alzheimers disease (AD) accounts for a significant proportion of long-term care costs. The recent discovery that the e4 allele of the ApoE gene indicates a predisposition to earlier onset of AD raises questions about the potential for adverse selection in long-term care insurance, about long-term care costs in general, and about the potential effects on costs of gene therapy, or better targetted treatments for AD. This paper describes a simple Markov model for AD, and the estinaation of the transition intensities from the medical and epidemiological literature.

The genetics of breast and ovarian cancer II:A model of critical illness insurance

We present a model of breast cancer (BC) and ovarian cancer (OC) and other events that would lead to a claim under a Critical Illness (CI) insurance policy, and estimate its transition intensities, mainly using United Kingdom population data. We use this to estimate the costs of CI insurance in the presence of a family history of BC or OC, using the probabilities from Part I of carrying a BRCA1 or BRCA2 mutation, given the family history. In practice, the family history may not include all relevant facts; we look at the range of costs depending on what is known. We show the effect of lower penetrance than is observed in high-risk families. Finally, we consider what the cost of adverse selection might be, were insurers unable to use genetic test or family history information.

An International Comparison of Recent Trends in Population Mortality

This survey continues a series of international mortality comparisons, of which the most recent were Giles & Wilkie (1973) and Wilkie (1976). The first part of the paper is a descriptive survey of mortality data from United Nations sources over the period 1970-90. The second part is based on short reports prepared by contributors from the actuarial associations in various countries, and aims in particular to provide a comprehensive bibliography.

An Actuarial Survey of Statistical Models for Decrement and Transition Data - I: Multiple State, Poisson and Binomial Models

This paper surveys some statistical models of survival data. A basic model of a random lifetime is defined, and censoring is introduced. Methods based on observations of small segments of lifetimes are compared. Markov and semi-Markov (multiple state) models are recommended as well-understood and flexible models well suited to actuarial data. A Poisson model is discussed as an approximation to a two state model, while traditional Binomial-type models are shown to be more restricted and less tractable than multiple state models.

Moratoria on the Use of Genetic Tests and Family History for Mortgage-Related Life Insurance

The Human Genetics Commission intends to study the use of family history in underwriting, regarding it as genetic information in a broad sense. We survey the developments in genetics and insurance that led up to this decision. We propose a model for studying the possible costs of adverse selection in the mortgage-related life insurance market (which is important in the United Kingdom) with and without moratoria on the use of family history. We consider both level and decreasing term assurances, finding that the cost of adverse selection is slightly higher for the latter. Several assumptions about mutation penetrance, incidence of additional mortality, prevalence of genetic testing and insurance-buying behaviour are considered. Overall we conclude that: (a) a moratorium on genetic test results alone will lead to negligible adverse selection costs; while (b) a moratorium extended to family history will lead to premium increases just by redefining underwriting classes, with adverse selection being possible as well, but only in extreme circumstances would all premium increases be likely to exceed about 10%. However, we give examples in a model of a smaller life insurance market that show that our benign conclusions might not apply more generally.

Genetics, Alzheimer’s Disease, and Long-Term Care Insurance

Abstract This paper applies a model of Alzheimer’s disease (AD) developed by Macdonald and Pritchard (2000) to the question of the potential for adverse selection in long-term care (LTC) insurance introduced by the existence of DNA tests for variants of the ApoE gene, the ε4 allele of which is known to predispose one to earlier onset of AD. It computes the expected present values (EPVs) of model LTC benefits with respect to AD for each of five ApoE genotypes, weighted average EPVs with and without adverse selection, and sample underwriting ratings. The paper concludes that adverse selection could increase costs significantly in a small LTC insurance market only if current population genetic risk is not much smaller than that observed in case-based studies, and if carriers of the ε4 allele are very much more likely to buy LTC insurance. Finally, the paper considers the cost of a combined retirement package, providing both pension and LTC insurance, and shows that it can reduce adverse selection.