Regressive models for risk prediction of repeated multinomial outcomes: An illustration using Health and Retirement Study data

Life expectancy is increasing in many countries and this may lead to a higher frequency of adverse health outcomes. Therefore, there is a growing demand for predicting the risk of a sequence of events based on specified factors from repeated outcomes. We proposed regressive models and a framework to predict the joint probabilities of a sequence of events for multinomial outcomes from longitudinal studies. The Markov chain is used to link marginal and sequence of conditional probabilities to predict the joint probability. Marginal and sequence of conditional probabilities are estimated using marginal and regressive models. An application is shown using the Health and Retirement Study data. The bias of parameter estimates for all models from all bootstrap simulation is less than 1% in most of the cases. The estimated mean squared error is also very low. Results from the simulation study show negligible bias and the usefulness of the proposed model. The proposed model and framework would be useful to solve real-life problems from various fields and big data analysis.     

Health transition: examples from the western Pacific.

The Industrial Revolution ushered in a rapid transition from agriculture to industrialization. Some biological effects of this transition included increasing life expectancy, reduced infant mortality, and some decline in fertility. Reduced infant mortality first brought about an increase in life expectancy, but as humans were able to control infectious diseases, child and adult mortality also decreased. Now, accidents and chronic diseases are responsible for most mortality in many age groups. This shift from infectious diseases to accidents and chronic diseases is called the health transition. Japan and US are Pacific Basin countries which have relatively high life expectancy and low infant mortality (1988, 75.54 years vs. 71.38 years, and 4.4 vs. 9.9, respectively). These figures suggest that these countries rather advanced in the health transition. Japan may have better life expectancy than the US because of the effect of environmental factors, ethnic diversity, and health care differentials by social class on cardiovascular disease and cancer mortality. China and Thailand hold intermediate positions (67.98 years (1985-1990) vs. 63.82 years (1985-1986), and 32.4 vs. 39, respectively). Some research indicates that urban conditions and factory work increase the cardiovascular disease risk among the Chinese. Recent research suggests that access to immunization and modern medical care for acute disease are the only critical variables of the health transition rather than other variables. Papua New Guinea is not progressing very well (53.18 years and 58). Papua New Guinea has not yet been able to control infectious diseases, especially malaria. This comparison illustrates that populations progress through the health transition at different rates.     

Relationship of income and childlessness

ABSTRACT

We investigated the impact of diabetes on US life expectancy by sex and race/ethnicity using a prospective cohort study design. Cohorts were drawn from 1997 to 2009 waves of the National Health Interview Survey and linked to death records through December 31, 2011. We combined data on the prevalence of diabetes among decedents with estimates of the hazard ratios of individuals diagnosed with diabetes to calculate population attributable fractions (PAFs) by age, sex, and race/ethnicity at ages 30 and above. These estimates were then applied to deaths in the official US life table for 2010 to estimate effects of diabetes on life expectancy.

Diabetes was responsible for a reduction of 0.83 years of life expectancy for men at age 30 and 0.89 years for 30-year-old women. The impact was greatest among Black women at 1.05 years. Estimates based on traditional demographic and actuarial methods using the frequency with which a disease appears as an underlying cause of death on death certificates produced a reduction in life expectancy at age 30 of only 0.33 years.

We conclude that diabetes is substantially reducing US longevity and that its effect is seriously underestimated when using data on underlying causes of death.     

Calculation of longevity and life expectancy in captive elephants

The concepts of longevity (longest lived) and life expectancy (typical age at death) are common demographic parameters that provide insight into a population. Defined as the longest lived individual, longevity is easily calculated but is not representative, as only one individual will live to this extreme. Longevity records for North American Asian elephants (Elephas maximus) and African elephants (Loxodonta africana) have not yet been set, as the oldest individuals (77 and 53 years, respectively) are still alive. One Asian elephant lived to 86 years in the Taipei Zoo. This is comparable to the maximum (though not typical) longevity estimated in wild populations. Calculation of life expectancy, however, must use statistics that are appropriate for the data available, the distribution of the data, and the species' biology. Using a simple arithmetic mean to describe the non‐normally distributed age at death for elephant populations underestimates life expectancy. Use of life‐table analysis to estimate median survivorship or survival analysis to estimate average survivorship are more appropriate for the species' biology and the data available, and provide more accurate estimates. Using a life‐table, the median life expectancy for female Asian elephants (Lx=0.50) is 35.9 years in North America and 41.9 years in Europe. Survival analysis estimates of average life expectancy for Asian elephants are 47.6 years in Europe and 44.8 years in North America. Survival analysis estimates for African elephants are less robust due to less data. Currently the African elephant average life expectancy estimate in North America is 33.0 years, but this is likely to increase with more data, as it has over the past 10 years. Zoo Biol 23:365–373, 2004. © 2004 Wiley‐Liss, Inc.     

transition priors for protein hidden Markov models: an empirical study towards maximum discrimination.

Insertions and deletions in a profile hidden Markov model (HMM) are modeled by transition probabilities between insert, delete and match states. These are estimated by combining observed data and prior probabilities. The transition prior probabilities can be defined either ad hoc or by maximum likelihood (ML) estimation. We show that the choice of transition prior greatly affects the HMM's ability to discriminate between true and false hits. HMM discrimination was measured using the HMMER 2.2 package applied to 373 families from Pfam. We measured the discrimination between true members and noise sequences employing various ML transition priors and also systematically scanned the parameter space of ad hoc transition priors. Our results indicate that ML priors produce far from optimal discrimination, and we present an empirically derived prior that considerably decreases the number of misclassifications compared to ML. Most of the difference stems from the probabilities for exiting a delete state. The ML prior, which is unaware of noise sequences, estimates a delete-to-delete probability that is relatively high and does not penalize noise sequences enough for optimal discrimination.     

Measuring Burden of Unhealthy Behaviours Using a Multivariable Predictive Approach: Life Expectancy Lost in Canada Attributable to Smoking,Alcohol, Physical Inactivity,and Diet

BackgroundBehaviours such as smoking, poor diet, physical inactivity, and unhealthy alcohol consumption are leading risk factors for death. We assessed the Canadian burden attributable to these behaviours by developing, validating, and applying a multivariable predictive model for risk of all-cause death.MethodsA predictive algorithm for 5 y risk of death—the Mortality Population Risk Tool (MPoRT)—was developed and validated using the 2001 to 2008 Canadian Community Health Surveys. There were approximately 1 million person-years of follow-up and 9,900 deaths in the development and validation datasets. After validation, MPoRT was used to predict future mortality and estimate the burden of smoking, alcohol, physical inactivity, and poor diet in the presence of sociodemographic and other risk factors using the 2010 national survey (approximately 90,000 respondents). Canadian period life tables were generated using predicted risk of death from MPoRT. The burden of behavioural risk factors attributable to life expectancy was estimated using hazard ratios from the MPoRT risk model.FindingsThe MPoRT 5 y mortality risk algorithms were discriminating (C-statistic: males 0.874 [95% CI: 0.867–0.881]; females 0.875 [0.868–0.882]) and well calibrated in all 58 predefined subgroups. Discrimination was maintained or improved in the validation cohorts. For the 2010 Canadian population, unhealthy behaviour attributable life expectancy lost was 6.0 years for both men and women (for men 95% CI: 5.8 to 6.3 for women 5.8 to 6.2). The Canadian life expectancy associated with health behaviour recommendations was 17.9 years (95% CI: 17.7 to 18.1) greater for people with the most favourable risk profile compared to those with the least favourable risk profile (88.2 years versus 70.3 years). Smoking, by itself, was associated with 32% to 39% of the difference in life expectancy across social groups (by education achieved or neighbourhood deprivation).ConclusionsMultivariable predictive algorithms such as MPoRT can be used to assess health burdens for sociodemographic groups or for small changes in population exposure to risks, thereby addressing some limitations of more commonly used measurement approaches. Unhealthy behaviours have a substantial collective burden on the life expectancy of the Canadian population.     

Clinical Management and Burden of Prostate Cancer: A Markov Monte Carlo Model

Background

Prostate cancer (PCa) is the most common non-skin cancer among men in developed countries. Several novel treatments have been adopted by healthcare systems to manage PCa. Most of the observational studies and randomized trials on PCa have concurrently evaluated fewer treatments over short follow-up. Further, preceding decision analytic models on PCa management have not evaluated various contemporary management options. Therefore, a contemporary decision analytic model was necessary to address limitations to the literature by synthesizing the evidence on novel treatments thereby forecasting short and long-term clinical outcomes.

Objectives

To develop and validate a Markov Monte Carlo model for the contemporary clinical management of PCa, and to assess the clinical burden of the disease from diagnosis to end-of-life.

Methods

A Markov Monte Carlo model was developed to simulate the management of PCa in men 65 years and older from diagnosis to end-of-life. Health states modeled were: risk at diagnosis, active surveillance, active treatment, PCa recurrence, PCa recurrence free, metastatic castrate resistant prostate cancer, overall and PCa death. Treatment trajectories were based on state transition probabilities derived from the literature. Validation and sensitivity analyses assessed the accuracy and robustness of model predicted outcomes.

Results

Validation indicated model predicted rates were comparable to observed rates in the published literature. The simulated distribution of clinical outcomes for the base case was consistent with sensitivity analyses. Predicted rate of clinical outcomes and mortality varied across risk groups. Life expectancy and health adjusted life expectancy predicted for the simulated cohort was 20.9 years (95%CI 20.5–21.3) and 18.2 years (95% CI 17.9–18.5), respectively.

Conclusion

Study findings indicated contemporary management strategies improved survival and quality of life in patients with PCa. This model could be used to compare long-term outcomes and life expectancy conferred of PCa management paradigms.     

Closing the Gap: Increases in Life Expectancy among Treated HIV-Positive Individuals in the United States and Canada

Background

Combination antiretroviral therapy (ART) has significantly increased survival among HIV-positive adults in the United States (U.S.) and Canada, but gains in life expectancy for this region have not been well characterized. We aim to estimate temporal changes in life expectancy among HIV-positive adults on ART from 2000–2007 in the U.S. and Canada.

Methods

Participants were from the North American AIDS Cohort Collaboration on Research and Design (NA-ACCORD), aged ≥20 years and on ART. Mortality rates were calculated using participants'' person-time from January 1, 2000 or ART initiation until death, loss to follow-up, or administrative censoring December 31, 2007. Life expectancy at age 20, defined as the average number of additional years that a person of a specific age will live, provided the current age-specific mortality rates remain constant, was estimated using abridged life tables.

Results

The crude mortality rate was 19.8/1,000 person-years, among 22,937 individuals contributing 82,022 person-years and 1,622 deaths. Life expectancy increased from 36.1 [standard error (SE) 0.5] to 51.4 [SE 0.5] years from 2000–2002 to 2006–2007. Men and women had comparable life expectancies in all periods except the last (2006–2007). Life expectancy was lower for individuals with a history of injection drug use, non-whites, and in patients with baseline CD4 counts <350 cells/mm³.

Conclusions

A 20-year-old HIV-positive adult on ART in the U.S. or Canada is expected to live into their early 70 s, a life expectancy approaching that of the general population. Differences by sex, race, HIV transmission risk group, and CD4 count remain.     

Survival Expectations of the Obese: Is Excess Mortality Reflected in Perceptions?

Objective: This study compared self‐reported subjective life expectancy (i.e., probability of living to age 75) for normal‐weight, overweight, and obese weight groups to examine whether individuals are internalizing information about the health risks due to excessive weight. Research Methods and Procedures: Using data from the Health and Retirement Study, a total of 9035 individuals 51 to 61 years old were analyzed by BMI category. The primary outcome measure was individuals’ reports about their own expectations of survival to age 75. Absolute and relative risks of survival were compared with published estimates of survival to age 75. Results: Consistently, higher levels of BMI were associated with lower self‐estimated survival probabilities. Differences relative to normal weight ranged from 4.9% (p < 0.01) for male nonsmokers to 8.8% (p < 0.001) for female nonsmokers. However, these differences were substantially less than those obtained from published survival curve estimates, suggesting that obese individuals tended to underestimate mortality risks. Discussion: Individuals appeared to underestimate the mortality risks of excessive weight; thus, knowledge campaigns about the risks of obesity should remain a top priority.     

Analysis of mortality metrics associated with a comprehensive range of disorders in Denmark, 2000 to 2018: A population-based cohort study

BackgroundThe provision of different types of mortality metrics (e.g., mortality rate ratios [MRRs] and life expectancy) allows the research community to access a more informative set of health metrics. The aim of this study was to provide a panel of mortality metrics associated with a comprehensive range of disorders and to design a web page to visualize all results.Methods and findingsIn a population-based cohort of all 7,378,598 persons living in Denmark at some point between 2000 and 2018, we identified individuals diagnosed at hospitals with 1,803 specific categories of disorders through the International Classification of Diseases-10th Revision (ICD-10) in the National Patient Register. Information on date and cause of death was obtained from the Registry of Causes of Death. For each of the disorders, a panel of epidemiological and mortality metrics was estimated, including incidence rates, age-of-onset distributions, MRRs, and differences in life expectancy (estimated as life years lost [LYLs]). Additionally, we examined models that adjusted for measures of air pollution to explore potential associations with MRRs. We focus on 39 general medical conditions to simplify the presentation of results, which cover 10 broad categories: circulatory, endocrine, pulmonary, gastrointestinal, urogenital, musculoskeletal, hematologic, mental, and neurologic conditions and cancer. A total of 3,676,694 males and 3,701,904 females were followed up for 101.7 million person-years. During the 19-year follow-up period, 1,034,273 persons (14.0%) died. For 37 of the 39 selected medical conditions, mortality rates were larger and life expectancy shorter compared to the Danish general population. For these 37 disorders, MRRs ranged from 1.09 (95% confidence interval [CI]: 1.09 to 1.10) for vision problems to 7.85 (7.77 to 7.93) for chronic liver disease, while LYLs ranged from 0.31 (0.14 to 0.47) years (approximately 16 weeks) for allergy to 17.05 (16.95 to 17.15) years for chronic liver disease. Adjustment for air pollution had very little impact on the estimates; however, a limitation of the study is the possibility that the association between the different disorders and mortality could be explained by other underlying factors associated with both the disorder and mortality.ConclusionsIn this study, we show estimates of incidence, age of onset, age of death, and mortality metrics (both MRRs and LYLs) for a comprehensive range of disorders. The interactive data visualization site (https://nbepi.com/atlas) allows more fine-grained analysis of the link between a range of disorders and key mortality estimates.

In a population-based study, Oleguer Plana-Ripoll and colleagues report on and develop an online resource to study mortality metrics and life expectancy associated with different health conditions among individuals living in Denmark.     

Marriage and mortality: a life table analysis

This paper examines the effects of age at marriage and differential mortality of males and females on the incidence of widowhood between the sexes. Abridged life tables constructed from marital status and death registration data of a rural area of Bangladesh for the period 1974-79 were used. The difference in life expectancy between males and females varies from 0.4 to 2.2 years at the ages 0 to 65 years and over. The mortality differentials show that the probabilities of a male or a female surviving the other spouse would be approximately the same, were there no other influence. But the incidence of widows is about ten times that of widowers. Other relevant factors, under a given regime of mortality, are age at marriage and age difference between husband and wife.     

The early bronze age graveyards of Franzhausen I, lower Austria. 2. Demographic analysis]

In a recent study of 714 graves of the Early Bronze Age cemetery, Franzhausen I, 658 individuals were demographically analysed. The masculinity rate and the mortality rate in the age groups were of similar order compared with estimates derived from other series of this period. On the base of a stationary population model, life tables were calculated showing life expectancy at birth to be 25.8 years and at the age of 20, 17.7 years. Also computed were: the crude death rate (Z = 38.8); and the population size (P = 31 or 65). The lack of infants were estimated by regressions (5q0 = 58%) and the results are discussed.     

Socioeconomic factors affecting the longevity of the Japanese population: a study for 1980 and 1985.

The effects of urbanisation, low income and rejuvenation of the population on life expectancy at birth and at 20, 40 and 65 years of age for males and females in Japan were examined twice, in 1980 and 1985. For males, urbanisation was the major factor determining life expectancy at birth and at age 20 years, and low income was the key determinant of decreased life expectancy except at 65 years of age. For females high income was the factor significantly decreasing life expectancy at 65 years of age in 1980, and rejuvenation of the population inversely influenced life expectancy except at birth in 1985. Life expectancy for all age groups in 1985 was significantly longer than in 1980 for both males and females.     

Maximum likelihood estimate of life expectancy in the prehistoric Jomon: Canine pulp volume reduction suggests a longer life expectancy than previously thought

Recent theoretical progress potentially refutes past claims that paleodemographic estimations are flawed by statistical problems, including age mimicry and sample bias due to differential preservation. The life expectancy at age 15 of the Jomon period prehistoric populace in Japan was initially estimated to have been ～16 years while a more recent analysis suggested 31.5 years. In this study, we provide alternative results based on a new methodology. The material comprises 234 mandibular canines from Jomon period skeletal remains and a reference sample of 363 mandibular canines of recent‐modern Japanese. Dental pulp reduction is used as the age‐indicator, which because of tooth durability is presumed to minimize the effect of differential preservation. Maximum likelihood estimation, which theoretically avoids age mimicry, was applied. Our methods also adjusted for the known pulp volume reduction rate among recent‐modern Japanese to provide a better fit for observations in the Jomon period sample. Without adjustment for the known rate in pulp volume reduction, estimates of Jomon life expectancy at age 15 were dubiously long. However, when the rate was adjusted, the estimate results in a value that falls within the range of modern hunter‐gatherers, with significantly better fit to the observations. The rate‐adjusted result of 32.2 years more likely represents the true life expectancy of the Jomon people at age 15, than the result without adjustment. Considering ～7% rate of antemortem loss of the mandibular canine observed in our Jomon period sample, actual life expectancy at age 15 may have been as high as ～35.3 years.     

Estimated life expectancy and risk of death from cancer by quartiles in the older Japanese population: 2010 vital statistics

Data on life expectancies and risk of death from cancer are essential information to have when making informed decisions about cancer screening and treatment options, but has never been presented in a way that is readily available to use for physicians in Japan. We provided estimates of life expectancies and predicted risk of death from seven most common types of cancer (lung, gastric, liver, colon, prostate, breast, and cervical) by quartiles for the older Japanese population above 50 years old, using 2010 life tables and cancer mortality statistics data. We found that there was a large difference in life expectancy between older persons in the upper and lower quartiles. Risk of death from breast cancer was low. By using this data, physicians can more accurately obtain life expectancy estimates by assessing which quartile the patient is most likely to fall under, and help patients make better informed decisions.     

Impact of Pregnancy-Related Deaths on Female Life Expectancy in Zambia: Application of Life Table Techniques to Census Data

Introduction

Since 2000, the world has been coalesced around efforts to reduce maternal mortality. However, few studies have estimated the significance of eliminating maternal deaths on female life expectancy. We estimated, based on census data, the potential gains in female life expectancy assuming complete elimination of pregnancy-related mortality in Zambia.

Methods

We used data on all-cause and pregnancy-related deaths of females aged 15–49 reported in the Zambia 2010 census, and evaluated, adjusted and smoothed them using existing and verified techniques. We used associated single decrement life tables, assuming complete elimination of pregnancy-related deaths to estimate the potential gains in female life expectancy at birth, at age 15, and over the ages 15–49. We compared these gains with the gains from eliminating deaths from accidents, injury, violence and suicide.

Results

Complete elimination of pregnancy-related deaths would extend life expectancy at birth among Zambian women by 1.35 years and life expectancy at age 15 by 1.65 years. In rural areas, this would be 1.69 years and 2.19 years, respectively, and in urban areas, 0.78 years and 0.85 years. An additional 0.72 years would be spent in the reproductive age group 15–49; 1.00 years in rural areas and 0.35 years in urban areas. Eliminating deaths from accidents, injury, suicide and violence among women aged 15–49 would cumulatively contribute 0.55 years to female life expectancy at birth.

Conclusion

Eliminating pregnancy-related mortality would extend female life expectancy in Zambia substantially, with more gains among adolescents and females in rural areas. The application of life table techniques to census data proved very valuable, although rigorous evaluation and adjustment of reported deaths and age was necessary to attain plausible estimates. The collection of detailed high quality cause-specific mortality data in future censuses is indispensable.     

Estimating Attributable Life Expectancy Under the Proportional Mean Residual Life Model

In population-based health research, the so-called population attributable fraction is an important quantity that calculates the percentage of excess risk of morbidity and mortality associated with modifiable risk factors for a given population. While the concept of “risk” is usually measured by event probabilities, in practice it may be of a more direct interest to know the excess life expectancy associated with the modifiable risk factors instead, particularly when mortality is of the ultimate concern. In this paper, we thus propose to study a novel quantity, termed “attributable life expectancy,” to measure the population attributable fraction of life expectancy. We further develop a model-based approach for the attributable life expectancy under the Oakes–Dasu proportional mean residual life model, and establish its asymptotic properties for inferences. Numerical studies that include Monte-Carlo simulations and an actual analysis of the mortality associated with smoking cessation in an Asia Cohort Consortium are conducted to evaluate the performance of our proposed method.

     

Effect of search method and age class on mark-recapture parameter estimation in a population of red-backed salamanders

Mark-recapture methods are generally considered to more accurately reflect population trends than count data, which is especially important for indicator species. Terrestrial salamanders are often used as indicators of forest ecosystem health and may be monitored through diurnal cover object searches or nocturnal activity searches. Our goal was to determine whether search method affected encounter probabilities, whether these probabilities differed between age classes, and whether the inclusion of search method in mark-recapture models affected abundance estimates. We used program MARK to analyze 3 years of red-backed salamander (Plethodon cinereus) mark-recapture data using Pollock’s robust design taken from a 144 m² plot. Initial encounter probabilities during night searches were consistently greater than during diurnal cover object searches. As a result, inclusion of search method in models sometimes affected abundance estimates. There was no difference between adult and juvenile encounter probabilities nor were abundance estimates affected by inclusion of age class, but there was yearly variation in the juvenile abundance estimates. For these reasons, we recommend that sampling of terrestrial salamanders include nocturnal activity searches and be conducted over multiple years. Monitoring programs of other species should take into account whether the selected search method(s) may be more likely to sample different subsets of the population of interest and how this may restrict their inferences.