Matrix methods in health demography: a new approach to the stochastic analysis of healthy longevity and DALYs

Flexible transition timing in discrete-time multistate life tables using Markov chains with rewards

Discrete-time multistate life tables are attractive because they are easier to understand and apply in comparison with their continuous-time counterparts. While such models are based on a discrete time grid, it is often useful to calculate derived magnitudes (e.g. state occupation times), under assumptions which posit that transitions take place at other times, such as mid-period. Unfortunately, currently available models allow very few choices about transition timing. We propose the use of Markov chains with rewards as a general way of incorporating information on the timing of transitions into the model. We illustrate the usefulness of rewards-based multistate life tables by estimating working life expectancies using different retirement transition timings. We also demonstrate that for the single-state case, the rewards approach matches traditional life-table methods exactly. Finally, we provide code to replicate all results from the paper plus R and Stata packages for general use of the method proposed.

Efficacy of cognitive training on executive functions in healthy older adults: a systematic review with meta-analysis of randomized controlled trials

OBJECTIVE

Systematically review randomized controlled trials on the efficacy of cognitive training on executive functions in healthy older people.

MEASURES

The outcome measures were related to inhibitory control, working memory, and cognitive flexibility.

RESULTS

Thirty-one trials were included in the systematic review and thirteen trials in the meta-analysis. In the overall analysis, the cognitive training enhanced inhibitory control when measured by the Stroop task (p < .001, d = 1.64) and working memory when measured by the Corsi Block task (p = .002, d = .16). A marginal significance was found for working memory in the Digit Span task - Forward (p = .06, d = .92). However, cognitive training did not enhance inhibitory control when measured by the Go/No-Go task (p = .76, d = .59), working memory when measured by the Digit Span - Backward (p = .72, d = .95) and N-Back (p = .10, d = .26) tasks, and cognitive flexibility when measured by Trail Making - Part B (p = .08, d = .27) and Semantic Fluency (p = .49, d = .06) tasks.

CONCLUSION

Mixed evidence was found for inhibitory control and working memory; cognitive flexibility showed no evidence of improvement.

Racial, Ethnic, Nativity, and Educational Disparities in Cognitive Impairment and Activity Limitations in the United States, 1998-2016

Despite extensive research on cognitive impairment and limitations in basic activities of daily living, no study has investigated the burden of their co-occurrence (co-impairment). Using the Health and Retirement Study data and incidence-based multistate models, we study the population burden of co-impairment using three key indicators: mean age at onset, lifetime risk, and health expectancy. We examine patterns by gender, race, ethnicity, nativity, education, and their interactions for U.S. residents aged 50-100. Furthermore, we analyze what fractions of racial, ethnic, and nativity disparities in co-impairment are attributable to inequalities in educational attainment. Results reveal that an estimated 56% of women and 41% of men aged 50 will experience co-impairment in their remaining life expectancy. Men experience an earlier onset of co-impairment than women (74 vs. 77 years), and women live longer in co-impairment than men (3.4 vs. 1.9 years). Individuals who are Black, Latinx, and lower educated, especially those experiencing intersecting disadvantages, have substantially higher lifetime risk of co-impairment, earlier co-impairment onset, and longer life in co-impairment than their counterparts. Up to 75% of racial, ethnic, and nativity disparity is attributable to inequality in educational attainment. This study provides novel insights into the burden of co-impairment and offers evidence of dramatic disparities in the older U.S. population.

Well-Being Adjusted Health Expectancy: A New Summary Measure of Population Health

We propose a new summary measure of population health (SMPH), the well-being-adjusted health expectancy (WAHE). WAHE belongs to a subgroup of health-adjusted life expectancy indicators and gives the number of life years equivalent to full health. WAHE combines health and mortality information into a single indicator with weights that quantify the reduction in well-being associated with decreased health. WAHE's advantage over other SMPHs lies in its ability to differentiate between the consequences of health limitations at various levels of severity and its transparent, simple valuation function. Following the guidelines of a Committee on Summary Measures of Population Health, we discuss WAHE's validity, universality, feasibility sensitivity and ensure its reproducibility. We evaluate WAHE's performance compared to life expectancy, the most commonly used indicators of health expectancy (HE) and disability-adjusted life expectancy (DALE) in an empirical application for 29 European countries. Data on health and well-being are taken from the 2018 EU-SILC, and the life tables are from Eurostat. DALE is taken from the database of the Global Burden of Disease Programme. WAHE's sensitivity to univariate and multivariate state specifications is studied using the three Minimum European Health Module health dimensions: chronic morbidity, limitations in activities of daily living, and self-rated health. The empirical tests of the indicators' correspondence reveal that WAHE has the strongest correlation with the other SMPHs. Moreover, WAHE estimates are in agreement with all other SMPHs. Additionally, WAHE and all other SMPHs form a group of reliable indicators for studying population health in European countries. Finally, WAHE estimates are robust, regardless of whether health is defined across one or multiple simultaneous dimensions of health. We conclude that WAHE is a useful and reliable indicator of population health and performs at least as well as other commonly used SMPHs.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10680-022-09628-1.

Estimating the number and length of episodes in disability using a Markov chain approach

Background

Markov models are a key tool for calculating expected time spent in a state, such as active life expectancy and disabled life expectancy. In reality, individuals often enter and exit states recurrently, but standard analytical approaches are not able to describe this dynamic. We develop an analytical matrix approach to calculating the expected number and length of episodes spent in a state.

Methods

The approach we propose is based on Markov chains with rewards. It allows us to identify the number of entries into a state and to calculate the average length of episodes as total time in a state divided by the number of entries. For sampling variance estimation, we employ the block bootstrap. Two case studies that are based on published literature illustrate how our methods can provide new insights into disability dynamics.

Results

The first application uses a classic textbook example on prednisone treatment and liver functioning among liver cirrhosis patients. We replicate well-known results of no association between treatment and survival or recovery. Our analysis of the episodes of normal liver functioning delivers the new insight that the treatment reduced the likelihood of relapse and extended episodes of normal liver functioning. The second application assesses frailty and disability among elderly people. We replicate the prior finding that frail individuals have longer life expectancy in disability. As a novel finding, we document that frail individuals experience three times as many episodes of disability that were on average twice as long as the episodes of nonfrail individuals.

Conclusions

We provide a simple analytical approach for calculating the number and length of episodes in Markov chain models. The results allow a description of the transition dynamics that goes beyond the results that can be obtained using standard tools for Markov chains. Empirical applications using published data illustrate how the new method is helpful in unraveling the dynamics of the modeled process.

Estimating lifetime malnourished period and its statistics based on the concept of Markov chain with reward

Malnutrition among women, accessed through body mass index, has great consequences for achieving key national targets. This study introduces the concept of lifetime malnourished period (LMP): the number of years a woman would remain malnourished, either as underweight or overweight given that she is currently malnourished, and its measures of variation. Markov chain with rewards was used to compute the moments of LMP based on age-specific mortality rates and proportion of women of reproductive age that were either underweight or overweight using data from the 2013 Nigeria Demographic and Health Survey. Each of the two malnutrition status was treated as a Bernoulli-distributed reward with probability taken as the proportion of overweight or underweight women at specific age. Findings indicate that the average LMP for an underweight woman in Nigeria at age 15 years is 2.3 years but 5.8 for overweight. The remaining LMP for underweight is lower among women who attain higher level of education than for those with no or primary level of education with standard deviation reducing with age. Further, we found overweight women from the richest households and those from urban areas to have longer years of remaining in that state of health than their other counterparts, and that longevity contributes more to the variance in LMP for overweight than for underweight women.

Variance as a life history outcome: Sensitivity analysis of the contributions of stochasticity and heterogeneity

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Individuals vary in traits or in luck; both cause variance in life history outcomes.

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The variance components are calculated from a multistate group-stage cohort model.

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Sensitivity analysis shows how variance components relate to demographic parameters.

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Both mortality and fertility affect the variance components.

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Effects depend on life history timing, and the nature and mixture of differences.

Variance in life history outcomes among individuals is a requirement for natural selection, and a determinant of the ecological dynamics of populations. Heterogeneity among individuals will cause such variance, but so will the inherently stochastic nature of their demography. The relative contributions of these variance components – stochasticity and heterogeneity – to life history outcomes are presented here in a general, demographic calculation. A general formulation of sensitivity analysis is provided for the relationship between the variance components and the demographic rates within the life cycle. We illustrate these novel methods with two examples; the variance in longevity within and between frailty groups in a laboratory population of fruit flies, and the variance in lifetime reproductive output within and between initial environment states in a perennial herb in a stochastic fire environment. In fruit flies, an increase in mortality would increase the variance due to stochasticity and reduce that due to heterogeneity. In the plant example, increasing mortality reduces, and increasing fertility increases both variance components. Sensitivity analyses such as these can provide a powerful tool in identifying patterns among life history stages and heterogeneity groups and their contributions to variance in life history outcomes.