Use of a Markov Model to Estimate Long-Term Insured Lives’ Mortality Risk Associated With BRCA1 and BRCA2 Gene Mutations

Abstract

There is uncertainty regarding the degree of insurance risk associated with BRCA1/2, the gene mutations associated with breast cancer. Most reports to date have been based on high-risk populations selected from families with multiple and/or early-onset cancers; more favorable data have been reported in studies without this selection bias.

This paper discusses use of a Markov model to estimate mortality risk associated with BRCA1/2 gene mutations in female life insurance applicants. The goal is to derive a range of risk estimates based on different assumptions of breast and ovarian cancer incidence. A particular strength of the model is that transition probabilities after cancer diagnosis vary with age and cancer stage, as do excess hazard rates.

Data calculated by the model indicate that no single mortality curve characterizes risk for all life insurance applicants with a BRCA1/2 mutation. Rather, mortality risk depends on breast and ovarian cancer incidence rates and subsequent mortality rates, and on the method used to deal with competing breast and ovarian cancer incidence and mortality rates. Further refinement of risk estimates will depend on better incidence data and on resolution of complex statistical problems, such as informative censoring.

Widespread use of genetic information by insurance consumers could have important economic implications. For companies that sell individually underwritten products, profitability might decrease. Consumers might find higher prices and reduced availability, with a corresponding decrease in quantity of insurance purchased. Insurance and consumer ramifications would vary by cover, with living-benefit products, such as critical-illness insurance, most adversely affected. Societal choices are limited. Given assumptions in the cited scenario, it is likely premiums would rise and quantity of insurance purchased would decrease even with no change in existing social policy; attempted legal or regulatory remedies would further accentuate price increases and reductions in quantity purchased.     

Pricing Term Insurance in the Presence of a Family History of Breast or Ovarian Cancer

Abstract

We estimate the increased mortality and term life insurance costs for women who have a family history of breast or ovarian cancer. Using data from the medical literature on age-specific and family history-specific incidence rates, we develop double-decrement models to evaluate the actuarial impact of breast cancer and ovarian cancer in the family. We also calculate the increased mortality and term insurance costs for women who test positive for the BRCA1 or BRCA2 gene mutation. We find that the type of affected relative and her age at onset of the disease are key underwriting factors. We find substantial mortality increases (up to 100%) for women with two relatives with cancer and women with a first-degree relative who developed cancer at an early age. Mortality increases for women with the BRCA gene mutation reach 150%. While some females with a family history of cancer can be accepted at standard rates, others may need to be quoted substandard rates, depending on the underwriting policy of the company. Females with the gene mutation can possibly be accepted at a rate that incorporates a severe mortality surcharge.     

Recurrent PSA after prostatectomy for prostate cancer: implications of PSA doubling time

After radical prostatectomy for prostate cancer, men frequently develop detectable levels of prostate specific antigen (PSA). A slow rate of increase, as characterized by the PSA doubling time (PSADT) is the principal marker for a favorable prognosis. Data and results presented in 2 recent clinical articles studying cohorts of men with clinical stage T1/T2 prostate cancer are reviewed and used to develop mortality analyses. Life-table analysis shows a mortality ratio of 257% at 5 years for Gleason score < 8, PSA recurrence > 2 years after surgery for clinical stage T1/T2 disease, and PSA doubling time (PSADT) > 10 months. Markov modeling using transition probabilities derived from the clinical articles to develop a life table analysis yields a mortality ratio of 145% at 10 years for similar patients.     

Breast cancer: a review of the literature

This article presents a comprehensive review of the Breast Cancer literature examining epidemiology, diagnosis, pathology, "benign" breast disease, breast carcinoma in situ syndromes, staging, and post-treatment surveillance among many topics. Breast cancer remains the most commonly occurring cancer in women. Breast cancer detection, treatment, and prevention are prominent issues in public health and medical practice. Background information on developments in these arenas is provided so that medical directors can continue to update their approach to the assessment of breast cancer risk.     

The genetics of breast and ovarian cancer V: application to income protection insurance

In Part IV we presented a comprehensive model of a life history of a woman at risk of breast cancer (BC), in which relevant events such as diagnosis, treatment, recovery and recurrence were represented explicitly, and corresponding transition intensities were estimated. In this part, we study some applications to income protection insurance (IPI) business. We calculate premiums based either on genetic test results or more practically on a family history of BC. We then extend the model into an IPI market model by incorporating rates of insurance-buying behaviour, in order to estimate the possible costs of adverse selection, in terms of increased premiums, under various moratoria on the use of genetic information.     

Mortality outcomes of various causes of syncope

Syncope, especially in older-age applicants, presents a risk selection quandary. When the etiology is established, risk classification is based on the causative impairment. However, often no diagnosis is ascertained. The lack of diagnosis presents a dilemma for the medical director. Underwriting decisions must be based on sound actuarial principles or related to actual and reasonable anticipated experience. The mortality outcome of various causes of syncope from participants of the Framingham Heart Study is presented in this abstract. The primary value to the medical director is the mortality outcome of those applicants without a specific etiologic diagnosis; those belonging to the unknown, the vasovagal or other causes groups. Over a 24-year observation period, patients whose syncope was attributed to vasovagal or other causes had a mortality ratio of 14% and an excess death rate of 20. Neurogenic syncope had a mortality ratio of 168% and an excess death rate of 34. No excess mortality was observed when those with seizures were excluded from analysis. Those whose cause of syncope was unknown had a mortality ratio of 192% and an excess death rate of 46. Individuals whose syncope was deemed to be cardiac exhibited a mortality ratio of 270% and an excess death rate of 82.     

Genetic developments in breast cancer

In this paper I have reviewed the current literature on the genetic mutations found in association with breast cancer. More emphasis has been given to BRCA1 because of the excitement generated with the cloning of this breast cancer susceptibility gene. A number of somatic mutations have been described (loss of heterozygosity, overexpression, and other mutations) in breast cancers. While strides have been made in unraveling the genetic basis of hereditary breast cancer (10 to 15 percent of all breast cancers), the genetic causes of most sporadic breast cancer (which comprise 85 to 90 percent) have yet to be discovered but they are likely the result of a step wise progression of cumulative genetic events, similar to those seen in colon cancer.     

Breast cancer risk perceptions and breast cancer worry: what predicts what?

This longitudinal study explored the relationship between perceived breast cancer risk and worry. We measured both absolute and comparative risk perceptions, and also used the Gail algorithm to assess the accuracy of participants' risk perceptions. Three hundred and one women ages 40–75 participated in a two‐part study assessing how format of breast cancer risk presentation affected perceptions of risk. Relative to their Gail scores, women were biased pessimistically about their own absolute breast cancer risk and yet largely accurate about their comparative breast cancer risk. Perceived comparative risk, but not perceived absolute risk or biases in absolute or comparative risk, predicted subsequent worry. Worry predicted subsequent perceived absolute risk and biases in absolute and comparative risk. These results suggest that women's emotional reactions to breast cancer risk are based on accurate (unbiased) perceptions of their comparative risks. In turn, greater worry prompts a re‐evaluation of absolute risk as well as changes in risk biases. Implications for screening are discussed.     

Population-based mortality outcome of rheumatoid arthritis in females

Rheumatoid arthritis (RA) is a systemic disease whose morbidity exceeds its mortality. This abstract quantifies the mortality of RA in a general population over a 30-year period in females. The generic, across the spectrum of disease, mortality ratio is 136%; the excess death rate is 12. The mortality impact on males is minimal; the source publication noted a mortality ratio of 107%. Many selected cases of RA can be underwritten very favorably. PURPOSE: To quantify the excess mortality in females diagnosed with rheumatoid arthritis (RA) between 1955 to 1985. SUBJECTS AND METHODS: Medical records of all residents age 35 and over of Rochester, Minnesota, who met the American College of Rheumatology 1987 diagnostic criteria for RA were reviewed. Based on the comprehensive statistical base for residents in Rochester, virtually complete ascertainment of all clinically recognized cases of RA were identified. An incidence cohort identifying the same residents with new cases of RA occurring between January 1, 1955, and January 1, 1985, was created. Three, 10-year prevalence cohorts were assembled as of July 1, 1965, 1975 and 1985. Patients in each cohort were followed longitudinally until death or migration from Rochester. Data of disease characteristics, course, co-morbidity and death were collected. During the follow-up period, 6.9% moved out of the county, and 5.1% moved into the county after the diagnosis of RA had been made elsewhere. Expected survival was based on age and sex adjusted survival from the same community in the same time period. Mortality was described using the Kaplan-Meier product-limit method. Cox proportional hazards modeling was used to examine the effects of age, sex and rheumatoid factor on survival. DATA: In the 1965, 1975 and 1985 prevalence cohorts, there were 163, 235 and 272 cases of RA, respectively. Some individuals were present in more than one. Deaths in each cohort were 54, 93 and 111, respectively. Median follow-up was 12.7 years for the entire group with the earlier groups being longer. Mean follow-up was 15.1 years. Seventy-three percent of patients were females. The average age at diagnosis was 60.2 years.     

Secondary cancer and relapse rates following radical prostatectomy for prostate-confined cancer

In the SEER database, it is relatively easy to identify secondary cancers that follow an initial diagnosis of cancer. However, the SEER public-use data does not explicitly capture relapse of the initial cancer. One can assume that organ-confined prostate cancer treated by radical prostatectomy will show no evidence of disease after treatment. Death due to prostate cancer in such cases can be assumed to follow a relapse of previously occult metastatic disease. We devised an estimate of the timing of these relapses and tabulated rates for both new primaries and relapses following radical prostatectomy for organ-confined prostate cancer.     

Radical prostatectomy versus watchful waiting in early prostate cancer

Prostate cancer continues to be a significant factor in morbidity and mortality. Due to high prevalence (most common cancer in U.S. males) and mortality (second most common cause of cancer deaths in males), prostate cancer is one of the most crucial health problems in men. The discussion of managing early prostate cancer is not only common, but also complicated. Treatment decisions involve scant survival data and quality of life issues such as impotence and urinary incontinence. Watchful waiting has also had to fight the paradigm of surgery curing cancer.     

Patterns of Aging-Related Changes on the Way to 100

Abstract

The objective of this paper is to investigate dynamic properties of age trajectories of physiological indices and their effects on mortality risk and longevity using longitudinal data on more than 5,000 individuals collected in biennial examinations of the Framingham Heart Study (FHS) original cohort during about 50 subsequent years of follow-up. We first performed empirical analyses of the FHS longitudinal data. We evaluated average age trajectories of indices describing physiological states for different groups of individuals and established their connections with mortality risk. These indices include body mass index, diastolic blood pressure, pulse pressure, pulse rate, level of blood glucose, hematocrit, and serum cholesterol. To be able to investigate dynamic mechanisms responsible for changes in the aging human organisms using available longitudinal data, we further developed a stochastic process model of human mortality and aging, by including in it the notions of “physiological norms,” “allostatic adaptation and allostatic load,” “stress resistance,” and other characteristics associated with the internal process of aging and the effects of external disturbances. In this model, the persistent deviation of physiological indices from their normal values contributes to an increase in morbidity and mortality risks. We used the stochastic process model in the statistical analyses of longitudinal FHS data. We found that different indices have different average age patterns and different dynamic properties. We also found that age trajectories of long-lived individuals differ from those of the shorter-lived members of the FHS original cohort for both sexes. Using methods of statistical modeling, we evaluated “normal” age trajectories of physiological indices and the dynamic effects of allostatic adaptation. The model allows for evaluating average patterns of aging-related decline in stress resistance. This effect is captured by the narrowing of the U-shaped mortality risk (considered a function of physiological state) with age. We showed that individual indices and their rates of change with age, as well as other measures of individual variability, manifested during the life course are important contributors to mortality risks. The advantages and limitations of the approach are discussed.     

Systematic Mortality Improvement Trends and Mortality Heterogeneity: Insights from Individual-Level HRS Data

Providers of life annuities and pensions need to consider both systematic mortality improvement trends and mortality heterogeneity. Although how mortality improvement varies with age and gender at the population level is well studied, how trends vary with risk factors remains relatively unexplored. This article assesses how systematic mortality improvement trends vary with individual risk characteristics using individual-level longitudinal data from the U.S. Health and Retirement Study between 1994 and 2009. Initially a Lee-Carter model is used to assess mortality improvement trends by grouping individuals with similar risk characteristics of gender, education, and race. We then fit a longitudinal mortality model to individual-level data allowing for heterogeneity and time trends in individual-level risk factors. Our results show how survey data can provide valuable insights into both mortality heterogeneity and improvement trends more effectively than commonly used aggregate models. We show how mortality improvement differs across individuals with different risk factors. Significantly, at an individual level, mortality improvement trends have been driven by changes in health history such as high blood pressure, cancer, and heart problems rather than risk factors such as education, marital status, body mass index, and smoker status.     

Continuous-time multi-cohort mortality modelling with affine processes

Continuous-time mortality models, based on affine processes, provide many advantages over discrete-time models, especially for financial applications, where such processes are commonly used for interest rate and credit risks. This paper presents a multi-cohort mortality model for age-cohort mortality rates with common factors across cohorts as well as cohort-specific factors. The mortality model is based on well-developed and used techniques from interest rate theory and has many applications including the valuation of longevity-linked products. The model has many appealing features. It is a multi-cohort model that describes the whole mortality surface, it captures cohort effects, it allows for observed imperfect correlation between different cohorts, it is shown to fit historical data at pension-related ages very well, it has closed-form expressions for survival curves and we show that it outperforms a number of other commonly used discrete-time mortality models in forecasting future survival curves.     

Women in development: Kenya's experience

In Kenya, the government has promoted economic policies, development programs, and a legal system geared to increase incentives and productive capacity for women. Economic strength, family health and population growth can be greatly effected by programs in women's education, health care, family planning and agriculture extension. There are 10 million women in Kenya and 60% are below 20 years of age. Women's groups have been successful in improving health and family planning practice. Women manage most small farms: 75% of the labor on the farms is provided by women. Kenya has introduced an extension system nationally focusing on women farmers as well as men. Women's demand for credit is strong and the government is considering helping expand credit through women's groups. Water is obtained by women and 9 of 10 spend more than an hour getting water each day for the family. By providing better access to water, more time can be spent on farming, family and other more important pursuits. There are many projects to improve community water supplies sponsored by both governmental and non- governmental organizations. About 1/3 girls and 2/5 boys complete primary school. Women that have more than 5 years of education have less than 3 children. There have been difficulties getting girls into later primary and secondary education, because fewer spots are allocated for girls in government-aided schools. The government it trying to improve this, but many girls drop out because of pregnancy. A third of the deaths of women between 15-35 is caused by maternal mortality. This high rate can be reduced with better prenatal care, better family planning, and more effective care at child birth. There are now about 100,000 new family planning acceptors each year. The World Bank and many international organizations have given support to the women's needs in the development process.     

The evolution of death rates and life expectancy in Denmark

From 1835 to date Denmark has experienced an increase in life expectancy at birth of about 40 years for both sexes. Over the course of the last 170 years, life expectancy at birth has increased from 40 to 80 years for women and from 36 to 76 years for men, and it continues to rise. Using a new methodology, we show that about half of the total historic increase can be attributed to the sharp decline in infant and young age death rates up to 1950. However, life expectancy gains from 1950 to date can be primarily attributed to improvements in the age-specific death rates for the age group from 50 to 80, although there is also a noticeable contribution from the further decline in infant mortality over this period. With age-specific death rates up to age 60 now at a very low absolute level, substantial future life expectancy improvements must necessarily arise from improvements in age-specific death rates for ages 60 and above. Using the developed methodology, we quantify the impact of further reductions in age-specific mortality. Despite being one of countries with the highest life expectancy at the beginning of the 20th century, and despite the spectacular historic increase in life expectancy since then, Denmark is, in fact, lagging behind compared to many other countries, notably the other Nordic countries. The main reason is an alarming excess mortality for cause-specific death rates related to ischaemic heart diseases and, in particular, a number of cancer diseases. Age-specific death rates continue to improve in most countries, and a likely scenario is that in the future Denmark will experience improvement rates at the international level or perhaps even higher as a result of a catch-up effect.     

Sentinel lymph node biopsy for breast cancer

The regional lymph node status is the most powerful predictor of survival in women with invasive breast cancer.     

Autoimmune hepatitis

Autoimmune hepatitis is an uncommon disease causing chronic inflammation of the liver and associated with various circulating autoantibodies. It shares some characteristics with other autoimmune liver diseases, such as primary biliary cirrhosis and sclerosing cholangitis. There has been confusion in past years regarding this entity, but there are now recognized diagnostic criteria by which to make a proper diagnosis. The disease is usually treatable with steroids. Certain proportions of treated patients become cured, although relapse is a problem often requiring chronic administration of steroid therapy. The expected mortality is close to normal in individuals who are cured or have only mild disease.     

Unintended consequences of expense ratio guidelines: The Avon breast cancer walks

This case study examines how donor and rating agency focus on percentage-based expense ratios exacerbated pressures on the Avon Product Foundation’s breast cancer walks. Beginning in 2002, Avon changed its business and accounting practices in ways that eventually helped it report better compliance with charity monitor guidelines. However, the number of walkers and amounts of funds raised dropped; the new accounting practices are less transparent and of questionable conformity with GAAP.     

Inequality in Mortality in Spain*

We analyse the evolution of mortality rates in Spain by age and gender between 1990 and 2018. We compare municipalities, ranked by socio‐economic status (SES) and grouped into bins of similar population size, to study changes not only in levels but also in inequality in mortality across the SES spectrum. We document large decreases in mortality rates throughout the period for all age groups, including children, even after 2000, and continuing after the Great Recession. These declines are stronger for boys and men, who had higher mortality rates to begin with. We find that inequality in mortality across municipalities was low among the young by 2018, while it was higher among adult men and older women. Inequality in fact increased over the period for older men. We explore the role of different causes of death and find that this increase in inequality is driven by stronger improvements in cancer‐related mortality among men living in richer areas. These improvements are not found among women, given their increases in mortality due to lung cancer.