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

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.

A multistate joint model for interval-censored event-history data subject to within-unit clustering and informative missingness, with application to neurocysticercosis research

We propose a multistate joint model to analyze interval-censored event-history data subject to within-unit clustering and nonignorable missing data. The model is motivated by a study of the neurocysticercosis (NC) cyst evolution at the cyst-level, taking into account the multiple cysts phases with intermittent missing data and loss to follow-up, as well as the intra-brain clustering of observations made on a predefined data collection schedule. Of particular interest in this study is the description of the process leading to cyst resolution, and whether this process varies by antiparasitic treatment. The model uses shared random effects to account for within-brain correlation and to explain the hidden heterogeneity governing the missing data mechanism. We developed a likelihood-based method using a Monte Carlo EM algorithm for the inference. The practical utility of the methods is illustrated using data from a randomized controlled trial on the effect of antiparasitic treatment with albendazole on NC cysts among patients from six hospitals in Ecuador. Simulation results demonstrate that the proposed methods perform well in the finite sample and misspecified models that ignore the data complexities could lead to substantial biases.

Cognitive functioning transitions, health expectancies, and inequalities among elderly people in China: A nationwide longitudinal study

OBJECTIVE

In China, cognitive impairment has become a huge challenge owing to the rapid aging process. We investigate cognitive health expectancy and potential factors leading to inequalities of cognitive health for Chinese older people.

METHODS

The study included 19 943 participants aged 65 to 95 at the first observation in Chinese Longitudinal Healthy Longevity Survey collected during 2002-2014. Cognitive impairment was categorized into none, mild, and severe by the score of cMMSE. Multistate models based on continuous-time Markov process were applied to calculate cognitive health expectancies and estimate hazard ratio from no impairment to impairment for potential factors.

RESULTS

Urban women and men aged 65 were expected to spend 31.18% and 19.82% of their remaining 17.46 and 15.45 years with cognitive impairment; meanwhile, rural women and men aged 65 were expected to spend 35.31% and 21.39% of their remaining 16.73 and 14.87 years with cognitive impairment. Women achieving lower educational attainment (HR_1-6 years  = 0.78, 95% CI, 0.71-0.87; HR_7+ years  = 0.59, 95% CI, 0.49-0.70) than men and rural residents having less access to medical service (HR = 0.79, 95% CI, 0.68-0.92) and doing less regular exercise (HR = 0.87, 95% CI, 0.80-0.96) than urban people caused the differences of cognitive health for genders and regions.

CONCLUSIONS

Women and rural people experience less cognitive health expectancies compared with their counterparts, respectively. Chinese government should pay more attention to rural women and make efforts to reduce the inequalities of cognitive health by increasing opportunities of education for women and improving access to medical service and healthy lifestyle for rural people.

Projections of health indicators for chronic disease under a semi-Markov assumption

Chronic diseases are a growing public health problem due to the population aging. Their economic, social and demographic burden will worsen in years to come. Up to now, the method used to provide projections and assess the future disease burden makes a non-homogeneous Markov assumption in an illness-death model. Both age and calendar year have been taken into account in all parameter estimations, but the time spent with the disease was not considered. This work develops the method with a semi-Markov assumption to model mortality among the diseased and considering the time spent with the disease. The method is applied to estimate several health indicators for dementia in France in 2030. We find that mortality among the individuals with dementia depends on age, calendar year and disease duration, and it is greater for men than for women at all ages. The projections for 2030 suggest a 27% increase of the number of dementia cases. The model proposed in this work has flexible assumptions that make it adaptable to provide projections for various diseases.

Impact of intervention targeting risk factors on chronic disease burden

The aging of the population is accompanied by a sharp rise of chronic disease prevalences, such as dementia. These diseases generally cannot be prevented or cured and persist over time, with a progressive deterioration of health, requiring specific care. To reduce the burden of these diseases, it is appropriate to propose interventions targeting disease risk factors, but the association between most of these risk factors and mortality makes it difficult to anticipate the potential impact of such interventions. A method was previously proposed to estimate changes in disease prevalence following an intervention targeting subjects at a given age where the incidence of the disease is supposed to be null. Here, we propose a general framework to make projections for life expectancies with and without the disease, the age at onset, and the lifelong probability of the disease, and to evaluate the consequences of preventive interventions targeting risk factors on these various measures of disease burden. The methodology takes into account the mortality trend over calendar time and age in both healthy and diseased subjects, and the change in mortality due to the intervention. The method is applied to make projections for dementia in 2030 according to several scenarios of public health interventions.

The methods and materials of health expectancy

Health expectancy is an essential population health indicator and can be used to monitor changes and/or assess differences in population health. This article provides a brief overview of health expectancy and the issues to be considered in operationalizing and interpreting health expectancy. The article introduces the concept of health expectancy, discusses measures used to compute health expectancy, and methods of calculation. The discussion of measures relates health expectancy to the concept of "health" and clarifies that values of health expectancy depend on how "health" is defined. Software available to compute health expectancy including IMaCh, SPACE and ELECT are also briefly introduced.

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.

Active cognitive lifestyle is associated with positive cognitive health transitions and compression of morbidity from age sixty-five

BACKGROUND

Three factors commonly used as measures of cognitive lifestyle are education, occupation, and social engagement. This study determined the relative importance of each variable to long term cognitive health in those with and without severe cognitive impairment.

METHODS

Data came from 12,470 participants from a multi-centre population-based cohort (Medical Research Council Cognitive Function and Ageing Study). Respondents were aged 65 years and over and were followed-up over 16 years. Cognitive states of no impairment, slight impairment, and moderate/severe impairment were defined, based on scores from the Mini-Mental State Examination. Multi-state modelling was used to investigate links between component cognitive lifestyle variables, cognitive state transitions over time, and death.

RESULTS

Higher educational attainment and a more complex mid-life occupation were associated with a lower risk of moving from a non-impaired to a slightly impaired state (hazard ratios 0.5 and 0.8), but with increased mortality from a severely impaired state (1.3 and 1.1). More socially engaged individuals had a decreased risk of moving from a slightly impaired state to a moderately/severely impaired state (0.7). All three cognitive lifestyle variables were linked to an increased chance of cognitive recovery back to the non-impaired state.

CONCLUSIONS

In those without severe cognitive impairment, different aspects of cognitive lifestyle predict positive cognitive transitions over time, and in those with severe cognitive impairment, a reduced life-expectancy. An active cognitive lifestyle is therefore linked to compression of cognitive morbidity in late life.

A semi-Markov model for stroke with piecewise-constant hazards in the presence of left, right and interval censoring

This paper presents a parametric method of fitting semi-Markov models with piecewise-constant hazards in the presence of left, right and interval censoring. We investigate transition intensities in a three-state illness–death model with no recovery. We relax the Markov assumption by adjusting the intensity for the transition from state 2 (illness) to state 3 (death) for the time spent in state 2 through a time-varying covariate. This involves the exact time of the transition from state 1 (healthy) to state 2. When the data are subject to left or interval censoring, this time is unknown. In the estimation of the likelihood, we take into account interval censoring by integrating out all possible times for the transition from state 1 to state 2. For left censoring, we use an Expectation–Maximisation inspired algorithm. A simulation study reflects the performance of the method. The proposed combination of statistical procedures provides great flexibility. We illustrate the method in an application by using data on stroke onset for the older population from the UK Medical Research Council Cognitive Function and Ageing Study. Copyright © 2012 John Wiley & Sons, Ltd.