Estimation of age of onset and progression of breast cancer by absolute risk dependent on polygenic risk score and other risk factors.

BACKGROUND: Genetic, lifestyle, reproductive, and anthropometric factors are associated with the risk of developing breast cancer. However, it is not yet known whether polygenic risk score (PRS) and absolute risk based on a combination of risk factors are associated with the risk of progression of breast cancer. This study aims to estimate the distribution of sojourn time (pre-clinical screen-detectable period) and mammographic sensitivity by absolute breast cancer risk derived from polygenic profile and the other risk factors. METHODS: The authors used data from a population-based case-control study. Six categories of 10-year absolute risk based on different combinations of risk factors were derived using the Breast and Ovarian Analysis of Disease Incidence and Carrier Estimation Algorithm. Women were classified into low, medium, and high-risk groups. The authors constructed a continuous-time multistate model. To calculate the sojourn time, they simulated the trajectories of subjects through the disease states. RESULTS: There was little difference in sojourn time with a large overlap in the 95% confidence interval (CI) between the risk groups across the six risk categories and PRS studied. However, the age of entry into the screen-detectable state varied by risk category, with the mean age of entry of 53.4 years (95% CI, 52.2-54.1) and 57.0 years (95% CI, 55.1-57.7) in the high-risk and low-risk women, respectively. CONCLUSION: In risk-stratified breast screening, the age at the start of screening, but not necessarily the frequency of screening, should be tailored to a woman's risk level. The optimal risk-stratified screening strategy that would improve the benefit-to-harm balance and the cost-effectiveness of the screening programs needs to be studied.

A multistate survival model of the natural history of cancer using data from screened and unscreened population.

One of the main aims of models using cancer screening data is to determine the time between the onset of preclinical screen-detectable cancer and the onset of the clinical state of the cancer. This time is called the sojourn time. One problem in using screening data is that an individual can be observed in preclinical phase or clinically diagnosed but not both. Multistate survival models provide a method of modeling the natural history of cancer. The natural history model allows for the calculation of the sojourn time. We developed a continuous-time Markov model and the corresponding likelihood function. The model allows for the use of interval-censored, left-truncated and right-censored data. The model uses data of clinically diagnosed cancers from both screened and nonscreened individuals. Parameters of age-varying hazards and age-varying misclassification are estimated simultaneously. The mean sojourn time is calculated from a micro-simulation using model parameters. The model is applied to data from a prostate screening trial. The simulation study showed that the model parameters could be estimated accurately.

Duration of preclinical, prodromal, and dementia stages of Alzheimer's disease in relation to age, sex, and APOE genotype.

INTRODUCTION: We estimated the age-specific duration of the preclinical, prodromal, and dementia stages of Alzheimer's disease (AD) and the influence of sex, setting, apolipoprotein E (APOE) genotype, and cerebrospinal fluid tau on disease duration. METHODS: We performed multistate modeling in a combined sample of 6 cohorts (n = 3268) with death as the end stage and estimated the preclinical, prodromal, and dementia stage duration. RESULTS: The overall AD duration varied between 24 years (age 60) and 15 years (age 80). For individuals presenting with preclinical AD, age 70, the estimated preclinical AD duration was 10 years, prodromal AD 4 years, and dementia 6 years. Male sex, clinical setting, APOE ε4 allele carriership, and abnormal cerebrospinal fluid tau were associated with a shorter duration, and these effects depended on disease stage. DISCUSSION: Estimates of AD disease duration become more accurate if age, sex, setting, APOE, and cerebrospinal fluid tau are taken into account. This will be relevant for clinical practice and trial design.

Hidden three-state survival model for bivariate longitudinal count data.

A model is presented that describes bivariate longitudinal count data by conditioning on a progressive illness-death process where the two living states are latent. The illness-death process is modelled in continuous time, and the count data are described by a bivariate extension of the binomial distribution. The bivariate distributions for the count data approach include the correlation between two responses even after conditioning on the state. An illustrative data analysis is discussed, where the bivariate data consist of scores on two cognitive tests, and the latent states represent two stages of underlying cognitive function. By including a death state, possible association between cognitive function and the risk of death is accounted for.

Flexible multistate models for interval-censored data: Specification, estimation, and an application to ageing research.

Continuous-time multistate survival models can be used to describe health-related processes over time. In the presence of interval-censored times for transitions between the living states, the likelihood is constructed using transition probabilities. Models can be specified using parametric or semiparametric shapes for the hazards. Semiparametric hazards can be fitted using P-splines and penalised maximum likelihood estimation. This paper presents a method to estimate flexible multistate models that allow for parametric and semiparametric hazard specifications. The estimation is based on a scoring algorithm. The method is illustrated with data from the English Longitudinal Study of Ageing.

Transitions across cognitive states and death among older adults in relation to education: A multistate survival model using data from six longitudinal studies.

INTRODUCTION: This study examines the role of educational attainment, an indicator of cognitive reserve, on transitions in later life between cognitive states (normal Mini-Mental State Examination (MMSE), mild MMSE impairment, and severe MMSE impairment) and death. METHODS: Analysis of six international longitudinal studies was performed using a coordinated approach. Multistate survival models were used to estimate the transition patterns via different cognitive states. Life expectancies were estimated. RESULTS: Across most studies, a higher level of education was associated with a lower risk of transitioning from normal MMSE to mild MMSE impairment but was not associated with other transitions. Those with higher levels of education and socioeconomic status had longer nonimpaired life expectancies. DISCUSSION: This study highlights the importance of education in later life and that early life experiences can delay later compromised cognitive health. This study also demonstrates the feasibility and benefit in conducting coordinated analysis across multiple studies to validate findings.

Posterior distributions for likelihood ratios in forensic science.

Evaluation of evidence in forensic science is discussed using posterior distributions for likelihood ratios. Instead of eliminating the uncertainty by integrating (Bayes factor) or by conditioning on parameter values, uncertainty in the likelihood ratio is retained by parameter uncertainty derived from posterior distributions. A posterior distribution for a likelihood ratio can be summarised by the median and credible intervals. Using the posterior mean of the distribution is not recommended. An analysis of forensic data for body height estimation is undertaken. The posterior likelihood approach has been criticised both theoretically and with respect to applicability. This paper addresses the latter and illustrates an interesting application area.

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.

Change point models for cognitive tests using semi-parametric maximum likelihood.

Random-effects change point models are formulated for longitudinal data obtained from cognitive tests. The conditional distribution of the response variable in a change point model is often assumed to be normal even if the response variable is discrete and shows ceiling effects. For the sum score of a cognitive test, the binomial and the beta-binomial distributions are presented as alternatives to the normal distribution. Smooth shapes for the change point models are imposed. Estimation is by marginal maximum likelihood where a parametric population distribution for the random change point is combined with a non-parametric mixing distribution for other random effects. An extension to latent class modelling is possible in case some individuals do not experience a change in cognitive ability. The approach is illustrated using data from a longitudinal study of Swedish octogenarians and nonagenarians that began in 1991. Change point models are applied to investigate cognitive change in the years before death.

Bivariate joint models for survival and change of cognitive function.

Changes in cognitive function over time are of interest in ageing research. A joint model is constructed to investigate. Generally, cognitive function is measured through more than one test, and the test scores are integers. The aim is to investigate two test scores and use an extension of a bivariate binomial distribution to define a new joint model. This bivariate distribution model the correlation between the two test scores. To deal with attrition due to death, the Weibull hazard model and the Gompertz hazard model are used. A shared random-effects model is constructed, and the random effects are assumed to follow a bivariate normal distribution. It is shown how to incorporate random effects that link the bivariate longitudinal model and the survival model. The joint model is applied to the English Longitudinal Study of Ageing data.

Smooth random change point models.

Change point models are used to describe processes over time that show a change in direction. An example of such a process is cognitive ability, where a decline a few years before death is sometimes observed. A broken-stick model consists of two linear parts and a breakpoint where the two lines intersect. Alternatively, models can be formulated that imply a smooth change between the two linear parts. Change point models can be extended by adding random effects to account for variability between subjects. A new smooth change point model is introduced and examples are presented that show how change point models can be estimated using functions in R for mixed-effects models. The Bayesian inference using WinBUGS is also discussed. The methods are illustrated using data from a population-based longitudinal study of ageing, the Cambridge City over 75 Cohort Study. The aim is to identify how many years before death individuals experience a change in the rate of decline of their cognitive ability.

A mixture model for the joint analysis of latent developmental trajectories and survival.

A general joint modeling framework is proposed that includes a parametric stratified survival component for continuous time survival data, and a mixture multilevel item response component to model latent developmental trajectories given mixed discrete response data. The joint model is illustrated in a real data setting, where the utility of longitudinally measured cognitive function as a predictor for survival is investigated in a group of elderly persons. The object is partly to determine whether cognitive impairment is accompanied by a higher mortality rate. Time-dependent cognitive function is measured using the generalized partial credit model given occasion-specific mini-mental state examination response data. A parametric survival model is applied for the survival information, and cognitive function as a continuous latent variable is included as a time-dependent explanatory variable along with other explanatory information. A mixture model is defined, which incorporates the latent developmental trajectory and the survival component. The mixture model captures the heterogeneity in the developmental trajectories that could not be fully explained by the multilevel item response model and other explanatory variables. A Bayesian modeling approach is pursued, where a Markov chain Monte Carlo algorithm is developed for simultaneous estimation of the joint model parameters. Practical issues as model building and assessment are addressed using the DIC and various posterior predictive tests.

The Importance of Engaging in Physical Activity in Older Adulthood for Transitions Between Cognitive Status Categories and Death: A Coordinated Analysis of 14 Longitudinal Studies.

BACKGROUND: Given increasing incidence of cognitive impairment and dementia, further understanding of modifiable factors contributing to increased healthspan is crucial. Extensive literature provides evidence that physical activity (PA) delays the onset of cognitive impairment; however, it is unclear whether engaging in PA in older adulthood is sufficient to influence progression through cognitive status categories. METHOD: Applying a coordinated analysis approach, this project independently analyzed 14 longitudinal studies (NTotal = 52 039; mean baseline age across studies = 69.9-81.73) from North America and Europe using multistate survival models to estimate the impact of engaging in PA on cognitive status transitions (nonimpaired, mildly impaired, severely impaired) and death. Multinomial regression models were fit to estimate life expectancy (LE) based on American PA recommendations. Meta-analyses provided the pooled effect sizes for the role of PA on each transition and estimated LEs. RESULTS: Controlling for baseline age, sex, education, and chronic conditions, analyses revealed that more PA is significantly associated with decreased risk of transitioning from nonimpaired to mildly impaired cognitive functioning and death, as well as substantially longer LE. Results also provided evidence for a protective effect of PA after onset of cognitive impairment (eg, decreased risk of transitioning from mild-to-severe cognitive impairment; increased likelihood of transitioning backward from severe-to-mild cognitive impairment), though between-study heterogeneity suggests a less robust association. CONCLUSIONS: These results yield evidence for the importance of engaging in PA in older adulthood for cognitive health, and a rationale for motivating older adults to engage consistently in PA.

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

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

Gait speed as predictor of transition into cognitive impairment: Findings from three longitudinal studies on aging.

OBJECTIVES: Very few studies looking at slow gait speed as early marker of cognitive decline investigated the competing risk of death. The current study examines associations between slow gait speed and transitions between cognitive states and death in later life. METHODS: We performed a coordinated analysis of three longitudinal studies with 9 to 25 years of follow-up. Data were used from older adults participating in H70 (Sweden; n = 441; aged ≥70 years), InCHIANTI (Italy; n = 955; aged ≥65 years), and LASA (the Netherlands; n = 2824; aged ≥55 years). Cognitive states were distinguished using the Mini-Mental State Examination. Slow gait speed was defined as the lowest sex-specific quintile at baseline. Multistate models were performed, adjusted for age, sex and education. RESULTS: Most effect estimates pointed in the same direction, with slow gait speed predicting forward transitions. In two cohort studies, slow gait speed predicted transitioning from mild to severe cognitive impairment (InCHIANTI: HR = 2.08, 95%CI = 1.40-3.07; LASA: HR = 1.33, 95%CI = 1.01-1.75) and transitioning from a cognitively healthy state to death (H70: HR = 3.30, 95%CI = 1.74-6.28; LASA: HR = 1.70, 95%CI = 1.30-2.21). CONCLUSIONS: Screening for slow gait speed may be useful for identifying older adults at risk of adverse outcomes such as cognitive decline and death. However, once in the stage of more advanced cognitive impairment, slow gait speed does not seem to predict transitioning to death anymore.

A piecewise-constant Markov model and the effects of study design on the estimation of life expectancies in health and ill health.

Multi-state models are frequently applied to describe transitions over time between three states: healthy, not healthy and death. The three-state model can be used to estimate life expectancies in health and ill health. In this article, continuous-time Markov models are specified for the transitions between the three states. Transition intensities are regressed on age as a time-dependent covariate. The covariate is handled in a piecewise-constant fashion where the time interval between two consecutive observations is divided into subintervals of fixed and equal lengths. Study design choices such as sample size, length of follow-up, and time intervals between observations are investigated in a simulation study. The effects on parameter estimation are discussed as well as the effects on the estimation of life expectancies. In addition, data taken from the UK Cognitive Functioning and Ageing Study are analysed.

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

BACKGROUND AND OBJECTIVE: There is increasing interest in multi-state modelling of health-related stochastic processes. Given a fitted multi-state model with one death state, it is possible to estimate state-specific and marginal life expectancies. This paper introduces methods and new software for computing these expectancies. METHODS: The definition of state-specific life expectancy given current age is an extension of mean survival in standard survival analysis. The computation involves the estimated parameters of a fitted multi-state model, and numerical integration. The new R package elect provides user-friendly functions to do the computation in the R software. RESULTS: The estimation of life expectancies is explained and illustrated using the elect package. Functions are presented to explore the data, to estimate the life expectancies, and to present results. CONCLUSIONS: State-specific life expectancies provide a communicable representation of health-related processes. The availability and explanation of the elect package will help researchers to compute life expectancies and to present their findings in an assessable way.

Changes in working life expectancy with disability in the Netherlands, 1992-2016.

Objectives Like other western countries, the Netherlands has abolished early retirement schemes and is currently increasing the statutory retirement age. It is likely that also older workers with disabilities will be required to work longer. We examine the change in working life expectancy (WLE) with disability of older workers by comparing data from three periods: 1992-1996, 2002-2006 and 2012-2016. Methods Data are from the Longitudinal Aging Study Amsterdam (LASA). Respondents aged 55-65 with a paid job at baseline were included (N=1074). Disability was measured using the Global Activity Limitations Indicator (GALI). First, a continuous-time three-state survival model was created. Second, WLE with and without disability were estimated using MSM and ELECT in R. The modifying effects of gender and educational level were examined. Results Among those initially in paid employment, total WLE increased over 20 years. For example at age 58, total WLE increased from 3.7 to 5.5 years. WLE with disability at age 58 increased from 0.8 to 1.5 years. There was no difference in WLE with disability between male and female workers or low- and highly educated workers. Conclusions Between the 1990s and the 2010s, subsequent generations of older workers with disabilities have extended their working lives. The findings emphasize the importance of workplace interventions that facilitate older workers with disabilities to maintain well-being and work ability. In addition, the question arises whether current exit routes out of the workforce are still adequate.

Socio-economic inequalities in life expectancy of older adults with and without multimorbidity: a record linkage study of 1.1 million people in England.

BACKGROUND: Age of onset of multimorbidity and its prevalence are well documented. However, its contribution to inequalities in life expectancy has yet to be quantified. METHODS: A cohort of 1.1 million English people aged 45 and older were followed up from 2001 to 2010. Multimorbidity was defined as having 2 or more of 30 major chronic diseases. Multi-state models were used to estimate years spent healthy and with multimorbidity, stratified by sex, smoking status and quintiles of small-area deprivation. RESULTS: Unequal rates of multimorbidity onset and subsequent survival contributed to higher life expectancy at age 65 for the least (Q1) compared with most (Q5) deprived: there was a 2-year gap in healthy life expectancy for men [Q1: 7.7 years (95% confidence interval: 6.4-8.5) vs Q5: 5.4 (4.4-6.0)] and a 3-year gap for women [Q1: 8.6 (7.5-9.4) vs Q5: 5.9 (4.8-6.4)]; a 1-year gap in life expectancy with multimorbidity for men [Q1: 10.4 (9.9-11.2) vs Q5: 9.1 (8.7-9.6)] but none for women [Q1: 11.6 (11.1-12.4) vs Q5: 11.5 (11.1-12.2)]. Inequalities were attenuated but not fully attributable to socio-economic differences in smoking prevalence: multimorbidity onset was latest for never smokers and subsequent survival was longer for never and ex smokers. CONCLUSIONS: The association between social disadvantage and multimorbidity is complex. By quantifying socio-demographic and smoking-related contributions to multimorbidity onset and subsequent survival, we provide evidence for more equitable allocation of prevention and health-care resources to meet local needs.

Bayesian inference for an illness-death model for stroke with cognition as a latent time-dependent risk factor.

Longitudinal data can be used to estimate the transition intensities between healthy and unhealthy states prior to death. An illness-death model for history of stroke is presented, where time-dependent transition intensities are regressed on a latent variable representing cognitive function. The change of this function over time is described by a linear growth model with random effects. Occasion-specific cognitive function is measured by an item response model for longitudinal scores on the Mini-Mental State Examination, a questionnaire used to screen for cognitive impairment. The illness-death model will be used to identify and to explore the relationship between occasion-specific cognitive function and stroke. Combining a multi-state model with the latent growth model defines a joint model which extends current statistical inference regarding disease progression and cognitive function. Markov chain Monte Carlo methods are used for Bayesian inference. Data stem from the Medical Research Council Cognitive Function and Ageing Study in the UK (1991-2005).