Cohort extensions of the Poisson common factor model for modelling both genders jointly

The earlier work on mortality modelling and forecasting has largely focused on the study of a single population. Recently, there is an emerging strand of literature that emphasises the interrelationship between multiple populations. In this paper, we examine some cohort extensions of the Poisson common factor model for modelling both genders jointly. The cohort effect is specified in six alternatives which are applied to data-sets from five developed regions. We find that direct parameterisation of cohort effect could improve model fitting, reduce the need for additional period factors, and produce consistent mortality forecasts for females and males. Furthermore, we find that the cohort effect appears to be gender indifferent for the populations examined and has an interaction effect with age in certain cases.     

Peripartum cardiomyopathy: mortality outcomes

Mortality estimates of peripartum cardiomyopathy have been reported to be between 18 and 56% without reference to time frames. Although this is an unusual impairment, medical directors need accurate information to meet the gold standard of underwriting: decisions must be based on sound underwriting and actuarial principles reasonably related to actual or anticipated loss experience. In an insurance purchasing population, the excess mortality in peripartum cardiomyopathy can be nearly eliminated by not insuring those with the impairment within the first 6 months postpartum or until all abnormal physiologic parameters have resolved. Thereafter, the risk is probably negligible. This abstract illustrates the challenge to determine expected mortality when the study population exhibits strong racial diversity and when available expected life tables contain raw data of only alive and dead at each yearly interval.     

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.     

Evaluation of survival in medically treated patients with homozygous beta thalassemia by the quick hit method

Articles published in medical journals often evaluate the survival and/or prognosis of a medical impairment. The conclusions of these articles can be very misleading if correct mortality methodology is not utilized. Authors evaluating survival in a cohort of individuals with Thalassemia Major concluded the prognosis was excellent. This was based solely on observed mortality. When the cohort is properly compared to the expected mortality of a similar nonimpaired population the result is quite different. Their survival is far from excellent. This article uses the quick hit method to evaluate the survival of this cohort having Thalassemia Major.     

Reference mortality K2004 of personal life insurance policies in Finland

This article presents the reference mortality model K2004 approved by the Actuarial Society of Finland and the technique that was implemented in developing it. Initially, I will present the historical development of individual mortality rates in Finland. Then, the requirements posed for a modern mortality modelling will be presented. Reference mortality model K2004 is based on total population mortality rates, which were adjusted to correspond with that portion of the population that has a life insurance policy. First, the model presents a margin of the observed life insurance mortality rate in the total population with a Lee-Carter method together with a forecast, where the downward trend in mortality rates is expected to continue at the rate illustrated since the 1960s. Then, the mortality rate has been adjusted into life insurance mortality per age so that it corresponds to the differences observed between total population and the portion of population that has a life insurance during 1991–2001. Finally, a cohort and gender-specific functional margin will be presented to obtained data.     

Marfan syndrome: literature review of mortality studies

Marfan syndrome is an autosomal dominant heritable disorder of fibrous connective tissue due to mutation in the fibrillin-1 gene, located on chromosome 15. Early mortality from Marfan syndrome results from aortic dilatation. The medical literature contains long-term follow-up series of patients with Marfan syndrome accrued at major medical centers that address overall survival following surgical intervention, and prognosis in relation to certain risk factors such as family history and aortic root diameter. Mortality analyses based on these data are presented in this paper. Advances in surgical and medical therapy have improved mortality of affected individuals over the past 2-3 decades. However, significant mortality occurs, peaking in the third and fourth decades of life. Although surgery is successful treatment of aortic dissection, one cannot conclude that surgical repair confers a mortality advantage. Emergency surgery and history of aortic complications in first-degree relatives are associated with a higher mortality. Chronic beta-blocker therapy may slow the rate of aortic dilatation and may be associated with more favorable prognosis. Clinical research evaluating beta-blockade, echo assessment of the aortic root diameter progression, and gene mutation analysis may provide tools useful for future morality assessments.     

Infant mortality: an insured population perspective

Many insurers offer life coverage to individuals during the first year of life. The policies tend to have small face values, but frequently contain premium waiver or additional purchase options. General population mortality is significantly higher at this age relative to older children and even middle-aged adults. This article presents the mortality experience of an insured cohort in which death occurred under 1 year of age. In summary, the insured population's mortality rate was significantly lower and the leading causes of death were different than the general population.     

Rethinking age-period-cohort mortality trend models

Longevity risk arising from uncertain mortality improvement is one of the major risks facing annuity providers and pension funds. In this article, we show how applying trend models from non-life claims reserving to age-period-cohort mortality trends provides new insight in estimating mortality improvement and quantifying its uncertainty. Age, period and cohort trends are modelled with distinct effects for each age, calendar year and birth year in a generalised linear models framework. The effects are distinct in the sense that they are not conjoined with age coefficients, borrowing from regression terminology, we denote them as main effects. Mortality models in this framework for age-period, age-cohort and age-period-cohort effects are assessed using national population mortality data from Norway and Australia to show the relative significance of cohort effects as compared to period effects. Results are compared with the traditional Lee–Carter model. The bilinear period effect in the Lee–Carter model is shown to resemble a main cohort effect in these trend models. However, the approach avoids the limitations of the Lee–Carter model when forecasting with the age-cohort trend model.     

Computerised detection and stochastic forecast of age, period and cohort effects

In this study, we adapt and apply suitable methods of image processing and computer vision to actuarial science. In particular, we design a multistage algorithm based on the well known Canny operator with a view to detecting abrupt changes in incremental mortality development factors by age over time. These edges indicate the boundaries between areas of higher and lower mortality improvements. The computerised detection algorithm allows for a more objective judgement concerning the existence of specific mortality patterns. Furthermore, we propose a stochastic mortality forecast model that may be viewed as a Lévy process. First, objectively identified mortality patterns are removed from the matrix of mortality improvement rates. We then forecast residual mortality development factors by applying a non-parametric block bootstrap simulation. Finally, future age, period and cohort effects are superimposed on a simulation basis. Notably, our stochastic mortality model is capable of incorporating specific stress scenarios such as mortality shocks.     

An analytic method for longitudinal mortality studies

Our knowledge of mortality risks comes largely from longitudinal (cohort) studies. The most commonly used analytic tool is the Cox proportional hazards model for survival analysis. An alternative approach is a simple cross-sectional analysis of person-years. The key to the method is logistic regression, where the outcome variable is lived/died in the given year and the explanatory variables are age, sex, and other potential risk factors. This approach can be used to model any dichotomous outcome and has several important advantages over the more traditional survival analysis. As an example, we compare the two methods using a large data base of patients with spinal cord injury.     

Predictive Modeling of Obesity Prevalence for the U.S. Population

Modeling obesity prevalence is an important part of the evaluation of mortality risk. A large volume of literature exists in the area of modeling mortality rates, but very few models have been developed for modeling obesity prevalence. In this study we propose a new stochastic approach for modeling obesity prevalence that accounts for both period and cohort effects as well as the curvilinear effects of age. Our model has good predictive power as we utilize multivariate ARIMA models for forecasting future obesity rates. The proposed methodology is illustrated on the U.S. population, aged 23–90, during the period 1988–2012. Forecasts are validated on actual data for the period 2013–2015 and it is suggested that the proposed model performs better than existing models.     

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.     

Stochastic Mortality Modeling: Key Drivers and Dependent Residuals

This article proposes an alternative framework for modeling the stochastic dynamics of mortality rates. A simple age basis combined with two stochastic period factors is used to explain the key mortality drivers, while the remaining structure is modeled via a multivariate autoregressive residuals model. The latter captures the stationary mortality dynamics and introduces dependencies between adjacent age-period cells of the mortality matrix that, among other things, can be structured to capture cohort effects in a transparent manner and incorporate across ages correlations in a natural way. Our approach is compared with models with and without a univariate cohort process. The age- and period-related latent states of the mortality basis are more robust when the residuals surface is modeled via the multivariate time-series model, implying that the process indeed acts independently of the assumed mortality basis. Under the Bayesian paradigm, the posterior distribution of the models is considered to explore coherently the extent of parameter uncertainty. Samples from the posterior predictive distribution are used to project mortality, and an in-depth sensitivity analysis is conducted. The methodology is easily extendable in multiple ways that give a different form and degree of significance to the different components of mortality dynamics.     

Temporal Evolution of Mortality Indicators

Abstract

In Spain, as in other developed countries, significant changes in mortality patterns have occurred during the 20th and 21st centuries. One reflection of these changes is life expectancy, which has improved in this period, although the robustness of this indicator prevents these changes from being of the same order as those for the probability of death. If, moreover, we bear in mind that life expectancy offers no information as to whether this improvement is the same for different age groups, it is important and necessary to turn to other mortality indicators whose past and future evolution in Spain we are going to study. These indicators are applied to Spanish mortality data for the period 1981–2008, for the age range 0–99. To study its future evolution, the mortality ratios have to be projected using an adequate methodology, namely, the Lee-Carter model. Confidence intervals for these predictions can be calculated using the methodology that Lee and Carter apply in their original article for expected lifetime confidence intervals, but they take into account only the error in the prediction of the mortality index obtained from the ARIMA model adjusted to its temporal series, excluding other sources of error such as that introduced by estimations of the other parameters in the model. That is why bootstrap procedures are preferred, permitting the combination of all sources of uncertainty.     

Factors driving aggregate mortality rates in postwar Germany

Using German data over the period 1956–2006, this study provides a comprehensive empirical analysis of factors driving aggregate mortality rates over time. It differs from previous contributions in this field by simultaneously considering an extensive set of macroeconomic, socioeconomic, and ecological factors as explanatory variables. Our regression analysis shows that sex- and age-specific mortality rates vary substantially in their response to external factors. Strongest associations are found with changes in real GDP, flu epidemics, and the two lifestyle variables—alcohol and cigarette consumption—in both univariate and multivariate setups. Further analysis indicates that these effects are primarily contemporary, whereas other indicators, such as weather conditions, exert lagged effects. We derive optimal multivariate models for every age group that provide a good fit to the observed variation in annual mortality rates, and thereby confirm the relevance of the identified factors.     

Asset Allocation Via The Conditional First Exit Time or How To Avoid Outliving Your Money

The risk of outliving your money (or shortfall) with low risk, low return investments is very often more serious than the risk of losing money on high risk investments, until quite late in life. A stochastic process model incorporating mortality tables for men and women of retirement age, random rates of return and fixed initial wealth and desired level of consumption provides the analytical tool. A simulation using Canadian mortality tables and rates of return shows that almost all retirees should invest some of their wealth in equity, and for many the optimal allocation is 70–100% equity. The risk of shortfall is surprisingly high for a reasonable range of values of the variables, especially for an allocation of 100% in treasury bills. Women face much greater risk of shortfall than men. The analytical model also permits calculation of the distribution of the bequest and hence allows an individual to trade off changes in shortfall risk against changes in the expected bequest to the heirs.     

How Genes Modulate Patterns of Aging-Related Changes on the Way to 100: Biodemographic Models and Methods in Genetic Analyses of Longitudinal Data

In this article we clarify mechanisms of genetic regulation of human aging and longevity traits. The objective of this article is to address the issues in previous research of not reaching a genome-wide level of statistical significance and lack of replication in the studies of independent populations. We performed GWAS of human life span using different subsets of data from the original Framingham Heart Study cohort corresponding to different quality control procedures, and we used one subset of selected genetic variants for further analyses. We used a simulation study to show that this approach to combining data improves the quality of GWAS with FHS longitudinal data to compare average age trajectories of physiological variables in carriers and noncarriers of selected genetic variants. We used a stochastic process model of human mortality and aging to investigate genetic influence on hidden biomarkers of aging and on dynamic interaction between aging and longevity. We investigated properties of genes related to selected variants and their roles in signaling and metabolic pathways and showed that the use of different quality control procedures results in different sets of genetic variants associated with life span. We selected 24 genetic variants negatively associated with life span and showed that the joint analyses of genetic data at the time of biospecimen collection and follow-up data substantially improved significance of associations of 24 selected SNPs with life span. We also showed that aging-related changes in physiological variables and in hidden biomarkers of aging differ for the groups of carriers and noncarriers of selected variants. The results of these analyses demonstrated benefits of using biodemographic models and methods in genetic association studies of these traits. Our findings showed that the absence of a large number of genetic variants with deleterious effects may make substantial contribution to exceptional longevity. These effects are dynamically mediated by a number of physiological variables and hidden biomarkers of aging. The results of these research demonstrated benefits of using integrative statistical models of mortality risks in genetic studies of human aging and longevity.     

Intergenerational Transfers and Insurance Policy Design

Abstract

Group health insurance policies offering an identical benefit package to every member of the group result in lower expected health benefits for younger cohorts than older cohorts. The dispersion in insurance benefits across age groups differs among insurance policies. Simulation results presented in this paper demonstrate that a shift from comprehensive health insurance to high-deductible health insurance decreases the share of expected benefits going to younger cohorts. An estimated 81.5% of the 23-to-32-year-old cohort is expected to receive less than $500 in health benefits during a year for one prototypical high-deductible health plan. Low expected benefits for younger relatively healthy cohorts could increase the number of younger individuals who eschew health coverage. Age-rated premiums are probably the most straightforward way to stimulate demand for high-deductible health plans among younger healthier individuals.     

Pivot tables for mortality analysis, or who needs life tables anyway?

Actuarial life-table analysis has long been used by life insurance medical directors for mortality abstraction from clinical studies. Ironically, today's life actuary instead uses pivot tables to analyze mortality. Pivot tables (a feature/function in MS Excel) collapse various dimensions of data that were previously arranged in an "experience study" format. Summary statistics such as actual deaths, actual and expected mortality (usually measured in dollars), and calculated results such as actual to expected ratios, are then displayed in a 2-dimensional grid. The same analytic process, excluding the dollar focus, can be used for clinical mortality studies. For raw survival data, especially large datasets, this combination of experience study data and pivot tables has clear advantages over life-table analysis in both accuracy and flexibility. Using the SEER breast cancer data, we compare the results of life-table analysis and pivot-table analysis.     

Bonds versus stocks: Investors’ age and risk taking

It has become increasingly popular to advise investors to relocate their funds from a primarily stock portfolio to a primarily bond portfolio as they get older. However, the well-known decision rules such as mean–variance or stochastic dominance rules are unable to explain this common practice. Almost stochastic dominance (ASD) and almost mean–variance (AMV) approaches are used to examine the dominance of stock and bond portfolios. ASD and AMV rules unambiguously support the popular practice of advising higher stock to bond ratio for long investment horizons. Hence, we provide an explanation to the practitioners’ recommendation within the expected utility paradigm.