Unobserved Heterogeneity in Multiple-Spell Multiple-States Duration Models

In survival analysis a large literature using frailty models, or models with unobserved heterogeneity, exist. In the growing literate on multiple spell multiple states duration models, or multistate models, modeling this issue is only at its infant phase. Ignoring unobserved heteogeneity can, however, produce incorrect results. This paper presents how unobserved heterogeneity can be incorporated into multistate models, with an emphasis on semi-Markov multistate models with a mixed proportional hazard structure. First, the aspects of frailty modeling in univariate (proportional hazard, Cox) duration models are addressed and some important models with unobserved heterogeneity are discussed. Second, the domain is extended to modeling of parallel/clustered multivariate duration data with unobserved heterogeneity. The implications of choosing shared or correlated unobserved heterogeneity is highlighted. The relevant differences with recurrent events data is covered next. They include the choice of the time scale and risk set which both have important implications for the way unobserved heterogeneity influence the model. Multistate duration models can have both parallel and recurrent events. Incorporating unobserved heterogeneity in multistate models, therefore, brings all the previously addressed issues together. Although some estimation procedures are covered the emphasis is on conceptual issues. The importance of including unobserved heterogeneity in multistate duration models is illustrated with data on labour market and migration dynamics of recent immigrants to The Netherlands.multiple spell multiple state duration, mixed proportional hazard, multistate model, unobserved heterogeneity, frailty

Bivariate Interval-Censored Failure Time Data

This is the peer reviewed version of the following article: Cook, R. J., Zeng, L. and Lee, K.-A. (2008), A Multistate Model for Bivariate Interval-Censored Failure Time Data. Biometrics, 64: 1100–1109. doi: 10.1111/j.1541-0420.2007.00978.x, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1111/j.1541-0420.2007.00978.x/abstract. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving. The definitive version is available at http://onlinelibrary.wiley.com/doi/10.1111/j.1541-0420.2007.00978.x/abstract’Interval-censored life-history data arise when the events of interest are only detectable at periodic assessments. When interest lies in the occurrence of two such events, bivariate-interval censored event time data are obtained. We describe how to fit a four-state Markov model useful for characterizing the association between two interval-censored event times when the assessment times for the two events may be generated by different inspection processes. The approach treats the two events symmetrically and enables one to fit multiplicative intensity models that give estimates of covariate effects as well as relative risks characterizing the association between the two events. An expectation-maximization (EM) algorithm is described for estimation in which the maximization step can be carried out with standard software. The method is illustrated by application to data from a trial of HIV patients where the events are the onset of viral shedding in the blood and urine among individuals infected with cytomegalovirus.Natural Sciences and Engineering Research Council of Canada (RGPIN 155849); Canadian Institutes for Health Research (FRN 13887); Canada Research Chair (Tier 1) – CIHR funded (950-226626

p3state.msm: Analyzing Survival Data from an Illness-Death Model

In longitudinal studies of disease, patients can experience several events across a followup period. Analysis of such studies can be successfully performed by multi-state models. In the multi-state framework, issues of interest include the study of the relationship between covariates and disease evolution, estimation of transition probabilities, and survival rates. This paper introduces p3state.msm, a software application for R which performs inference in an illness-death model. It describes the capabilities of the program for estimating semi-parametric regression models and for implementing nonparametric estimators for several quantities. The main feature of the package is its ability for obtaining nonMarkov estimates for the transition probabilities. Moreover, the methods can also be used in progressive three-state models. In such a model, estimators for other quantities, such as the bivariate distribution function (for sequentially ordered events), are also given. The software is illustrated using data from the Stanford Heart Transplant Study.

Statistical Degradation Models for Electronics

With increasing presence of electronics in modern systems and in every-day products, their reliability is inextricably dependent on that of their electronics. We develop reliability models for failure-time prediction under small failure-time samples and information on individual degradation history. The development of the model extends the work of Whitmore et al. 1998, to incorporate two new data-structures common to reliability testing. Reliability models traditionally use lifetime information to evaluate the reliability of a device or system. To analyze small failure-time samples within dynamic environments where failure mechanisms are unknown, there is a need for models that make use of auxiliary reliability information. In this thesis we present models suitable for reliability data, where degradation variables are latent and can be tracked by related observable variables we call markers. We provide an engineering justification for our model and develop parametric and predictive inference equations for a data-structure that includes terminal observations of the degradation variable and longitudinal marker measurements. We compare maximum likelihood estimation and prediction results obtained by Whitmore et. al. 1998 and show improvement in inference under small sample sizes. We introduce modeling of variable failure thresholds within the framework of bivariate degradation models and discuss ways of incorporating covariates. In the second part of the thesis we investigate anomaly detection through a Bayesian support vector machine and discuss its place in degradation modeling. We compute posterior class probabilities for time-indexed covariate observations, which we use as measures of degradation. Lastly, we present a multistate model used to model a recurrent event process and failure-times. We compute the expected time to failure using counting process theory and investigate the effect of the event process on the expected failure-time estimates

Composite likelihood for multiple multistate processes

This is a pre-copyedited, author-produced PDF of an article accepted for publication in Biostatistics following peer review. The version of record Biostat (2014) 15 (4): 690-705 first published online April 9, 2014 doi:10.1093/biostatistics/kxu011 is available online at: http://dx.doi.org/10.1093/biostatistics/kxu011A copula-based model is described which enables joint analysis of multiple progressive multistate processes. Unlike intensity-based or frailty-based approaches to joint modeling, the copula formulation proposed herein ensures that a wide range of marginal multistate processes can be specified and the joint model will retain these marginal features. The copula formulation also facilitates a variety of approaches to estimation and inference including composite likelihood and two-stage estimation procedures. We consider processes with Markov margins in detail, which are often suitable when chronic diseases are progressive in nature. We give special attention to the setting in which individuals are examined intermittently and transition times are consequently interval-censored. Simulation studies give empirical insight into the different methods of analysis and an application involving progression in joint damage in psoriatic arthritis provides further illustration.Natural Sciences and Engineering Research Council || RGPIN/155849 Canadian Institutes for Health Research (FRN 13887

The bootstrap approach to the multistate life table method using Stata: Does accounting for complex survey designs matter?

Objective: I aim to develop a Stata program that estimates multistate life table quantities and their confidence intervals while controlling for covariates of interest, as well as adjusting for complex survey designs. Using the Health and Retirement Study (HRS) (2000-2016), I use the new program to estimate US females' total, healthy, and unhealthy life expectancies and their intervals by race/ethnicity at age 52 (the youngest age in the sample), while adjusting for education. Methods: Using the nonparametric bootstrap technique (with replacement), the present study offers and validates an age-inhomogeneous first-order Markov chain multistate life table program. The current proposed Stata program is the maximum likelihood version of Lynch and Brown's Bayesian approach to the multistate life table method, which has been developed in R. I use the estimates from the Bayesian approach to validate the estimates from the unweighted bootstrap approach. I also account for the HRS complex survey design using the HRS baseline survey design indicators (clustering, strata, and sample weights). I utilize the estimates from the unweighted and weighted bootstrap models to evaluate the extent to which ignoring the HRS complex survey design alters the estimates. Results: The health expectancy estimates obtained from the unweighted bootstrap approach are consistent with estimates from the Bayesian approach, which ignores complex survey designs. This indicates that the bootstrap approach developed in the current paper is valid. Also, the results show that ignoring the HRS complex survey design does not meaningfully alter the estimates. Contribution: The paper contributes to the multistate life table methods literature by providing a flexible, valid, and user-friendly program to estimate multistate life table quantities and their variabilities in Stata

Flexible Methods for the Analysis of Clustered Event Data in Observational Studies

Clustered event data are frequently encountered in observational studies. In this dissertation, I am focusing on correlated event outcomes clustered by subjects (multivariate events), facilities, and both hierarchically. The main approaches to analyzing correlated event data include frailty models with random effects and marginal models with robust variance estimation. Difficulties for the existing methods include a) computational demands and speed in the presence of numerous clusters (e.g., recurrent events); b) lacking rigorous diagnostic tools to prespecify the distribution of the random effects; c) analyzing a multi-state model that follows a semi-Markov renewal process. The growing need for flexible, computationally fast, and accurate estimating approaches to analyzing clustered event data motivates my methodological exploration in the following chapters. In Chapter II, I propose a log-normal correlated frailty model to analyze recurrent event incidence rates and duration jointly. The regression parameters are estimated through a penalized partial likelihood, and the variance-covariance matrix of the frailty is estimated via a recursive estimating formula. The proposed methods are more flexible and faster than existing approaches and have the potential to be extended to other frequently encountered data structures (e.g., joint modeling with longitudinal outcomes). In Chapter III, I propose a class of semiparametric frailty models that leave the distribution of frailties unspecified. Parameter estimation proceeds through estimating equations derived from first- and second-moment conditions. Estimation techniques have been developed for three different models, including a shared frailty model for a single event; a correlated frailty model for multiple events; and a hierarchically structured nested failure time model. Extensive simulation studies demonstrate that the proposed approach can accurately estimate the regression parameters, baseline event rates, and variance components. Moreover, the computation time is fast, permitting application to very large data sets. In Chapter IV, I develop a class of multi-state rate models to study the association of exposure to lead, a major endocrine disruptive agent, with behavioral changes captured by accelerometer measurements from wearable device ActiGraph GT3X. Categorized from personal activity counts over time by validated cutoffs, activity states are defined and analyzed through their in-state transitions using the proposed multi-state rate models in which the baseline rates are estimated nonparametrically. The proposed models combine the advantage of regular event rate models with the concept of competing risks, allowing to incorporate a daily renewal property and share baselines in the activity transition rates across different days. The regression parameters are specified in the event rate functions, leading to a semiparametric modeling framework. Statistical inference is based on a robust sandwich variance estimator that accounts for correlations between different event types and their recurrences. I found that the evaluated exposure to lead is associated with an increased transition from low activity to vigorous activity. Chapter V is a special project of modeling the COVID-19 surveillance data in China, in which I develop two extended susceptible-infected-recovered (SIR) state-space models under a Bayesian state-space model framework. I propose to include a time-varying transmission rate or a time-dependent quarantine process in the classical SIR model to assess the effectiveness of macro-control measures issued by the government to mitigate the pandemic. The proposed compartment models enable to predict both short-term and long-term prevalence of the COVID-19 infection with quantification of prediction uncertainty. I provide and maintain an open-source R package on GitHub (lilywang1988/eSIR) for the developed analytics.PHDBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163013/1/lilywang_1.pd

Developing prediction models to estimate the risk of two survival outcomes both occurring: A comparison of techniques

IntroductionThis study considers the prediction of the time until two survival outcomes have both occurred. We compared a variety of analytical methods motivated by a typical clinical problem of multimorbidity prognosis.MethodsWe considered five methods: product (multiply marginal risks), dual-outcome (directly model the time until both events occur), multistate models (msm), and a range of copula and frailty models. We assessed calibration and discrimination under a variety of simulated data scenarios, varying outcome prevalence, and the amount of residual correlation. The simulation focused on model misspecification and statistical power. Using data from the Clinical Practice Research Datalink, we compared model performance when predicting the risk of cardiovascular disease and type 2 diabetes both occurring.ResultsDiscrimination was similar for all methods. The product method was poorly calibrated in the presence of residual correlation. The msm and dual-outcome models were the most robust to model misspecification but suffered a drop in performance at small sample sizes due to overfitting, which the copula and frailty model were less susceptible to. The copula and frailty model's performance were highly dependent on the underlying data structure. In the clinical example, the product method was poorly calibrated when adjusting for 8 major cardiovascular risk factors.DiscussionWe recommend the dual-outcome method for predicting the risk of two survival outcomes both occurring. It was the most robust to model misspecification, although was also the most prone to overfitting. The clinical example motivates the use of the methods considered in this study

A Joint Model for Multistate Disease Processes and Random Informative Observation Times, with Applications to Electronic Medical Records Data

Multistate models are used to characterize individuals\u27 natural histories through diseases with discrete states. Observational data resources based on electronic medical records pose new opportunities for studying such diseases. However, these data consist of observations of the process at discrete sampling times, which may either be pre-scheduled and non-informative, or symptom-driven and informative about an individual\u27s underlying disease status. We have developed a novel joint observation and disease transition model for this setting. The disease process is modeled according to a latent continuous time Markov chain; and the observation process, according to a Markov-modulated Poisson process with observation rates that depend on the individual\u27s underlying disease status. The disease process is observed at informative or non-informative sampling times, with possible misclassification error. We demonstrate that the model is computationally tractable and devise an expectation-maximization algorithm for parameter estimation. Using simulated data, we show how estimates from our joint observation and disease transition model lead to less biased and more precise estimates of the disease rate parameters. We apply the model to a study of secondary breast cancer events, utilizing mammography and biopsy records from a sample of women with a history of primary breast cancer