Multilevel joint frailty model for hierarchically clustered binary and survival data.

Hierarchical data arise when observations are clustered into groups. Multilevel models are practically useful in these settings, but these models are elusive in the context of hierarchical data with mixed multivariate outcomes. In this article, we consider binary and survival outcomes and assume the hierarchical structure is induced by clustering of both outcomes within patients and clustering of patients within hospitals which frequently occur in multicenter studies. We introduce a multilevel joint frailty model that analyzes the outcomes simultaneously to jointly estimate their regression parameters and explicitly model within-patient correlation between the outcomes and within-hospital correlation separately for each outcome. Estimation is facilitated by a computationally efficient residual maximum likelihood method that further predicts cluster-specific frailties for both outcomes and circumvents the formidable challenges induced by multidimensional integration that complicates the underlying likelihood. The performance of the model and estimation procedure is investigated via extensive simulation studies. The practical utility of the model is illustrated through simultaneous modeling of disease-free survival and binary endpoint of platelet recovery in a multicenter allogeneic bone marrow transplantation dataset that motivates this study.

Gender, education, and cohort differences in healthy working life expectancy at age 50 years in Australia: a longitudinal analysis.

BACKGROUND: We aimed to estimate healthy working life expectancy (HWLE) at age 50 years by gender, cohort, and level of education in Australia. METHODS: We analysed data from two nationally representative cohorts in the Household Income and Labour Dynamics in Australia survey. Each cohort was followed up annually from 2001 to 2010 and from 2011 to 2020. Poor health was defined by a self-reported, limiting, long-term health condition. Work was defined by current employment status. HWLEs were estimated with Interpolated Markov Chain multi-state modelling. FINDINGS: We included data from 4951 participants in the cohort from 2001 to 2010 (2605 [53%] women and 2346 [47%] men; age range 50-100 years) and 6589 participants in the cohort from 2011 to 2020 (3518 [53%] women and 3071 [47%] men; age range 50-100 years). Baseline characteristics were similar between groups. Working life expectancy increased over time for all groups, regardless of gender or educational attainment. However, health expectancies only increased for men and people of either gender with higher education. Years working in good health at age 50 years for men were 9·9 years in 2001 (95% CI 9·3-10·4) and 10·8 years (10·4-11·3) in 2011. The corresponding HWLEs for women were 7·9 years (7·3-8·5) and 9·0 years (8·5-9·6). For people with low education level, HWLE was 7·9 years (7·3-8·5) in 2001 and 8·4 years (7·9-8·9) in 2011, and for those with high education level, HWLE rose from 9·6 years in 2001 (9·1-10·1) to 10·5 years in 2011 (10·2-10·9). Across all groups, there were at least 2·5 years working in poor health and 6·7 years not working in good health. INTERPRETATION: Increases in length of working life have not been accompanied by similar gains in healthy life expectancy for women or people of any gender with low education, and it is not unusual for workers older than 50 years to work with long-term health limitations. Strategies to achieve longer working lives should address life-course inequalities in health and encourage businesses and organisations to recruit, train, and retain mature-age workers. FUNDING: Australian Research Council.

Lifecourse socioeconomic position and cohort differences in health expectancy in Australia: a longitudinal cohort study.

BACKGROUND: There is a need to know how changes in health expectancy differ for population subgroups globally. The aim of this study was to estimate 10-year trends in health expectancies by individual markers of socioeconomic position from three points over the lifecourse, evaluating how compression and expansion of morbidity have varied within a national population. METHODS: We analysed data from two cohorts of the Household Income and Labour Dynamics in Australia survey. The cohorts were followed annually from 2001 to 2007 (n=4720; baseline age range 50-100 years) and 2011 to 2017 (n=6632; baseline age range 50-99 years). Health expectancies were estimated at age 65 years for four outcomes reflecting activity limitations, disability, perceived health, and mental health. Cohort differences were compared by gender, age left school, occupational prestige, and housing tenure. FINDINGS: Women with low socioeconomic position were the only group with no improvements in life expectancy across the two cohorts. Among men with low education and all women gains in life expectancy comprised entirely of years lived with global activity limitations. Compression of years lived with severe-disability, poor self-rated health, and poor mental health was most consistently observed for men and women with high education and home ownership. Occupational prestige did not greatly differentiate cohort differences in health expectancies. INTERPRETATION: Over the past two decades in Australia, social disparities in health expectancies have at least been maintained, and have increased for some outcomes. Equitable gains in health expectancies should be a major public health goal, and will help support sustainable health and social care systems. FUNDING: Australian Research Council.

Joint frailty modeling of time-to-event data to elicit the evolution pathway of events: a generalized linear mixed model approach.

Multimorbidity constitutes a serious challenge on the healthcare systems in the world, due to its association with poorer health-related outcomes, more complex clinical management, increases in health service utilization and costs, but a decrease in productivity. However, to date, most evidence on multimorbidity is derived from cross-sectional studies that have limited capacity to understand the pathway of multimorbid conditions. In this article, we present an innovative perspective on analyzing longitudinal data within a statistical framework of survival analysis of time-to-event recurrent data. The proposed methodology is based on a joint frailty modeling approach with multivariate random effects to account for the heterogeneous risk of failure and the presence of informative censoring due to a terminal event. We develop a generalized linear mixed model method for the efficient estimation of parameters. We demonstrate the capacity of our approach using a real cancer registry data set on the multimorbidity of melanoma patients and document the relative performance of the proposed joint frailty model to the natural competitor of a standard frailty model via extensive simulation studies. Our new approach is timely to advance evidence-based knowledge to address increasingly complex needs related to multimorbidity and develop interventions that are most effective and viable to better help a large number of individuals with multiple conditions.

Trends in disability-free life expectancy at age 50 years in Australia between 2001 and 2011 by social disadvantage.

BACKGROUND: The aims of this study were (1) to estimate 10-year trends in disability-free life expectancy (DFLE) by area-level social disadvantage and (2) to examine how incidence, recovery and mortality transitions contributed to these trends. METHODS: Data were drawn from the nationally representative Household Income and Labour Dynamics in Australia survey. Two cohorts (baseline age 50+ years) were followed up for 7 years, from 2001 to 2007 and from 2011 to 2017, respectively. Social disadvantage was indicated by the Socio-Economic Indexes for Areas (SEIFA). Two DFLEs based on a Global Activity Limitation Indicator (GALI) and difficulties with activities of daily living (ADLs) measured by the 36-Item Short Form Survey physical function subscale were estimated by cohort, sex and SEIFA tertile using multistate models. RESULTS: Persons residing in the low-advantage tertile had more years lived with GALI and ADL disability than those in high-advantage tertiles. Across the two cohorts, dynamic equilibrium for GALI disability was observed among men in mid-advantage and high-advantage tertiles, but expansion of GALI disability occurred in the low-advantage tertile. There was expansion of GALI disability for all women irrespective of their SEIFA tertile. Compression of ADL disability was observed for all men and for women in the high-advantage tertile. Compared to the 2001 cohort, disability incidence was lower for the 2011 cohort of men within mid-advantage and high-advantage tertiles, whereas recovery and disability-related mortality were lower for the 2011 cohort of women within the mid-advantage tertile. CONCLUSION: Overall, compression of morbidity was more common in high-advantage areas, whereas expansion of morbidity was characteristic of low-advantage areas. Trends also varied by sex and disability severity.

Mixture cure models with time-varying and multilevel frailties for recurrent event data.

Many medical studies yield data on recurrent clinical events from populations which consist of a proportion of cured patients in the presence of those who experience the event at several times (uncured). A frailty mixture cure model has recently been postulated for such data, with an assumption that the random subject effect (frailty) of each uncured patient is constant across successive gap times between recurrent events. We propose two new models in a more general setting, assuming a multivariate time-varying frailty with an AR(1) correlation structure for each uncured patient and addressing multilevel recurrent event data originated from multi-institutional (multi-centre) clinical trials, using extra random effect terms to adjust for institution effect and treatment-by-institution interaction. To solve the difficulties in parameter estimation due to these highly complex correlation structures, we develop an efficient estimation procedure via an EM-type algorithm based on residual maximum likelihood (REML) through the generalised linear mixed model (GLMM) methodology. Simulation studies are presented to assess the performances of the models. Data sets from a colorectal cancer study and rhDNase multi-institutional clinical trial were analyzed to exemplify the proposed models. The results demonstrate a large positive AR(1) correlation among frailties across successive gap times, indicating a constant frailty may not be realistic in some situations. Comparisons of findings with existing frailty models are discussed.

A bivariate joint frailty model with mixture framework for survival analysis of recurrent events with dependent censoring and cure fraction.

In the study of multiple failure time data with recurrent clinical endpoints, the classical independent censoring assumption in survival analysis can be violated when the evolution of the recurrent events is correlated with a censoring mechanism such as death. Moreover, in some situations, a cure fraction appears in the data because a tangible proportion of the study population benefits from treatment and becomes recurrence free and insusceptible to death related to the disease. A bivariate joint frailty mixture cure model is proposed to allow for dependent censoring and cure fraction in recurrent event data. The latency part of the model consists of two intensity functions for the hazard rates of recurrent events and death, wherein a bivariate frailty is introduced by means of the generalized linear mixed model methodology to adjust for dependent censoring. The model allows covariates and frailties in both the incidence and the latency parts, and it further accounts for the possibility of cure after each recurrence. It includes the joint frailty model and other related models as special cases. An expectation-maximization (EM)-type algorithm is developed to provide residual maximum likelihood estimation of model parameters. Through simulation studies, the performance of the model is investigated under different magnitudes of dependent censoring and cure rate. The model is applied to data sets from two colorectal cancer studies to illustrate its practical value.

Multilevel model with random effects for clustered survival data with multiple failure outcomes.

We present a multilevel frailty model for handling serial dependence and simultaneous heterogeneity in survival data with a multilevel structure attributed to clustering of subjects and the presence of multiple failure outcomes. One commonly observes such data, for example, in multi-institutional, randomized placebo-controlled trials in which patients suffer repeated episodes (eg, recurrent migraines) of the disease outcome being measured. The model extends the proportional hazards model by incorporating a random covariate and unobservable random institution effect to respectively account for treatment-by-institution interaction and institutional variation in the baseline risk. Moreover, a random effect term with correlation structure driven by a first-order autoregressive process is attached to the model to facilitate estimation of between patient heterogeneity and serial dependence. By means of the generalized linear mixed model methodology, the random effects distribution is assumed normal and the residual maximum likelihood and the maximum likelihood methods are extended for estimation of model parameters. Simulation studies are carried out to evaluate the performance of the residual maximum likelihood and the maximum likelihood estimators and to assess the impact of misspecifying random effects distribution on the proposed inference. We demonstrate the practical feasibility of the modeling methodology by analyzing real data from a double-blind randomized multi-institutional clinical trial, designed to examine the effect of rhDNase on the occurrence of respiratory exacerbations among patients with cystic fibrosis.

Patterns of multimorbid health conditions: a systematic review of analytical methods and comparison analysis.

Background: The latest review of studies on multimorbidity patterns showed high heterogeneity in the methodology for identifying groups of multimorbid conditions. However, it is unclear how analytical methods used influence the identified multimorbidity patterns. Methods: We undertook a systematic review of analytical methods used to identify multimorbidity patterns in PubMed and EMBASE from their inception to January 2017. We conducted a comparison analysis to assess the effect the analytical methods had on the multimorbidity patterns identified, using the Australian National Health Survey (NHS) 2007-08 data. Results: We identified 13 194 studies and excluded 13 091 based on titles/abstracts. From the full-text reviews of the 103 remaining publications, we identified 41 studies that used five different analytical methods to identify multimorbid conditions in the studies. Thirty-seven studies (90%) adopted either the factor-analysis or hierarchical-clustering methods, but heterogeneity arises for the use of different proximity measures within each method to form clusters. Our comparison analysis showed the variation in identified groups of multimorbid conditions when applying the methods to the same NHS data. We extracted main similarities among the groupings obtained by the five methods: (i) cardiovascular and metabolic diseases, (ii) mental health problems and (iii) allergic diseases. Conclusion: We showed the extent of effects for heterogeneous analytical methods on identification of multimorbidity patterns. However, more work is needed to guide investigators for choosing the best analytical method to improve the validity and generalizability of findings. Investigators should also attempt to compare results obtained by various methods for a consensus grouping of multimorbid conditions.