A MARKOV TRANSITION MODEL TO DEMENTIA WITH DEATH AS A COMPETING EVENT

The research on multi-state Markov transition model is motivated by the nature of the longitudinal data from the Nun Study (Snowdon, 1997), and similar information on the BRAiNS cohort (Salazar, 2004). Our goal is to develop a flexible methodology for handling the categorical longitudinal responses and competing risks time-to-event that characterizes the features of the data for research on dementia. To do so, we treat the survival from death as a continuous variable rather than defining death as a competing absorbing state to dementia. We assume that within each subject the survival component and the Markov process are linked by a shared latent random effect, and moreover, these two pieces are conditionally independent given the random effect and their corresponding predictor variables. The problem of the dependence among observations made on the same subject (repeated measurements) is addressed by assuming a first order Markovian dependence structure. A closed-form expression for the individual and thus overall conditional marginal likelihood function is derived, which we can evaluate numerically to produce the maximum likelihood estimates for the unknown parameters. This method can be implemented using standard statistical software such as SAS Proc Nlmixed©. We present the results of simulation studies designed to show how the model’s ability to accurately estimate the parameters can be affected by the distributional form of the survival term. Then we focus on addressing the problem by accommodating the residual life time of the subject’s confounding in the nonhomogeneous chain. The convergence status of the chain is examined and the formulation of the absorption statistics is derived. We propose using the Delta method to estimate the variance terms for construction of confidence intervals. The results are illustrated with applications to the Nun Study data in details

MULTI-STATE MODELS FOR INTERVAL CENSORED DATA WITH COMPETING RISK

Multi-state models are often used to evaluate the effect of death as a competing event to the development of dementia in a longitudinal study of the cognitive status of elderly subjects. In this dissertation, both multi-state Markov model and semi-Markov model are used to characterize the flow of subjects from intact cognition to dementia with mild cognitive impairment and global impairment as intervening transient, cognitive states and death as a competing risk. Firstly, a multi-state Markov model with three transient states: intact cognition, mild cognitive impairment (M.C.I.) and global impairment (G.I.) and one absorbing state: dementia is used to model the cognitive panel data. A Weibull model and a Cox proportional hazards (Cox PH) model are used to fit the time to death based on age at entry and the APOE4 status. A shared random effect correlates this survival time with the transition model. Secondly, we further apply a Semi-Markov process in which we assume that the wait- ing times are Weibull distributed except for transitions from the baseline state, which are exponentially distributed and we assume no additional changes in cognition occur between two assessments. We implement a quasi-Monte Carlo (QMC) method to calculate the higher order integration needed for the likelihood based estimation. At the end of this dissertation we extend a non-parametric “local EM algorithm” to obtain a smooth estimator of the cause-specific hazard function (CSH) in the presence of competing risk. All the proposed methods are justified by simulation studies and applications to the Nun Study data, a longitudinal study of late life cognition in a cohort of 461 subjects

PARAMETRIC ESTIMATION IN COMPETING RISKS AND MULTI-STATE MODELS

The typical research of Alzheimer\u27s disease includes a series of cognitive states. Multi-state models are often used to describe the history of disease evolvement. Competing risks models are a sub-category of multi-state models with one starting state and several absorbing states. Analyses for competing risks data in medical papers frequently assume independent risks and evaluate covariate effects on these events by modeling distinct proportional hazards regression models for each event. Jeong and Fine (2007) proposed a parametric proportional sub-distribution hazard (SH) model for cumulative incidence functions (CIF) without assumptions about the dependence among the risks. We modified their model to assure that the sum of the underlying CIFs never exceeds one, by assuming a proportional SH model for dementia only in the Nun study. To accommodate left censored data, we computed non-parametric MLE of CIF based on Expectation-Maximization algorithm. Our proposed parametric model was applied to the Nun Study to investigate the effect of genetics and education on the occurrence of dementia. After including left censored dementia subjects, the incidence rate of dementia becomes larger than that of death for age \u3c 90, education becomes significant factor for incidence of dementia and standard errors for estimates are smaller. Multi-state Markov model is often used to analyze the evolution of cognitive states by assuming time independent transition intensities. We consider both constant and duration time dependent transition intensities in BRAiNS data, leading to a mixture of Markov and semi-Markov processes. The joint probability of observing a sequence of same state until transition in a semi-Markov process was expressed as a product of the overall transition probability and survival probability, which were simultaneously modeled. Such modeling leads to different interpretations in BRAiNS study, i.e., family history, APOE4, and sex by head injury interaction are significant factors for transition intensities in traditional Markov model. While in our semi-Markov model, these factors are significant in predicting the overall transition probabilities, but none of these factors are significant for duration time distribution

CONTINUOUS TIME MULTI-STATE MODELS FOR INTERVAL CENSORED DATA

Continuous-time multi-state models are widely used in modeling longitudinal data of disease processes with multiple transient states, yet the analysis is complex when subjects are observed periodically, resulting in interval censored data. Recently, most studies focused on modeling the true disease progression as a discrete time stationary Markov chain, and only a few studies have been carried out regarding non-homogenous multi-state models in the presence of interval-censored data. In this dissertation, several likelihood-based methodologies were proposed to deal with interval censored data in multi-state models. Firstly, a continuous time version of a homogenous Markov multi-state model with backward transitions was proposed to handle uneven follow-up assessments or skipped visits, resulting in the interval censored data. Simulations were used to compare the performance of the proposed model with the traditional discrete time stationary Markov chain under different types of observation schemes. We applied these two methods to the well-known Nun study, a longitudinal study of 672 participants aged ≥ 75 years at baseline and followed longitudinally with up to ten cognitive assessments per participant. Secondly, we constructed a non-homogenous Markov model for this type of panel data. The baseline intensity was assumed to be Weibull distributed to accommodate the non-homogenous property. The proportional hazards method was used to incorporate risk factors into the transition intensities. Simulation studies showed that the Weibull assumption does not affect the accuracy of the parameter estimates for the risk factors. We applied our model to data from the BRAiNS study, a longitudinal cohort of 531 subjects each cognitively intact at baseline. Last, we presented a parametric method of fitting semi-Markov models based on Weibull transition intensities with interval censored cognitive data with death as a competing risk. We relaxed the Markov assumption and took interval censoring into account by integrating out all possible unobserved transitions. The proposed model also allowed for incorporating time-dependent covariates. We provided a goodness-of-fit assessment for the proposed model by the means of prevalence counts. To illustrate the methods, we applied our model to the BRAiNS study

SmoothHazard:An R package for fitting regression models to interval-censored observations of illness-death models

The irreversible illness-death model describes the pathway from an initial state to an absorbing state either directly or through an intermediate state. This model is frequently used in medical applications where the intermediate state represents illness and the absorbing state represents death. In many studies, disease onset times are not known exactly. This happens for example if the disease status of a patient can only be assessed at follow-up visits. In this situation the disease onset times are interval-censored. This article presents the SmoothHazard package for R. It implements algorithms for simultaneously fitting regression models to the three transition intensities of an illness-death model where the transition times to the intermediate state may be interval-censored and all the event times can be right-censored. The package parses the individual data structure of the subjects in a data set to find the individual contributions to the likelihood. The three baseline transition intensity functions are modelled by Weibull distributions or alternatively by M -splines in a semi-parametric approach. For a given set of covariates, the estimated transition intensities can be combined into predictions of cumulative event probabilities and life expectancies

Temporal trend in dementia incidence since 2002 and projections for prevalence in England and Wales to 2040 : modelling study

OBJECTIVE To forecast dementia prevalence with a dynamic modelling approach that integrates calendar trends in dementia incidence with those for mortality and cardiovascular disease. DESIGN Modelling study. SETTING General adult population of England and Wales. PARTICIPANTS The English Longitudinal Study of Ageing (ELSA) is a representative panel study with six waves of data across 2002-13. Men and women aged 50 or more years, selected randomly, and their cohabiting partners were recruited to the first wave of ELSA (2002-03). 11392 adults participated (response rate 67%). To maintain representativeness, refreshment participants were recruited to the study at subsequent waves. The total analytical sample constituted 17 906 people. Constant objective criteria based on cognitive and functional impairment were used to ascertain dementia cases at each wave. MAIN OUTCOME MEASURES To estimate calendar trends in dementia incidence, correcting for bias due to loss to follow-up of study participants, a joint model of longitudinal and time-to-event data was fitted to ELSA data. To forecast future dementia prevalence, the probabilistic Markov model IMPACT-BAM (IMPACT-Better Ageing Model) was developed. IMPACT-BAM models transitions of the population aged 35 or more years through states of cardiovascular disease, cognitive and functional impairment, and dementia, to death. It enables prediction of dementia prevalence while accounting for the growing pool of susceptible people as a result of increased life expectancy and the competing effects due to changes in mortality, and incidence of cardiovascular disease. RESULTS In ELSA, dementia incidence was estimated at 14.3 per 1000 person years in men and 17.0/1000 person years in women aged 50 or more in 2010. Dementia incidence declined at a relative rate of 2.7% (95% confidence interval 2.4% to 2.9%) for each year during 2002-13. Using IMPACT-BAM, we estimated there were approximately 767 000 (95% uncertainty interval 735 000 to 797 000) people with dementia in England and Wales in 2016. Despite the decrease in incidence and age specific prevalence, the number of people with dementia is projected to increase to 872 000, 1 092 000, and 1 205 000 in 2020, 2030, and 2040, respectively. A sensitivity analysis without the incidence decline gave a much larger projected growth, of more than 1.9 million people with dementia in 2040. CONCLUSIONS Age specific dementia incidence is declining. The number of people with dementia in England and Wales is likely to increase by 57% from 2016 to 2040. This increase is mainly driven by improved life expectancy.Peer reviewe

Cognitive Reserve and Mild Cognitive Impairment

Background and Objectives Little is known about the effect of education or other indicators of cognitive reserve on the rate of reversion from mild cognitive impairment (MCI) to normal cognition (NC) or the relative rate (RR) of reversion from MCI to NC vs progression from MCI to dementia. Our objectives were to (1) estimate transition rates from MCI to NC and dementia and (2) determine the effect of age, APOE, and indicators of cognitive reserve on the RR of reversion vs progression using multistate Markov modeling. Methods We estimated instantaneous transition rates between NC, MCI, and dementia after accounting for transition to death across up to 12 assessments in the Nun Study, a cohort study of religious sisters aged 75+ years. We estimated RRs of reversion vs progression for age, APOE, and potential cognitive reserve indicators: education, academic performance (high school grades), and written language skills (idea density, grammatical complexity). Results Of the 619 participants, 472 were assessed with MCI during the study period. Of these 472, 143 (30.3%) experienced at least one reverse transition to NC, and 120 of the 143 (83.9%) never developed dementia (mean follow-up = 8.6 years). In models adjusted for age group and APOE, higher levels of education more than doubled the RR ratio of reversion vs progression. Novel cognitive reserve indicators were significantly associated with a higher adjusted RR of reversion vs progression (higher vs lower levels for English grades: RR ratio = 1.83; idea density: RR ratio = 3.93; and grammatical complexity: RR ratio = 5.78). Discussion Knowledge of frequent reversion from MCI to NC may alleviate concerns of inevitable cognitive decline in those with MCI. Identification of characteristics predicting the rate of reversion from MCI to NC vs progression from MCI to dementia may guide population-level interventions targeting these characteristics to prevent or postpone MCI and dementia. Research on cognitive trajectories would benefit from incorporating predictors of reverse transitions and competing events, such as death, into statistical modeling. These results may inform the design and interpretation of MCI clinical trials, given that a substantial proportion of participants may experience improvement without intervention

MULTI-STATE MODELS WITH MISSING COVARIATES

Multi-state models have been widely used to analyze longitudinal event history data obtained in medical studies. The tools and methods developed recently in this area require the complete observed datasets. While, in many applications measurements on certain components of the covariate vector are missing on some study subjects. In this dissertation, several likelihood-based methodologies were proposed to deal with datasets with different types of missing covariates efficiently when applying multi-state models. Firstly, a maximum observed data likelihood method was proposed when the data has a univariate missing pattern and the missing covariate is a categorical variable. The construction of the observed data likelihood function is based on the model of a joint distribution of the response longitudinal event history data and the discrete covariate with missing values. Secondly, we proposed a maximum simulated likelihood method to deal with the missing continuous covariate when applying multi-state models. The observed data likelihood function was approximated by using the Monte Carlo simulation method. At last, an EM algorithm was used to deal with multiple missing covariates when estimating the parameters of multi-state model. The EM algorithm would be able to handle multiple missing discrete covariates in general missing pattern efficiently. All the proposed methods are justified by simulation studies and applications to the datasets from the SMART project, a consortium of 11 different high-quality longitudinal studies of aging and cognition