The Analysis of Panel Data under a Markov Assumption

A discrete approximation method for modeling interval-censored multistate data

Many longitudinal studies are designed to monitor participants for major events related to the progression of diseases. Data arising from such longitudinal studies are usually subject to interval censoring since the events are only known to occur between two monitoring visits. In this work, we propose a new method to handle interval-censored multistate data within a proportional hazards model framework where the hazard rate of events is modeled by a nonparametric function of time and the covariates affect the hazard rate proportionally. The main idea of this method is to simplify the likelihood functions of a discrete-time multistate model through an approximation and the application of data augmentation techniques, where the assumed presence of censored information facilitates a simpler parameterization. Then the expectation-maximization algorithm is used to estimate the parameters in the model. The performance of the proposed method is evaluated by numerical studies. Finally, the method is employed to analyze a dataset on tracking the advancement of coronary allograft vasculopathy following heart transplantation.

Natural History of Type 2 Diabetes in Indians: Time to Progression

OBJECTIVE

To describe the natural history of diabetes in Indians.

RESEARCH DESIGN AND METHODS

Data are from participants older than 20 years in the Centre for Cardiometabolic Risk Reduction in South Asia longitudinal study. Glycemic states were defined per American Diabetes Association criteria. Markov models were used to estimate annual transition probabilities and sojourn time through states.

RESULTS

Among 2,714 diabetes-free participants, 641 had isolated impaired fasting glucose (iIFG), and 341 had impaired glucose tolerance (IGT). The annual transition to diabetes for those with IGT was 13.9% (95% CI 12.0, 15.9) versus 8.6% (7.3, 9.8) for iIFG. In the normoglycemia ↔ iIFG → diabetes model, mean sojourn time in normoglycemia was 40.3 (34.6, 48.2) years, and sojourn time in iIFG was 9.7 (8.4, 11.4) years. For the normoglycemia ↔ IGT → diabetes model, mean sojourn time in normoglycemia was 34.5 (29.5, 40.8) years, and sojourn time in IGT was 6.1 (5.3, 7.1) years.

CONCLUSIONS

Individuals reside in normoglycemia for 35-40 years; however, progression from prediabetes to diabetes is rapid.

Utilizing a multi-stage transition model for analysing child stunting in two urban slum settlements of Nairobi: A longitudinal analysis, 2011-2014

INTRODUCTION

Stunting is common among children in many low and middle income countries, particularly in rural and urban slum settings. Few studies have described child stunting transitions and the associated factors in urban slum settlements. We describe transitions between stunting states and associated factors among children living in Nairobi slum settlements.

METHODS

This study used data collected between 2010 and 2014 from the Nairobi Urban and Demographic Surveillance System (NUHDSS) and a vaccination study nested within the surveillance system. A subset of 692 children aged 0 to 3 years, with complete anthropometric data, and household socio-demographic data was used for the analysis. Height-for-age Z-scores (HAZ) was used to define stunting: normal (HAZ ≥ 1), marginally stunted (-2 ≤ HAZ < -1), moderately stunted (-3 ≤ HAZ < -2), and severely stunted (HAZ < -3). Transitions from one stunting level to another and in the reverse direction were computed. The associations between explanatory factors and the transitions between four child stunting states were modeled using a continuous-time multi-state model.

RESULTS

We observed that 48%, 39%, 41%, and 52% of children remained in the normal, marginally stunted, moderately stunted, and severely stunted states, respectively. About 29% transitioned from normal to marginally stunted state, 15% to the moderately stunted state, and 8% to the severely stunted state. Also, 8%, 12%, and 29% back transitioned from severely stunted, moderately stunted, and marginally stunted states, to the normal state, respectively. The shared common factors associated with all transitions to a more severe state include: male gender, ethnicity (only for mild and severe transition states), child's age, and household food insecurity. In Korogocho, children whose parents were married and those whose mothers had attained primary or post-primary education were associated with a transition from a mild state into a moderately stunted state. Children who were breastfed exclusively were less likely to transition from moderate to severe stunting state.

CONCLUSION

These findings reveal a high burden of stunting and transitions in urban slums. Context-specific interventions targeting the groups of children identified by the socio-demographic factors are needed. Improving food security and exclusive breastfeeding could potentially reduce stunting in the slums.

Conditional modeling of panel count data with partly interval-censored failure event

In longitudinal follow-up studies, panel count data arise from discrete observations on recurrent events. We investigate a more general situation where a partly interval-censored failure event is informative to recurrent events. The existing methods for the informative failure event are based on the latent variable model, which provides indirect interpretation for the effect of failure event. To solve this problem, we propose a failure-time-dependent proportional mean model with panel count data through an unspecified link function. For estimation of model parameters, we consider a conditional expectation of least squares function to overcome the challenges from partly interval-censoring, and develop a two-stage estimation procedure by treating the distribution function of the failure time as a functional nuisance parameter and using the B-spline functions to approximate unknown baseline mean and link functions. Furthermore, we derive the overall convergence rate of the proposed estimators and establish the asymptotic normality of finite-dimensional estimator and functionals of infinite-dimensional estimator. The proposed estimation procedure is evaluated by extensive simulation studies, in which the finite-sample performances coincide with the theoretical results. We further illustrate our method with a longitudinal healthy longevity study and draw some insightful conclusions.

Semiparametric estimation and testing for panel count data with informative interval-censored failure event

Panel count data and interval-censored data are two types of incomplete data that often occur in event history studies. Almost all existing statistical methods are developed for their separate analysis. In this paper, we investigate a more general situation where a recurrent event process and an interval-censored failure event occur together. To intuitively and clearly explain the relationship between the recurrent current process and failure event, we propose a failure time-dependent mean model through a completely unspecified link function. To overcome the challenges arising from the blending of nonparametric components and parametric regression coefficients, we develop a two-stage conditional expected likelihood-based estimation procedure. We establish the consistency, the convergence rate and the asymptotic normality of the proposed two-stage estimator. Furthermore, we construct a class of two-sample tests for comparison of mean functions from different groups. The proposed methods are evaluated by extensive simulation studies and are illustrated with the skin cancer data that motivated this study.

Study design for restricted mean time analysis of recurrent events and death

The restricted mean time in favor (RMT-IF) of treatment has just been added to the analytic toolbox for composite endpoints of recurrent events and death. To help practitioners design new trials based on this method, we develop tools to calculate the sample size and power. Specifically, we formulate the outcomes as a multistate Markov process with a sequence of transient states for recurrent events and an absorbing state for death. The transition intensities, in this case the instantaneous risks of another nonfatal event or death, are assumed to be time-homogeneous but nonetheless allowed to depend on the number of past events. Using the properties of Coxian distributions, we derive the RMT-IF effect size under the alternative hypothesis as a function of the treatment-to-control intensity ratios along with the baseline intensities, the latter of which can be easily estimated from historical data. We also reduce the variance of the nonparametric RMT-IF estimator to calculable terms under a standard set-up for censoring. Simulation studies show that the resulting formulas provide accurate approximation to the sample size and power in realistic settings. For illustration, a past cardiovascular trial with recurrent-hospitalization and mortality outcomes is analyzed to generate the parameters needed to design a future trial. The procedures are incorporated into the rmt package along with the original methodology on the Comprehensive R Archive Network (CRAN).

Risk factors for stroke-related functional disability and mortality at Felege Hiwot Referral Hospital, Ethiopia

BACKGROUND

Stroke is one of the top causes of functional disability around the world. The main objective was to identify stroke-related functional outcomes and risk factors. A good functional outcome is defined as the absence of problems secondary to the stroke event, a poor functional outcome as the presence of complications, and mortality as the existence of complications.

METHOD

A retrospective cohort analysis was used to observe factors in 298 eligible adult (18 or older) stroke patients who attend outpatient clinics every three months at Felege Hiwot Referral Hospital between September 2019 and August 2021 to predict outcomes.

RESULT

The likelihood of dying from a poor outcome was 9%, and the likelihood of recovering was 24%. The average time spent on good and poor outcomes for different levels of independent variables varies according to their risk. During the first three years of follow-up, the instantaneous risk with a 95% confidence interval of transitioning from good to poor outcome in the women, aged 60 or older, with hypertension, atrial fibrillation, and hemorrhage stroke versus men stroke patients, aged 18 to 59, without hypertension, atrial fibrillation, and ischemic stroke were 1.54 (1.10, 2.15), 1.73 (1.19, 2.52), 2.34 (1.55, 3.53), 2.74 (1.64, 4.56), and 1.52 (1.10, 2.19) respectively. The hazard ratio of transitioning from poor outcome to death for patients with diabetes mellitus and atrial fibrillation versus those without diabetes mellitus and atrial fibrillation was estimated to be 1.95 (1.10, 3.46) and 3.39 (1.67, 6.89), respectively.

CONCLUSION

Women over 60 with hypertension, atrial fibrillation, and hemorrhagic stroke were more likely to progress from a good to a poor outcome. Diabetes and atrial fibrillation were also risk factors for progressing from a poor outcome to death. The states and transitions, as well as a clinical control of the hazards for the transition through states, should improve the physician's decision-making process. Since gender and age are difficult to control, early intervention by patients and the hospital may be critical in influencing functional outcomes.

Evaluation of the natural history of disease by combining incident and prevalent cohorts: application to the Nun Study

The Nun study is a well-known longitudinal epidemiology study of aging and dementia that recruited elderly nuns who were not yet diagnosed with dementia (i.e., incident cohort) and who had dementia prior to entry (i.e., prevalent cohort). In such a natural history of disease study, multistate modeling of the combined data from both incident and prevalent cohorts is desirable to improve the efficiency of inference. While important, the multistate modeling approaches for the combined data have been scarcely used in practice because prevalent samples do not provide the exact date of disease onset and do not represent the target population due to left-truncation. In this paper, we demonstrate how to adequately combine both incident and prevalent cohorts to examine risk factors for every possible transition in studying the natural history of dementia. We adapt a four-state nonhomogeneous Markov model to characterize all transitions between different clinical stages, including plausible reversible transitions. The estimating procedure using the combined data leads to efficiency gains for every transition compared to those from the incident cohort data only.

A scalable approach for continuous time Markov models with covariates

Existing methods for fitting continuous time Markov models (CTMM) in the presence of covariates suffer from scalability issues due to high computational cost of matrix exponentials calculated for each observation. In this article, we propose an optimization technique for CTMM which uses a stochastic gradient descent algorithm combined with differentiation of the matrix exponential using a Padé approximation. This approach makes fitting large scale data feasible. We present two methods for computing standard errors, one novel approach using the Padé expansion and the other using power series expansion of the matrix exponential. Through simulations, we find improved performance relative to existing CTMM methods, and we demonstrate the method on the large-scale multiple sclerosis NO.MS data set.

A new framework for semi-Markovian parametric multi-state models with interval censoring

There are few computational and methodological tools available for the analysis of general multi-state models with interval censoring. Here, we propose a general framework for parametric inference with interval censored multi-state data. Our framework can accommodate any parametric model for the transition times, and covariates may be included in various ways. We present a general method for constructing the likelihood, which we have implemented in a ready-to-use R package, smms, available on GitHub. The R package also computes the required high-dimensional integrals in an efficient manner. Further, we explore connections between our modelling framework and existing approaches: our models fall under the class of semi-Markovian multi-state models, but with a different, and sparser parameterisation than what is often seen. We illustrate our framework through a dataset monitoring heart transplant patients. Finally, we investigate the effect of some forms of misspecification of the model assumptions through simulations.

The role of corruption control and regulatory quality in energy efficiency transition tendencies in Africa

This study answers an important policy question related to energy efficiency transition tendencies and the role that control of corruption and regulatory quality can play, using the Stochastic Frontier and Panel Markov-Switching techniques with panel data from 46 African countries. We have demonstrated in this study that African countries have been locked in a low energy-efficient state, with tendencies to transition out considered low to moderate with a 21-24% chance and more likely in the long term (i.e., after a decade). This raises serious concerns about the robust nature of current energy efficiency policies implemented and the kind of investment in technology undertaken in Africa. The results further illustrate that improving regulatory quality and controlling corruption can increase African countries' likelihood to leapfrog out of the low energy-efficient state. Thus, the findings underscore the importance of developing better and proper institutions to achieve the UN SDG target 7.3.

Intraindividual Change in Cognitive Function Among Adults With Systemic Lupus Erythematosus: A Markov Analysis Over 7 Years

OBJECTIVE

Cognitive impairment is prevalent in systemic lupus erythematosus (SLE). There remain gaps in understanding cognition and SLE longitudinally. We studied intraindividual change in cognition in SLE over time.

METHODS

Data were from the University of California, San Francisco Lupus Outcome Study, which included 1281 adults with SLE. The Hopkins Verbal Learning Test-Revised (HVLT-R) and the Controlled Oral Word Association Test (COWAT) were administered annually over 7 years. A two-state Markov analysis was used to model transition intensities for probabilities of change in cognition. Logistic regression examined the association between clinical variables and cognitive change.

RESULTS

Minimal transition between cognitive states was observed in the Markov analysis. Using the COWAT, higher levels of self-reported depression were associated with decreased likelihood of cognitive improvement (Relative Risk [RR]: 0.98; 95% confidence interval [CI]: 0.96-0.99), and higher self-reported disease severity was associated with cognitive decline (RR: 1.05; 95% CI: 1.02-1.09). Using the HVLT-R, increasing age (RR: 1.02; 95% CI: 1.01-1.03) and higher education level (RR: 1.82; 95% CI: 1.28-2.58) were associated with cognitive improvement, and higher self-reported disease severity (RR: 1.02; 95% CI: 1.01-1.03) and depression (RR: 1.05; 95% CI: 1.03-1.07) were associated with cognitive decline.

CONCLUSION

Most individuals with SLE did not transition between states of high (Z score ≥ -1.5) or low (Z score < -1.5) cognition in a Markov analysis over a 7-year assessment period, highlighting a degree of relative stability in cognition over time. Increasing age and higher education levels were associated with greater likelihood of cognitive improvement. Greater self-reported SLE disease severity and depression were associated with cognitive decline.

Time course of health complaints attributed to RF-EMF exposure and predictors of electromagnetic hypersensitivity over 10 years in a prospective cohort of Dutch adults

BACKGROUND

Some individuals attribute health complaints to radiofrequency electromagnetic field (RF-EMF) exposure. This condition, known as idiopathic environmental intolerance attributed to RF-EMFs (IEI-RF) or electromagnetic hypersensitivity (EHS), can be disabling for those who are affected. In this study we assessed factors related to developing, maintaining, or discarding IEI-RF over the course of 10 years, and predictors of developing EHS at follow-up using a targeted question without the condition of reporting health complaints attributed to RF-EMF exposure.

METHODS

Participants (n = 892, mean age 50 at baseline, 52 % women) from the Dutch Occupational and Environmental Health Cohort Study AMIGO filled in questionnaires in 2011/2012 (T₀), 2013 (T₁), and 2021 (T₄) where information pertaining to perceived RF-EMF exposure and risk, non-specific symptoms, sleep problems, IEI-RF, and EHS was collected. We fitted multi-state Markov models to represent how individuals transitioned between states ("yes", "no") of IEI-RF.

RESULTS

At each time point, about 1 % of study participants reported health complaints that they attributed to RF-EMF exposure. While this percentage remained stable, the individuals who reported such complaints changed over time: of nine persons reporting health complaints at T₀, only one reported IEI-RF at both T₁ and T₄, and two newly reported health complaints at T₄. Overall, participants had a 95 % chance of transitioning from "yes" to "no" over a time course of 10 years, and a chance of 1 % of transitioning from "no" to "yes". Participants with high perceived RF-EMF exposure and risk had a general tendency to move more frequently between states.

CONCLUSIONS

We observed a low prevalence of IEI-RF in our population. Prevalence did not vary strongly over time but there was a strong aspect of change: over 10 years, there was a high probability of not attributing symptoms to RF-EMF exposure anymore. IEI-RF appears to be a more transient condition than previously assumed.

Statistical Inference of the Class of Nonparametric Tests for the Panel Count and Current Status Data from the Perspective of the Saddlepoint Approximation

Many statisticians resort to using the asymptotic normal approximation method to carry out statistical inference for many statistical tests, especially nonparametric ones. In this article, the saddlepoint approximation method is proposed as an alternative to the asymptotic normal approximation method to carry out statistical inference for a number of nonparametric tests for an important type of data that appears frequently in many clinical studies such as cancer and tumorigenicity studies. In clinical trials, there are many strategies through which treatments are assigned to patients. Equal allocation of both treatments is a largely prevalent approach in clinical trials to eliminate experimental bias and increase power. Accordingly, the statistical analysis is carried out based on the truncated binomial design, which is one of the designs that achieve a perfect balance between the two treatments. To clarify the accuracy of the proposed approximation method, two sets of real data are analyzed, and for the same purpose, a comprehensive simulation study is carried out.

Obesity in Late-Life as a Protective Factor Against Dementia and Dementia-Related Mortality

OBJECTIVE

We estimated the conversion from cognitively normal to mild cognitive impairment (MCI) to probable dementia and death for underweight, normal, overweight, and obese older adults, where the timing of examinations is associated with the severity of dementia.

METHODS

We analyzed six waves of the National Health and Aging Trends Study (NHATS). Body mass (BMI) was computed from height and weight. Multi-state survival models (MSMs) examined misclassification probability, time-to-event ratios, and cognitive decline.

RESULTS

Participants (n = 6078) were 77 years old, 62% had overweight and/or obese BMI. After adjusting for the effects of cardiometabolic factors, age, sex, and race, obesity was protective against developing dementia (aHR=.44; 95%CI [.29-.67]) and dementia-related mortality (aHR=.63; 95%CI [.42-.95]).

DISCUSSION

We found a negative relationship between obesity and dementia and dementia-related mortality, a finding that has been underreported in the literature. The continuing obesity epidemic might complicate the diagnosis and treatment of dementia.

Risk factors for neonatal hypothermia at Arba Minch General Hospital, Ethiopia

BACKGROUND

The first few minutes after birth are the most dangerous for the survival of an infant. Babies in neonatal intensive care units are either under heated or overheated, and hypothermic infants remain hypothermic or develop a fever. As a result, special attention must be paid to monitoring and maintaining the time of recovery from hypothermia states. Despite numerous studies, only a few have examined the transition from neonatal hypothermia and associated risk factors in depth.

METHOD

A retrospective observational study was conducted to track axillary temperatures taken at the time of neonatal intensive care unit admission, which were then tracked every 30 minutes until the newborn's temperature stabilized. All hypothermic neonates admitted to the neonatal intensive care unit between January 2018 and December 2020 was included in the study. Temperature data were available at birth and within the first three hours of admission for 391 eligible hypothermic neonates. The effect of factors on the transition rate in different states of hypothermia was estimated using a multi-state Markov model.

RESULT

The likelihood of progressing from mild to severe hypothermia was 5%, while the likelihood of progressing to normal was 34%. The average time spent in a severe hypothermia state was 48, 35, and 24 minutes for three different levels of birth weight, and 53, 41, and 31 minutes for low, moderate, and normal Apgar scores, respectively. Furthermore, the mean sojourn time in a severe hypothermia state was 48, 39, and 31 minutes for three different levels of high, normal, and low pulse rate, respectively.

CONCLUSION

For hypothermic survivors within the first three hours of life, very low birth weight, low Apgar, and high pulse rate had the strongest association with hypothermia and took the longest time to improve/recover. As a result, there is an urgent need to train all levels of staff dealing with maintaining the time of recovery from neonatal hypothermia.

Hierarchical continuous-time inhomogeneous hidden Markov model for cancer screening with extensive followup data

Continuous-time hidden Markov models are an attractive approach for disease modeling because they are explainable and capable of handling both irregularly sampled, skewed and sparse data arising from real-world medical practice, in particular to screening data with extensive followup. Most applications in this context consider time-homogeneous models due to their relative computational simplicity. However, the time homogeneous assumption is too strong to accurately model the natural history of many diseases including cancer. Moreover, cancer risk across the population is not homogeneous either, since exposure to disease risk factors can vary considerably between individuals. This is important when analyzing longitudinal datasets and different birth cohorts. We model the heterogeneity of disease progression and regression using piece-wise constant intensity functions and model the heterogeneity of risks in the population using a latent mixture structure. Different submodels under the mixture structure employ the same types of Markov states reflecting disease progression and allowing both clinical interpretation and model parsimony. We also consider flexible observational models dealing with model over-dispersion in real data. An efficient, scalable Expectation-Maximization algorithm for inference is proposed with the theoretical guaranteed convergence property. We demonstrate our method's superior performance compared to other state-of-the-art methods using synthetic data and a real-world cervical cancer screening dataset from the Cancer Registry of Norway. Moreover, we present two model-based risk stratification methods that identify the risk levels of individuals.

A Markov jump process approach to modeling blood donor status: Donor retention and attrition rates at a blood service center in Zimbabwe

Background

Blood service agencies depend upon the availability of regular blood donors for sustainability. The knowledge and understanding of the stochastic behavior of donors is the first step toward sustaining the blood supply. Analyzing the changes in the donor status within the donor pool will help the blood service authorities to manage the blood donation process.

Objectives

The study presents a multistate Markov jump model in analyzing the changes in blood donor status during their blood donation career. Relevant covariates are used to aid in explaining the transitions.

Materials and Methods

The status of a blood donor i that can be in one of four states S = {1; 2; 3; 4}. A new donor (s = 1), repeat/regular donor (s = 2), occasional donor (s = 3), and lapsed donor (s = 4). A Continuous‐time Markov model was used to estimate blood donor progression during their blood donation career. Frequencies of blood donations made in a given time interval determines the state occupied.

Results

In the early years of blood donation career, first‐time donors have a higher likelihood of becoming regular donors. Donor attrition increases with time whilst donor retention decreases with time. The results show that when the jump process is currently in an occasional state, the probability that it moves into lapsed state when it leaves the occasional state is given as 69.06%. Similarly, donors are forecasted to spend 21.193 months (1.8 years) in the occasional state before lapsing. Repeat donors can spend 39.342 months (3.3 years) in the regular state before the transition to other states. The study established that donor‐specific demographic factors such as age and gender are critical in donor status transitions.

Conclusions

With the passage of time, donor status evolves, with trend inclined towards reduction in the frequency of blood donations as more donors become inactive or lapsed. The transition of donors in various states can be described by a time homogeneous Markov model.

Motivational Drivers of Temporal Dynamics in Postretirement Work

OBJECTIVES

Many retirees continue to work in retirement, but the temporal dynamics of this process are not well understood. This article examined the extent to which retirees increase, decrease, and exit their work engagement over time. We hypothesized that different motives for postretirement work-financial, social, personal, and organizational-have differential affects on changes in work extent.

METHODS

We analyzed 7 waves of the HEalth, Aging and Retirement Transitions in Sweden study (n = 3,123). Postretirement work was defined as working for pay while receiving pension benefits. Changes in work extent were estimated with multistate models and examined in relation to the 4 motives.

RESULTS

Results showed a gradual decrease in work extent following retirement. Financial motives increased the likelihood to take up more work and decreased the likelihood to reduce work hours. Social motives increased the likelihood to reduce and exit work, while personal motives decreased the likelihood for those same pathways. Organizational (demand-driven) motives increased the likelihood to stop working.

DISCUSSION

Our findings suggest that financial motives constitute an important driver for taking up more work in retirement, while motives related to the personal meaning of work explain why retirees maintain their level of engagement over time. The social function of work, on the other hand, may be gradually replaced by social activities outside of work, resulting in a gradual disengagement from work. Finally, demand-driven motives appear insufficient to remain in the labor force, highlighting the need to acknowledge the diversity of motives for continuing to work.

A comparison of two frameworks for multi-state modelling, applied to outcomes after hospital admissions with COVID-19

We compare two multi-state modelling frameworks that can be used to represent dates of events following hospital admission for people infected during an epidemic. The methods are applied to data from people admitted to hospital with COVID-19, to estimate the probability of admission to intensive care unit, the probability of death in hospital for patients before and after intensive care unit admission, the lengths of stay in hospital, and how all these vary with age and gender. One modelling framework is based on defining transition-specific hazard functions for competing risks. A less commonly used framework defines partially-latent subpopulations who will experience each subsequent event, and uses a mixture model to estimate the probability that an individual will experience each event, and the distribution of the time to the event given that it occurs. We compare the advantages and disadvantages of these two frameworks, in the context of the COVID-19 example. The issues include the interpretation of the model parameters, the computational efficiency of estimating the quantities of interest, implementation in software and assessing goodness of fit. In the example, we find that some groups appear to be at very low risk of some events, in particular intensive care unit admission, and these are best represented by using 'cure-rate' models to define transition-specific hazards. We provide general-purpose software to implement all the models we describe in the flexsurv R package, which allows arbitrarily flexible distributions to be used to represent the cause-specific hazards or times to events.

The polytomous discrimination index for prediction involving multistate processes under intermittent observation

With the increasing importance of predictive modeling in health research comes the need for methods to rigorously assess predictive accuracy. We consider the problem of evaluating the accuracy of predictive models for nominal outcomes when outcome data are coarsened at random. We first consider the problem in the context of a multinomial response modeled by polytomous logistic regression. Attention is then directed to the motivating setting in which class membership corresponds to the state occupied in a multistate disease process at a time horizon of interest. Here, class (state) membership may be unknown at the time horizon since disease processes are under intermittent observation. We propose a novel extension to the polytomous discrimination index to address this and evaluate the predictive accuracy of an intensity-based model in the context of a study involving patients with arthritis from a registry at the University of Toronto Centre for Prognosis Studies in Rheumatic Diseases.

The transitions and predictors of cognitive frailty with multi-state Markov model: a cohort study

BACKGROUND

Cognitive frailty (CF) is characterized by the simultaneous presence of physical frailty and cognitive impairment. Previous studies have investigated its prevalence and impact on different adverse health-related outcomes. Few studies have focused on the progression and reversibility of CF and their potential predictors.

METHODS

Data were derived from the China Health and Retirement Longitudinal Study (CHARLS). A total of 4051 older adults with complete data on three waves of the survey (2011, 2013, and 2015) were included and categorized into four groups: normal state (NS), cognitive impairment (CI) only, physical frailty (PF) only and CF (with both PF and CI). A multi-state Markov model was constructed to explore the transitions and predicting factors of CF.

RESULTS

The incidence and improvement rates of CF were 1.70 and 11.90 per 100 person-years, respectively. The 1-year transition probability of progression to CF in those with CI was higher than that in the PF population (0.340 vs. 0.054), and those with CF were more likely to move to PF (0.208). Being female [hazard ratio (HR) = 1.46, 95%CI = 1.06, 2.02)], dissatisfied with life (HR = 4.94, 95%CI = 1.04, 23.61), had a history of falls (HR = 2.36, 95%CI = 1.02, 5.51), rural household registration (HR = 2.98, 95%CI = 1.61, 5.48), multimorbidity (HR = 2.17, 95%CI = 1.03, 4.59), and depression (HR = 1.75, 95%CI = 1.26, 2.45) increased the risk of progression to CF, whereas literacy (HR = 0.46, 95%CI = 0.33, 0.64) decreased such risk. Depression (HR = 0.43, 95%CI = 0.22, 0.84) reduced the likelihood of CF improvement, whereas literacy (HR = 2.23, 95%CI = 1.63, 3.07) increased such likelihood.

CONCLUSIONS

Cognitive frailty is a dynamically changing condition in older adults. Possible interventions aimed at preventing the onset and facilitating the recovery of cognitive frailty should focus on improving cognitive function in older adults.

Enhanced-Sampling Simulations for the Estimation of Ligand Binding Kinetics: Current Status and Perspective

The dissociation rate (k off) associated with ligand unbinding events from proteins is a parameter of fundamental importance in drug design. Here we review recent major advancements in molecular simulation methodologies for the prediction of k off. Next, we discuss the impact of the potential energy function models on the accuracy of calculated k off values. Finally, we provide a perspective from high-performance computing and machine learning which might help improve such predictions.

A pre-symptomatic incubation model for precision strategies of screening, quarantine, and isolation based on imported COVID-19 cases in Taiwan

Facing the emerging COVID viral variants and the uneven distribution of vaccine worldwide, imported pre-symptomatic COVID-19 cases play a pivotal role in border control strategies. A stochastic disease process and computer simulation experiments with Bayesian underpinning was therefore developed to model pre-symptomatic disease progression during incubation period on which we were based to provide precision strategies for containing the resultant epidemic caused by imported COVID-19 cases. We then applied the proposed model to data on 1051 imported COVID-19 cases among inbound passengers to Taiwan between March 2020 and April 2021. The overall daily rate (per 100,000) of pre-symptomatic COVID-19 cases was estimated as 106 (95% credible interval (CrI): 95–117) in March–June 2020, fell to 37 (95% CrI: 28–47) in July–September 2020 (p < 0.0001), resurged to 141 (95% CrI: 118–164) in October–December 2020 (p < 0.0001), and declined to 90 (95% CrI: 73–108) in January–April 2021 (p = 0.0004). Given the median dwelling time, over 82% cases would progress from pre-symptomatic to symptomatic phase in 5-day quarantine. The time required for quarantine given two real-time polymerase chain reaction (RT-PCR) tests depends on the risk of departing countries, testing and quarantine strategies, and whether the passengers have vaccine jabs. Our proposed four-compartment stochastic process and computer simulation experiments design underpinning Bayesian MCMC algorithm facilitated the development of precision strategies for imported COVID-19 cases.

Association between self-reported body mass index and active life expectancy in a large community-dwelling sample of older U.S. adults

Background

Obesity may have a protective effect (greater survival) in older adults, a finding known as the “obesity paradox.” This study examined the association between self-reported body mass index (BMI) and active life expectancy (ALE) among older U.S. adults.

Methods

Using the Medicare Health Outcomes Survey Cohort 15 (2012 baseline, 2014 follow-up), we estimated life expectancy and ALE by participants’ baseline BMI and age using multi-state models. A participant was classified as in an active state if this person reported having no difficulty for any of these six activities of daily living (ADLs).

Results

Small differences in life expectancy were noted among persons in normal weight (BMI 18.5–24.9 kg/m²), overweight (BMI 25–29.9 kg/m²), and obesity ranges (BMI 30 kg/m² and higher). However, persons with obesity had a significantly lower ALE. ALE at age 65 was 11.1 (11.0–11.2) years for persons with obesity, 1.2 (1.1–1.3) years less than that for the normal weight and overweight persons (12.3 years for both, 12.2–12.4). Persons with class III obesity had a significantly lower life expectancy and ALE than normal weight persons. Although persons with class I or II obesity had a similar life expectancy as normal weight persons, they have a shorter ALE.

Conclusions

Although older adults with obesity have a similar life expectancy as normal weight persons, they have a significantly shorter ALE. Given the complex relationship of BMI and ALE, a “one size fits all” approach to weight management is not advisable.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12877-022-03021-7.

Impact of the Height of Buildings on the Maintainability of Natural Stone Claddings

The buildings’ surroundings’ environmental exposure conditions (e.g., orientation, location, altitude, distance from the sea, temperature, precipitation, presence of damp, exposure to prevailing winds, among others) have a considerable influence on the performance and durability of their envelope. Furthermore, the intensity of these conditions can vary significantly with the height of the building and, consequently, influence the degradation of different parts of the same building in different ways. In a tall building, the upper part is more prone to higher solar radiation levels, temperature variations, and exposure to wind–rain action. On the other hand, external elements at the bottom are more susceptible to high levels of pollution, especially in city centres. In this sense, the main purpose of this study was to analyse the degradation processes in buildings with different heights and understand whether the processes and maintenance requirements are statistically different. A sample of 203 natural stone claddings (NSC), located in Portugal, was used as case study. The sample was collected based on the diagnosis of the degradation condition of these claddings through in situ visual inspections. To predict the degradation process of NSC over time, a stochastic service life prediction model, based on Petri nets (PN), was implemented. This model allows evaluating the performance of NSC by encompassing the uncertainty of the future performance of the claddings. The results obtained through the degradation and maintenance models were compared with real case studies to highlight the real impact of buildings’ height subjected to environmental exposure conditions on the maintainability of NSC.

Differences in SARS-CoV-2 infections during the first and second wave of SARS-CoV-2 between six ethnic groups in Amsterdam, the Netherlands: A population-based longitudinal serological study

BACKGROUND

Surveillance data in high-income countries have reported more frequent SARS-CoV-2 diagnoses in ethnic minority groups. We examined the cumulative incidence of SARS-CoV-2 and its determinants in six ethnic groups in Amsterdam, the Netherlands.

METHODS

We analysed participants enrolled in the population-based HELIUS cohort, who were tested for SARS-CoV-2-specific antibodies and answered COVID-19-related questions between June 24-October 9, 2020 (after the first wave) and November 23, 2020-March 31, 2021 (during the second wave). We modelled SARS-CoV-2 incidence from January 1, 2020-March 31, 2021 using Markov models adjusted for age and sex. We compared incidence between ethnic groups over time and identified determinants of incident infection within ethnic groups.

FINDINGS

2,497 participants were tested after the first wave; 2,083 (83·4%) were tested during the second wave. Median age at first visit was 54 years (interquartile range=44-61); 56·6% were female. Compared to Dutch-origin participants (15·9%), cumulative SARS-CoV-2 incidence was higher in participants of South-Asian Surinamese (25·0%; adjusted hazard ratio [aHR]=1·66; 95%CI=1·16-2·40), African Surinamese (28·9%, aHR=1·97; 95%CI=1·37-2·83), Turkish (37·0%; aHR=2·67; 95%CI=1·89-3·78), Moroccan (41·9%; aHR=3·13; 95%CI=2·22-4·42), and Ghanaian (64·6%; aHR=6·00; 95%CI=4·33-8·30) origin. Compared to those of Dutch origin, differences in incidence became wider during the second versus first wave for all ethnic minority groups (all p-values for interaction<0·05), except Ghanaians. Having household members with suspected SARS-CoV-2 infection, larger household size, and low health literacy were common determinants of SARS-CoV-2 incidence across groups.

INTERPRETATION

SARS-CoV-2 incidence was higher in the largest ethnic minority groups of Amsterdam, particularly during the second wave. Prevention measures, including vaccination, should be encouraged in these groups.

FUNDING

ZonMw, Public Health Service of Amsterdam, Dutch Heart Foundation, European Union, European Fund for the Integration of non-EU immigrants.

Validation and application of a needs-based segmentation tool for cross-country comparisons

OBJECTIVE

To compare countries' health care needs by segmenting populations into a set of needs-based health states.

DATA SOURCES

We used seven waves of the Survey of Health, Aging and Retirement in Europe (SHARE) panel survey data.

STUDY DESIGN

We developed the Cross-Country Simple Segmentation Tool (CCSST), a validated clinician-administered instrument for categorizing older individuals by distinct, homogeneous health and related social service needs. Using clinical indicators, self-reported physician diagnosis of chronic disease, and performance-based tests conducted during the survey interview, individuals were assigned to 1-5 global impressions (GI) segments and assessed for having any of the four identifiable complicating factors (CFs). We used Cox proportional hazard models to estimate the risk of mortality by segment. First, we show the segmentation cross-sectionally to assess cross-country differences in the fraction of individuals with different levels of medical needs. Second, we compare the differences in the rate at which individuals transition between those levels and death.

DATA COLLECTION/EXTRACTION METHODS

We segmented 270,208 observations (from Austria, Belgium, Czech Republic, Denmark, France, Germany, Greece, Israel, Italy, the Netherlands, Poland, Spain, Sweden, and Switzerland) from 96,396 individuals into GI and CF categories.

PRINCIPAL FINDINGS

The CCSST is a valid tool for segmenting populations into needs-based states, showing Switzerland with the lowest fraction of individuals in high medical needs segments, followed by Denmark and Sweden, and Poland with the highest fraction, followed by Italy and Israel. Comparing hazard ratios of transitioning between health states may help identify country-specific areas for analysis of ecological and cultural risk factors.

CONCLUSIONS

The CCSST is an innovative tool for aggregate cross-country comparisons of both health needs and transitions between them. A cross-country comparison gives policy makers an effective means of comparing national health system performance and provides targeted guidance on how to identify strategies for curbing the rise of high-need, high-cost patients.

Nonparametric estimation in an illness-death model with component-wise censoring

In disease settings where study participants are at risk for death and a serious nonfatal event, composite endpoints defined as the time until the earliest of death or the nonfatal event are often used as the primary endpoint in clinical trials. In practice, if the nonfatal event can only be detected at clinic visits and the death time is known exactly, the resulting composite endpoint exhibits "component-wise censoring." The standard method used to estimate event-free survival in this setting fails to account for component-wise censoring. We apply a kernel smoothing method previously proposed for a marker process in a novel way to produce a nonparametric estimator for event-free survival that accounts for component-wise censoring. The key insight that allows us to apply this kernel method is thinking of nonfatal event status as an intermittently observed binary time-dependent variable rather than thinking of time to the nonfatal event as interval-censored. We also propose estimators for the probability in state and restricted mean time in state for reversible or irreversible illness-death models, under component-wise censoring, and derive their large-sample properties. We perform a simulation study to compare our method to existing multistate survival methods and apply the methods on data from a large randomized trial studying a multifactor intervention for reducing morbidity and mortality among men at above average risk of coronary heart disease.

Hidden mover-stayer model for disease progression accounting for misclassified and partially observed diagnostic tests: Application to the natural history of human papillomavirus and cervical precancer

Hidden Markov models (HMMs) have been proposed to model the natural history of diseases while accounting for misclassification in state identification. We introduce a discrete time HMM for human papillomavirus (HPV) and cervical precancer/cancer where the hidden and observed state spaces are defined by all possible combinations of HPV, cytology, and colposcopy results. Because the population of women undergoing cervical cancer screening is heterogeneous with respect to sexual behavior, and therefore risk of HPV acquisition and subsequent precancers, we use a mover-stayer mixture model that assumes a proportion of the population will stay in the healthy state and are not subject to disease progression. As each state is a combination of three distinct tests that characterize the cervix, partially observed data arise when at least one but not every test is observed. The standard forward-backward algorithm, used for evaluating the E-step within the E-M algorithm for maximum-likelihood estimation of HMMs, cannot incorporate time points with partially observed data. We propose a new forward-backward algorithm that considers all possible fully observed states that could have occurred across a participant's follow-up visits. We apply our method to data from a large management trial for women with low-grade cervical abnormalities. Our simulation study found that our method has relatively little bias and out preforms simpler methods that resulted in larger bias.

A kernel regression model for panel count data with nonparametric covariate functions

The local kernel pseudo-partial likelihood is employed for estimation in a panel count model with nonparametric covariate functions. An estimator of the derivative of the nonparametric covariate function is derived first, and the nonparametric function estimator is then obtained by integrating the derivative estimator. Uniform consistency rates and pointwise asymptotic normality are obtained for the local derivative estimator under some regularity conditions. Moreover, the baseline function estimator is shown to be uniformly consistent. Demonstration of the asymptotic results strongly relies on the modern empirical theory, which generally does not require the Poisson assumption. Simulation studies also illustrate that the local derivative estimator performs well in a finite-sample regardless of whether the Poisson assumption holds. We also implement the proposed methodology to analyze a clinical study on childhood wheezing.

A two-level deterministic reasoning pattern to curb the spread of COVID-19 in Africa

The emergence of the pandemic disease COVID-19, which keeps many nations on their toes to find a the solution for a cure, needs a more predetermined approach by investigating the pattern and speed with which the disease is spread from one individual to another. The predetermining method can also be used to solve the future occurrence of such diseases. The predetermined approach is s good reasoning model for proactive measures. This study presents a two-level deterministic reasoning model to curb the spread of COVID-19 in some populated and economically optimistic African countries. A Petri net was used as a predetermining model to ensure proactive measures for present and future control of the spread of deadly diseases such as COVID-19. Data were collected from a reliable organization, and the result of the use the normal distribution model on these sets of data was fed into the Petri net to determine the severity and rate at which people contract disease before and during lockdown in selected countries. The results from this model proved that the number of cases of COVID-19 is not a function of the death rate in the selected countries; the discharge rate had a stronger effect on the COVID-19 cases. The results of the normal statistical distribution of various instances of COVID-19 were compared with those of the Petri net and proved that the hybrid deterministic model is viable for future use on any pandemic disease.

Multistate Models for Examining the Progression of Intermittently Measured Patient-Reported Symptoms Among Patients With Cancer: The Importance of Accounting for Interval Censoring

CONTEXT

Patients with cancer in Ontario, Canada, receive symptom monitoring in a standardized fashion using the Edmonton Symptom Assessment System (ESAS). These measurements can be used to understand symptom progression during the cancer trajectory.

OBJECTIVES

This study demonstrates the implementation of multistate models for examining symptom progression, while appropriately accounting for intermittent observation. We also compare the estimates when the panel nature of the data is ignored.

METHODS

This was a population-based retrospective cohort study using linked administrative health-care databases. The cohort consisted of patients who were newly diagnosed with a primary cancer and had at least one ESAS assessment completed between 2007 and 2015 in Ontario, Canada. A 5-state model was developed to examine the progression of symptom severity, where estimation was conducted with and without accommodating for the panel nature of the symptom data.

RESULTS

The study cohort consisted of 212,615 patients diagnosed with cancer, collectively having 1,006,360 ESAS assessments within the first year after diagnosis. The median (interquartile range) of the number of ESAS assessments per patient was 3 (1-6), and the average gap time between consecutive assessments was approximately three months. The estimated mean sojourn time in each state was consistently and significantly greater when ignoring interval censoring than when accounting for it. This held true for all states and symptoms.

CONCLUSION

Our work demonstrates the use of multistate models and the importance of accommodating for intermittent observation when examining symptom progression using ESAS among patients with cancer. This work serves as a methodological guide for applied researchers interested in modeling disease progression under the presence of intermittent observation.

A generalized transition model for grouped longitudinal categorical data

Transition models are an important framework that can be used to model longitudinal categorical data. They are particularly useful when the primary interest is in prediction. The available methods for this class of models are suitable for the cases in which responses are recorded individually over time. However, in many areas, it is common for categorical data to be recorded as groups, that is, different categories with a number of individuals in each. As motivation we consider a study in insect movement and another in pig behaviou. The first study was developed to understand the movement patterns of female adults of Diaphorina citri, a pest of citrus plantations. The second study investigated how hogs behaved under the influence of environmental enrichment. In both studies, the number of individuals in different response categories was observed over time. We propose a new framework for considering the time dependence in the linear predictor of a generalized logit transition model using a quantitative response, corresponding to the number of individuals in each category. We use maximum likelihood estimation and present the results of the fitted models under stationarity and non-stationarity assumptions, and use recently proposed tests to assess non-stationarity. We evaluated the performance of the proposed model using simulation studies under different scenarios, and concluded that our modeling framework represents a flexible alternative to analyze grouped longitudinal categorical data.

Semiparametric regression of the illness-death model with interval censored disease incidence time: An application to the ACLS data

To investigate the effect of fitness on cardiovascular disease and all-cause mortality using the Aerobics Center Longitudinal Study, we develop a semiparametric illness-death model account for intermittent observations of the cardiovascular disease incidence time and the right censored data of all-cause mortality. The main challenge in estimation is to handle the intermittent observations (interval censoring) of cardiovascular disease incidence time and we develop a semiparametric estimation method based on the expectation-maximization algorithm for a Markov illness-death regression model. The variance of the parameters is estimated using profile likelihood methods. The proposed method is evaluated using extensive simulation studies and illustrated with an application to the Aerobics Center Longitudinal Study data.

Longitudinal transitions of cigarettes and electronic nicotine delivery systems among adolescents: Construction of a retrospective cohort using recall data from a cross-sectional sample

INTRODUCTION

A major concern regarding non-cigarette tobacco or nicotine products (NCTNPs) is whether they facilitate or mitigate overall tobacco or nicotine use. We examined longitudinal transitions of cigarettes and electronic nicotine delivery systems (ENDS) by constructing a retrospective cohort based on the recall data of a cross-sectional sample.

METHODS

Using the Korea Youth Risk Behavior Survey, we constructed crosssectional data of 59576 adolescents into retrospective cohort data. Participants were categorized into 4 mutually exclusive tobacco or nicotine use states. We used a multistate Markov model to identify transitions between the states to calculate transition intensity ratios (TIRs), and examined the current use of tobacco or nicotine products to assess both gateway effects to cigarettes, and whether ENDS use helps adolescents quit cigarette smoking.

RESULTS

Compared with never use, use of ENDS was associated with an increased risk of initiation of cigarette use (TIR=6.8; 95% CI: 4.5-10.2). The risk of transitioning from cigarette ever use to ENDS, compared with never use to ENDS, was even more pronounced (TIR=44.1; 95% CI: 34.1-56.9). The prevalence of current cigarette smoking was higher among those who started ENDS then cigarettes, compared to those who began cigarette use without experimenting with ENDS (43.1% vs 35.8%). Moreover, 27.8% (95% CI: 23.6-32.0%) of adolescents who experimented first with cigarettes then moved to ENDS were current users of cigarettes, and 46.4% (95% CI: 42.1-51.1%) of these adolescents were current users of both cigarettes and ENDS.

CONCLUSIONS

Based on the recall data of a cross-sectional sample, we demonstrate that ENDS experimentation increases the likelihood of cigarette smoking initiation. A significant proportion of these adolescents continue to use cigarettes. Moreover, those who experimented with cigarettes then ENDS also continue smoking cigarettes or both cigarettes and ENDS. We suggest comprehensive tobacco control policies for all tobacco/nicotine products and monitoring the timing of NCTNP initiation in cross-sectional surveys.

Gradients Do Grow on Trees: A Linear-Time O(N)-Dimensional Gradient for Statistical Phylogenetics

Calculation of the log-likelihood stands as the computational bottleneck for many statistical phylogenetic algorithms. Even worse is its gradient evaluation, often used to target regions of high probability. Order O(N)-dimensional gradient calculations based on the standard pruning algorithm require O(N2) operations, where N is the number of sampled molecular sequences. With the advent of high-throughput sequencing, recent phylogenetic studies have analyzed hundreds to thousands of sequences, with an apparent trend toward even larger data sets as a result of advancing technology. Such large-scale analyses challenge phylogenetic reconstruction by requiring inference on larger sets of process parameters to model the increasing data heterogeneity. To make these analyses tractable, we present a linear-time algorithm for O(N)-dimensional gradient evaluation and apply it to general continuous-time Markov processes of sequence substitution on a phylogenetic tree without a need to assume either stationarity or reversibility. We apply this approach to learn the branch-specific evolutionary rates of three pathogenic viruses: West Nile virus, Dengue virus, and Lassa virus. Our proposed algorithm significantly improves inference efficiency with a 126- to 234-fold increase in maximum-likelihood optimization and a 16- to 33-fold computational performance increase in a Bayesian framework.

Life expectancy and active life expectancy by disability status in older U.S. adults

Objectives

The Medicare Health Outcome Survey (HOS) is the largest longitudinal survey of the U.S. community-dwelling elderly population. This study estimated total life expectancy, active life expectancy (ALE), and disability-free life expectancy (DFLE) by disability status among HOS participants.

Methods

Data were from the Medicare HOS Cohort 15 (baseline 2012, follow-up 2014). We included respondents aged ≥ 65 years (n = 164,597). Participants’ disability status was assessed based on the following six activities of daily living (ADL): bathing, dressing, eating, getting in or out of chairs, walking, and using the toilet. The multi-state models were used to estimate life expectancy, ALE, and DFLE by participants’ baseline disability status and age.

Results

Persons who had higher-level ADL limitations had a shorter life expectancy, ALE, and DFLE. Also persons with disability had greater expected life years with disability than those with no limitations and those with mild limitations. For example, among 65-year old respondents with no limitations, mild limitations, and disability, life expectancy was 19.9, 18.6, and 17.1 years, respectively; ALE was 14.0, 9.5, and 7.2 years, respectively; DFLE was 17.3, 15.2, and 11.4 years, respectively; and expected years with disability was 2.6, 3.4, and 5.7 years, respectively.

Conclusions

This study demonstrated that greater levels of disability adversely impact life expectancy, ALE, DFLE, and expected number of years with a disability among U.S. older adults. Understanding levels of disability, and how these may change over time, would enhance health care quality and planning services related to home care and housing in this community-dwelling population.

Maintenance Modelling of Ceramic Claddings in Pitched Roofs Based on the Evaluation of Their In Situ Degradation Condition

Existing maintenance policies have several limitations, mainly due to the lack of knowledge regarding the durability and performance of buildings. Usually, the maintenance policies are insufficiently accurate, neglecting the risk of failure over time and the global costs associated with repairs. In this study, a condition-based maintenance model, based on Petri nets, is proposed to evaluate the impact of three maintenance strategies of ceramic claddings in pitched roofs (CCPR): MS1—only total replacement; MS2—composed of total replacement and minor intervention and MS3—composed of total replacement, minor intervention and cleaning operations. In this study, 146 CCPR were inspected in situ, with a total area of 43,991.6 m2. The remaining service life of the CCPR; the global costs over the claddings’ lifetime (considering inspection, maintenance, replacement and disposal costs); the claddings’ degradation condition and the number of replacements during the time horizon are used to evaluate the performance of the different maintenance strategies through a simplified multi-criteria analysis. The results show that the gains in performance, in terms of expected service life and durability, of the consideration of preventive maintenance actions (minor interventions or cleaning operations) outweigh the increase of the operation costs.

Life expectancy and active life expectancy by marital status among older U.S. adults: Results from the U.S. Medicare Health Outcome Survey (HOS)

Background

Previous investigations of the relationship between marital status and life expectancy and healthy life expectancy rely on the assumption that participants will remain in a given marital status until death. This study estimated total life expectancy (TLE) and active life expectancy (ALE) for respondents by their baseline marital status using a large longitudinal sample of the U.S. community-dwelling elderly population.

Methods

Data were from the Medicare Health Outcomes Survey Cohort 15 (2012 baseline, 2014 follow-up). We included respondents aged ≥65 years (n = 164,597). Multi-state models estimated TLE and ALE by marital status to allow participants’ marital status to change during the remaining lifetime.

Results

Between 65 and 85 years, married men and women had a longer TLE and ALE than unmarried men and women. For example, at 65 years, TLE for married men was 18.6 years, 2.2 years longer than unmarried men, and ALE for married men was 12.3 years, 2.4 years longer than unmarried men. Similarly, at 65 years, TLE for married women was 21.1 years, 1.5 years longer than unmarried women, and ALE for married women was 13.0 years, 2.0 years longer than unmarried women. Such marriage protection effects decreased with age. In subgroups of unmarried persons, never married persons had the shortest TLE and ALE among men, and never married, divorced, and widowed persons had a similar, and shorter, TLE and ALE among women. The difference in TLE between married and unmarried persons was smaller after adjusting for baseline activity limitation status.

Conclusions

This study provides additional evidence for marriage's protective effect, with the magnitude of protection being greater for younger as compared to older persons. Selection bias was a large contributor to longer life expectancy among married persons.

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Married persons are known to have lower mortality and longer life expectancy (LE) than unmarried.

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We estimated total and active life expectancy by marital status for community-dwelling elderly.

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Constructing multi-state models in large, longitudinal data set allowed marital status to change.

•

Married men and women had longer total and active LE than unmarried; protection decreased with age.

•

Selection bias was a large contributor to longer life expectancy among married persons.

Transition between [R]- and [S]-stereoisomers without bond breaking

The fifty-year old proposal of a nondissociative racemization reaction of a tetracoordinated tetrahedral center from one enantiomer to another via a planar transition state by Hoffmann and coworkers has been explored by many research groups over the past five decades. A number of stable molecules with planar tetracoordinated and higher-coordinated centers have been designed and experimentally realized; however, there has not been a single example of a molecular system that can possibly undergo such racemization. Here we show examples of molecular species that undergo inversion of stereochemistry around tetrahedral centers (Si, Al- and P+) either via a planar transition state or an intermediate state using quantum mechanical, ab initio quasi-classical dynamics calculations, and Born-Oppenheimer molecular dynamics (BOMD) simulations. This work is expected to provide potential leads for future studies on this fundamental phenomenon in chemistry.