Active life expectancy from annual follow-up data with missing responses

The association between multimorbidity and mobility disability-free life expectancy in adults aged 85 years and over: A modelling study in the Newcastle 85+ cohort

BACKGROUND

Mobility disability is predictive of further functional decline and can itself compromise older people's capacity (and preference) to live independently. The world's population is also ageing, and multimorbidity is the norm in those aged ≥85. What is unclear in this age group, is the influence of multimorbidity on (a) transitions in mobility disability and (b) mobility disability-free life expectancy (mobDFLE).

METHODS AND FINDINGS

Using multistate modelling in an inception cohort of 714 85-year-olds followed over a 10-year period (aged 85 in 2006 to 95 in 2016), we investigated the association between increasing numbers of long-term conditions and (1) mobility disability incidence, (2) recovery from mobility disability and (3) death, and then explored how this shaped the remaining life expectancy free from mobility disability at age 85. Models were adjusted for age, sex, disease group count, BMI and education. We defined mobility disability based on participants' self-reported ability to get around the house, go up and down stairs/steps, and walk at least 400 yards; participants were defined as having mobility disability if, for one or more these activities, they had any difficulty with them or could not perform them. Data were drawn from the Newcastle 85+ Study: a longitudinal population-based cohort study that recruited community-dwelling and institutionalised individuals from Newcastle upon Tyne and North Tyneside general practices. We observed that each additional disease was associated with a 16% increased risk of incident mobility disability (hazard ratio (HR) 1.16, 95% confidence interval (CI): 1.07 to 1.25, p < 0.001), a 26% decrease in the chance of recovery from this state (HR 0.74, 95% CI: 0.63 to 0.86, p < 0.001), and a 12% increased risk of death with mobility disability (HR: 1.12, 95% CI: 1.07- to .17, p < 0.001). This translated to reductions in mobDFLE with increasing numbers of long-term conditions. However, residual and unmeasured confounding cannot be excluded from these analyses, and there may have been unobserved transitions to/from mobility disability between interviews and prior to death.

CONCLUSIONS

We suggest 2 implications from this work. (1) Our findings support calls for a greater focus on the prevention of multimorbidity as populations age. (2) As more time spent with mobility disability could potentially lead to greater care needs, maintaining independence with increasing age should also be a key focus for health/social care and reablement services.

Mixed evidence for the compression of morbidity hypothesis for smoking elimination-a systematic literature review

BACKGROUND

There is debate around the composition of life years gained from smoking elimination. The aim of this study was to conduct a systematic review of the literature to synthesize existing evidence on the effect of smoking status on health expectancy and to examine whether smoking elimination leads to compression of morbidity.

METHODS

Five databases were systematically searched for peer-reviewed articles. Studies that presented quantitative estimates of health expectancy for smokers and non-/never-smokers were eligible for inclusion. Studies were searched, selected and reviewed by two reviewers who extracted the relevant data and assessed the risk of bias of the included articles independently.

RESULTS

The search identified 2491 unique records, whereof 20 articles were eligible for inclusion (including 26 cohorts). The indicators used to measure health included disability/activity limitations (n=9), health-related quality of life (EQ-5D) (n=2), weighted disabilities (n=1), self-rated health (n=9), chronic diseases (n=6), cardiovascular diseases (n=4) and cognitive impairment (n=1). Available evidence showed consistently that non-/never-smokers experience more healthy life years throughout their lives than smokers. Findings were inconsistent on the effect of smoking on the absolute number of unhealthy life years. Findings concerning the time proportionally spent unhealthy were less heterogeneous: nearly all included articles reported that non-/never-smokers experience relatively less unhealthy life years (e.g. relative compression of morbidity).

CONCLUSIONS

Support for the relative compression of morbidity due to smoking elimination was evident. Further research is needed into the absolute compression of morbidity hypothesis since current evidence is mixed, and methodology of studies needs to be harmonized.

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.

Estimation of life expectancies using continuous-time multi-state models

BACKGROUND AND OBJECTIVE

There is increasing interest in multi-state modelling of health-related stochastic processes. Given a fitted multi-state model with one death state, it is possible to estimate state-specific and marginal life expectancies. This paper introduces methods and new software for computing these expectancies.

METHODS

The definition of state-specific life expectancy given current age is an extension of mean survival in standard survival analysis. The computation involves the estimated parameters of a fitted multi-state model, and numerical integration. The new R package elect provides user-friendly functions to do the computation in the R software.

RESULTS

The estimation of life expectancies is explained and illustrated using the elect package. Functions are presented to explore the data, to estimate the life expectancies, and to present results.

CONCLUSIONS

State-specific life expectancies provide a communicable representation of health-related processes. The availability and explanation of the elect package will help researchers to compute life expectancies and to present their findings in an assessable way.

Sex, Race, and Age Differences in Observed Years of Life, Healthy Life, and Able Life among Older Adults in The Cardiovascular Health Study

Objective: Longevity fails to account for health and functional status during aging. We sought to quantify differences in years of total life, years of healthy life, and years of able life among groups defined by age, sex, and race. Design: Primary analysis of a cohort study. Setting: 18 years of annual evaluations in four U.S. communities. Participants: 5888 men and women aged 65 and older. Measurements: Years of life were calculated as the time from enrollment to death or 18 years. Years of total, healthy, and able life were determined from self-report during annual or semi-annual contacts. Cumulative years were summed across each of the age and sex groups. Results: White women had the best outcomes for all three measures, followed by white men, non-white women, and non-white men. For example, at the mean age of 73, a white female participant could expect 12.9 years of life, 8.9 of healthy life and 9.5 of able life, while a non-white female could expect 12.6, 7.0, and 8.0 years, respectively. A white male could expect 11.2, 8.1, and 8.9 years of life, healthy life, and able life, and a non-white male 10.3, 6.2, and 7.9 years. Regardless of starting age, individuals of the same race and sex groups spent similar amounts (not proportions) of time in an unhealthy or unable state. Conclusion: Gender had a greater effect on longevity than did race, but race had a greater effect on years spent healthy or able. The mean number of years spent in an unable or sick state was surprisingly independent of the lifespan.

A Systematic Literature Review of Studies Analyzing Inequalities in Health Expectancy among the Older Population

Aim

To collect, organize and appraise evidence of socioeconomic and demographic inequalities in health and mortality among the older population using a summary measure of population health: Health Expectancy.

Methods

A systematic literature review was conducted. Literature published in English before November 2014 was searched via two possible sources: three electronic databases (Web of Science, Medline and Embase), and references in selected articles. The search was developed combining terms referring to outcome, exposure and participants, consisting in health expectancy, socioeconomic and demographic groups, and older population, respectively.

Results

Of 256 references identified, 90 met the inclusion criteria. Six references were added after searching reference lists of included articles. Thirty-three studies were focused only on gender-based inequalities; the remaining sixty-three considered gender along with other exposures. Findings were organized according to two leading perspectives: the type of inequalities considered and the health indicators chosen to measure health expectancy. Evidence of gender-based differentials and a socioeconomic gradient were found in all studies. A remarkable heterogeneity in the choice of health indicators used to compute health expectancy emerged as well as a non-uniform way of defining same health conditions.

Conclusions

Health expectancy is a useful and convenient measure to monitor and assess the quality of ageing and compare different groups and populations. This review showed a general agreement of results obtained in different studies with regard to the existence of inequalities associated with several factors, such as gender, education, behaviors, and race. However, the lack of a standardized definition of health expectancy limits its comparability across studies. The need of conceiving health expectancy as a comparable and repeatable measure was highlighted as fundamental to make it an informative instrument for policy makers.

Predictions in an illness-death model

Multi-state models allow subjects to move among a finite number of states during a follow-up period. Most often, the objects of study are the transition intensities. The impact of covariates on them can also be studied by specifying regression models. Thus, estimation in multi-state models is usually focused on the transition intensities (or the cumulative transition intensities) and on the regression parameters. However, from a clinical or epidemiological point of view, other quantities could provide additional information and may be more relevant to answer practical questions. For example, given a set of covariates for a subject, it may be of interest to estimate the probability to experience a future event or the expected time without any event. To address these kinds of issues, we need to estimate quantities such as transition probabilities, cumulative probabilities and life expectancies. The purpose of this paper is to review a large number of these quantities in an illness-death model which is perhaps the most common multi-state model in the medical literature, and to propose a way to estimate them in addition to the transition intensities and the regression parameters. An illustration is given using interval-censored data from a large cohort study on cognitive ageing.

Higher education delays and shortens cognitive impairment: a multistate life table analysis of the US Health and Retirement Study

Improved health may extend or shorten the duration of cognitive impairment by postponing incidence or death. We assess the duration of cognitive impairment in the US Health and Retirement Study (1992–2004) by self reported BMI, smoking and levels of education in men and women and three ethnic groups. We define multistate life tables by the transition rates to cognitive impairment, recovery and death and estimate Cox proportional hazard ratios for the studied determinants. 95% confidence intervals are obtained by bootstrapping. 55 year old white men and women expect to live 25.4 and 30.0 years, of which 1.7 [95% confidence intervals 1.5; 1.9] years and 2.7 [2.4; 2.9] years with cognitive impairment. Both black men and women live 3.7 [2.9; 4.5] years longer with cognitive impairment than whites, Hispanic men and women 3.2 [1.9; 4.6] and 5.8 [4.2; 7.5] years. BMI makes no difference. Smoking decreases the duration of cognitive impairment with 0.8 [0.4; 1.3] years by high mortality. Highly educated men and women live longer, but 1.6 years [1.1; 2.2] and 1.9 years [1.6; 2.6] shorter with cognitive impairment than lowly educated men and women. The effect of education is more pronounced among ethnic minorities. Higher life expectancy goes together with a longer period of cognitive impairment, but not for higher levels of education: that extends life in good cognitive health but shortens the period of cognitive impairment. The increased duration of cognitive impairment in minority ethnic groups needs further study, also in Europe.

Estimating stroke-free and total life expectancy in the presence of non-ignorable missing values

A continuous time three-state model with time-dependent transition intensities is formulated to describe transitions between healthy and unhealthy states before death. By using time continuously, known death times can be taken into account. To deal with possible non-ignorable missing states, a selection model is proposed for the joint distribution of both the state and whether or not the state is observed. To estimate total life expectancy and its subdivision into life expectancy in health and ill health, the three-state model is extrapolated beyond the follow-up of the study. Estimation of life expectancies is illustrated by analysing data from a longitudinal study of aging where individuals are in a state of ill health if they have ever experienced a stroke. Results for the selection model are compared with results for a model where states are assumed to be missing at random and with results for a model that ignores missing states.

Joint modeling of self-rated health and changes in physical functioning

Self-rated health is an important indicator of future morbidity and mortality. Past research has indicated that self-rated health is related to both levels of and changes in physical functioning. However, no previous study has jointly modeled longitudinal functional status and self-rated health trajectories. We propose a joint model for self-rated health and physical functioning that describes the relationship between perceptions of health and the rate of change of physical functioning or disability. Our joint model uses a non-homogeneous Markov process for discrete physical functioning states and connects this to a logistic regression model for "healthy" versus "unhealthy" self-rated health through parameters of the physical functioning model. We use simulation studies to establish finite sample properties of our estimators and show that this model is robust to misspecification of the functional form of the relationship between self-rated health and rate of change of physical functioning. We also show that our joint model performs better than an empirical model based on observed changes in functional status. We apply our joint model to data from the Cardiovascular Health Study (CHS), a large, multi-center, longitudinal study of older adults. Our analysis indicates that self-rated health is associated both with level of functioning as indicated by difficulty with activities of daily living (ADL) and instrumental activities of daily living (IADL), and the risk of increasing difficulty with ADLs and IADLs.

Estimating dementia-free life expectancy for Parkinson's patients using Bayesian inference and microsimulation

Interval-censored longitudinal data taken from a Norwegian study of individuals with Parkinson's disease are investigated with respect to the onset of dementia. Of interest are risk factors for dementia and the subdivision of total life expectancy (LE) into LE with and without dementia. To estimate LEs using extrapolation, a parametric continuous-time 3-state illness–death Markov model is presented in a Bayesian framework. The framework is well suited to allow for heterogeneity via random effects and to investigate additional computation using model parameters. In the estimation of LEs, microsimulation is used to take into account random effects. Intensities of moving between the states are allowed to change in a piecewise-constant fashion by linking them to age as a time-dependent covariate. Possible right censoring at the end of the follow-up can be incorporated. The model is applicable in many situations where individuals are followed over a long time period. In describing how a disease develops over time, the model can help to predict future need for health care.

Modeling transition rates using panel current-status data: how serious is the bias?

Studies of disability dynamics and active life expectancy often rely on transition rates or probabilities that are estimated using panel survey data in which respondents report on current health or functional status. If respondents are contacted at intervals of one or two years, then relatively short periods of disability or recovery between surveys may be missed. Much published research that uses such data assumes that there are no unrecorded transitions, applying event-history techniques to estimate transition rates. In recent years, a different approach based on embedded Markov chains has received growing use. We assessed the performance of both approaches, using as a criterion their ability to reproduce the parameters of a "true" model based on panel data collected at one-month intervals. Neither of the widely used approaches performs particularly well, and neither is uniformly superior to the other.

Empirical estimation of life expectancy from large clinical trials: use of left-truncated, right-censored survival analysis methodology

In the current era of ever-increasing health care costs, economic analyses are an essential component in the comprehensive evaluation of new medical interventions. Cost-effectiveness analysis (CEA)--the most common form of economic analysis used in medicine--aids policy-makers in determining how to allocate finite health care dollars among possible alternative therapies. CEA relates the incremental benefits of a new technology to its incremental costs in a cost-effectiveness (CE) ratio. Although the generally agreed-upon standard of presentation for the CE ratio is the lifetime perspective (incremental lifetime cost to add one life year), this perspective presents an obvious challenge to the statistical analyst. Most large clinical trials collect limited follow-up data, and yet their findings form the basis of therapeutic recommendations that often extend far beyond the limits of the empirical data. Although clinical practice guidelines do not yet require explicit modeling to examine the long-term implications of their recommendations, health policy analyses routinely rely upon such extrapolations. This paper describes methods for using empirical patient-level data to extrapolate survival in large clinical trials and cohorts beyond a limited follow-up period in which most patients remain alive in order to estimate the entire survival distribution for a cohort of patients. We accomplish this task through a novel combination of models that estimate the hazard rate not only as a function of time but also as a function of patient age. Extrapolation of survival beyond a limited time frame is made possible by capitalizing on the extensive latitude of survival information available across the range of ages represented in the data. Variations in approach are presented, and issues arising in these analyses are discussed. The proposed methodology is developed, applied, and evaluated in both a large clinical trial cohort with 5-year follow-up on over 23,000 patients and a large observational database with long-term follow-up on over 4000 patients.

Improving knowledge about disability transitions by adding retrospective information to panel surveys. Population health metrics

Background

Panel data are often used to estimate key measures of public health, such as years lived with and without disability. Panel surveys commonly measure disability at intervals of one or two years, and occasionally more than two. It is likely that these intervals often include unreported changes in functional status. Unreported changes may bias estimates of disability transition probabilities, which are commonly used to estimate years lived with and without disability. Most surveys do not ask participants about periods with and without disability in the time since they last responded to the survey. We examined a way to improve the usefulness of panel surveys and our understanding of disability processes, by eliciting retrospective disability information.

Methods

Data were from the United States' National Long Term Care Survey. At each wave, this survey asks disabled respondents how long they have been disabled. We tested whether estimates of probabilities predicting changes in disability status can be improved by making use of this retrospective disability information. Methods included embedded Markov Chain analysis, microsimulation, and the Hausman specification test.

Results

Estimates based on data that include retrospective information are significantly different from those that use only the more limited information that is contemporaneous to the surveys. They are also more efficient. At age 65, all estimated probabilities for becoming disabled were higher when retrospective information was used, and all probabilities for remaining disabled were lower. Microsimulation revealed that using retrospective information increased the number of functional status transitions. For example, for women the mean number of transitions from nondisabled to disabled or dead was 52.7% greater when retrospective information was added to the analysis.

Conclusion

Our results suggest that the value of future panel studies for estimating transitions in disability could be notably enhanced by adding a small number of questions asking respondents for details about their disabilities–and lack of disabilities–in the period since a preceding survey wave. Information provided by such questions could substantially improve both the measurement of disability histories and estimates of disability processes.

Sex-related differences in the length of disability prior to death in older persons

BACKGROUND AND AIMS

It is acknowledged that, in spite of their generally worse health, women live longer than men. However, whether women also enjoy longer disability-free lives is still unclear. Using data from a representative, Italian cohort followed for 6 years, this study aimed at estimating differences between men and women in the age of disability onset and in total survival.

METHODS

In 1989, 651 persons aged > or = 65 years were interviewed and their medical status was assessed by a geriatrician. In 1995, the time of onset of disability was reconstructed by re-interviewing 392 survivors and collecting proxy information for 201 subjects who had died. No information was available for 58 subjects who refused to be re-interviewed or were lost to follow-up. Data on changes in functional status were also collected by proxy interview for 34 additional persons who had died during the follow-up period, although they had not been originally interviewed at baseline.

RESULTS

Of the 235 deaths, 113 were men and 122 were women. On average, the age at death was 3.5 years higher among women than among men. However, the age at onset of disability was similar in the two sexes. In survival analysis in which age was the time variable, women were as likely as men to develop disability, but significantly less likely to die over the follow-up period.

CONCLUSIONS

Compared with men, women experience longer disability before death. This may be due to sex-related differences in the lifetime prevalence of lethal vs. disabling diseases.