State transition modeling of complex monitored health data

This article considers the analysis of complex monitored health data, where often one or several signals are reflecting the current health status that can be represented by a finite number of states, in addition to a set of covariates. In particular, we consider a novel application of a non-parametric state intensity regression method in order to study time-dependent effects of covariates on the state transition intensities. The method can handle baseline, time varying as well as dynamic covariates. Because of the non-parametric nature, the method can handle different data types and challenges under minimal assumptions. If the signal that is reflecting the current health status is of continuous nature, we propose the application of a weighted median and a hysteresis filter as data pre-processing steps in order to facilitate robust analysis. In intensity regression, covariates can be aggregated by a suitable functional form over a time history window. We propose to study the estimated cumulative regression parameters for different choices of the time history window in order to investigate short- and long-term effects of the given covariates. The proposed framework is discussed and applied to resuscitation data of newborns collected in Tanzania.     

Quotas on runs of successes and failures in a multi-state markov chain

For the time-homogeneous multi-state Markov chain {X_n,n≧0} with states labeled as "0" (success) and "f"(failure), f=1,2,… the waiting time problems to be discussed arise by setting quotas on runs of success and failures. Some particular cases are considered.     

Optimal design and maintenance of a repairable multi-state system with standby components

The configuration of a repairable system directly influences its performance measures, such as mean time between failures and steady state availability. Additionally, maintenance strategies such as corrective, preventive, and condition-based can affect the performance of the system. The objective of this work is to investigate the trade-offs between the configuration of a repairable multi-state system with binary components and its maintenance strategy. The corresponding stochastic process for the proposed model is formulated using the continuous-time Markov process and important performance measures of such a multi-state system are derived. An optimization model is introduced for the cost-effective design of this repairable multi-state system. The results are demonstrated using a numerical example for a power generation system.     

Mixture Multi-state Markov Regression Model

Although heterogeneity across individuals may be reduced when a two-state process is extended into a multi-state process, the discrepancy between the observed and the predicted for some states may still exist owing to two possibilities, unobserved mixture distribution in the initial state and the effect of measured covariates on subsequent multi-state disease progression. In the present study, we developed a mixture Markov exponential regression model to take account of the above-mentioned heterogeneity across individuals (subject-to-subject variability) with a systematic model selection based on the likelihood ratio test. The model was successfully demonstrated by an empirical example on surveillance of patients with small hepatocellular carcinoma treated by non-surgical methods. The estimated results suggested that the model with the incorporation of unobserved mixture distribution behaves better than the one without. Complete and partial effects regarding risk factors on different subsequent multi-state transitions were identified using a homogeneous Markov model. The combination of both initial mixture distribution and homogeneous Markov exponential regression model makes a significant contribution to reducing heterogeneity across individuals and over time for disease progression.     

Choice between Semi-parametric Estimators of Markov and Non-Markov Multi-state Models from Coarsened Observations

Abstract.  We consider models based on multivariate counting processes, including multi-state models. These models are specified semi-parametrically by a set of functions and real parameters. We consider inference for these models based on coarsened observations, focusing on families of smooth estimators such as produced by penalized likelihood. An important issue is the choice of model structure, for instance, the choice between a Markov and some non-Markov models. We define in a general context the expected Kullback–Leibler criterion and we show that the likelihood-based cross-validation (LCV) is a nearly unbiased estimator of it. We give a general form of an approximate of the leave-one-out LCV. The approach is studied by simulations, and it is illustrated by estimating a Markov and two semi-Markov illness–death models with application on dementia using data of a large cohort study.     

The future of Australia’s Indigenous Population, 2011–61

Existing projections of Australia’s Indigenous Population suffer from a number of limitations: problematic input data, unsatisfactory projection model design, and poor forecast performance. The aim of this study was to create a new model for projecting that population that better represents the demographic processes at work, and that makes use of a newly available data source on identification change. A new projection model is presented that explicitly incorporates ethnic-identification change, and mixed (Indigenous/Non-Indigenous) partnering and childbearing. It is a composite static–dynamic model which takes a multi-state form where data allow. The model was used to produce projections for the 2011–61 period. Rapid growth of the Indigenous Population is expected, with population momentum, identification change, and mixed partnering and childbearing shown to contribute more to growth than above-replacement fertility and increasing life expectancy. The future growth of Australia’s Indigenous Population is thus intimately connected to its interaction with the Non-Indigenous Population.     

Estimation of multi-state models with missing covariate values based on observed data likelihood

Abstract

Continuous-time multi-state models are commonly used to study diseases with multiple stages. Potential risk factors associated with the disease are added to the transition intensities of the model as covariates, but missing covariate measurements arise frequently in practice. We propose a likelihood-based method that deals efficiently with a missing covariate in these models. Our simulation study showed that the method performs well for both “missing completely at random” and “missing at random” mechanisms. We also applied our method to a real dataset, the Einstein Aging Study.     

Weibull multi-state models with misclassification

It is often important to allow multi-state models (MSMs) to accommodate misclassification of states. We introduce Bayesian parametric MSMs with unknown misclassification of states and Weibull distributed waiting times between states. This allows transitions between states to depend on the time spent in the current state, a feature lacking in commonly used exponential waiting times model. To fit the proposed model, a MCMC algorithm was employed. An example on the progression of bipolar disorder is presented along with simulation results. There was evidence that Weibull waiting times are an improvement over exponential in the study of bipolar disorder.