A discrete approximation method for modeling interval-censored multistate data

Many longitudinal studies are designed to monitor participants for major events related to the progression of diseases. Data arising from such longitudinal studies are usually subject to interval censoring since the events are only known to occur between two monitoring visits. In this work, we propose a new method to handle interval-censored multistate data within a proportional hazards model framework where the hazard rate of events is modeled by a nonparametric function of time and the covariates affect the hazard rate proportionally. The main idea of this method is to simplify the likelihood functions of a discrete-time multistate model through an approximation and the application of data augmentation techniques, where the assumed presence of censored information facilitates a simpler parameterization. Then the expectation-maximization algorithm is used to estimate the parameters in the model. The performance of the proposed method is evaluated by numerical studies. Finally, the method is employed to analyze a dataset on tracking the advancement of coronary allograft vasculopathy following heart transplantation.

The spatial effects of the household's food insecurity levels in Ethiopia: by ordinal geo-additive model

Background

Food insecurity and vulnerability in Ethiopia are historical problems due to natural- and human-made disasters, which affect a wide range of areas at a higher magnitude with adverse effects on the overall health of households. In Ethiopia, the problem is wider with higher magnitude. Moreover, this geographical distribution of this challenge remains unexplored regarding the effects of cultures and shocks, despite previous case studies suggesting the effects of shocks and other factors. Hence, this study aims to assess the geographic distribution of corrected-food insecurity levels (FCSL) across zones and explore the comprehensive effects of diverse factors on each level of a household's food insecurity.

Method

This study analyzes three-term household-based panel data for years 2012, 2014, and 2016 with a total sample size of 11505 covering the all regional states of the country. An extended additive model, with empirical Bayes estimation by modeling both structured spatial effects using Markov random field or tensor product and unstructured effects using Gaussian, was adopted to assess the spatial distribution of FCSL across zones and to further explore the comprehensive effect of geographic, environmental, and socioeconomic factors on the locally adjusted measure.

Result

Despite a chronological decline, a substantial portion of Ethiopian households remains food insecure (25%) and vulnerable (27.08%). The Markov random field (MRF) model is the best fit based on GVC, revealing that 90.04% of the total variation is explained by the spatial effects. Most of the northern and south-western areas and south-east and north-west areas are hot spot zones of food insecurity and vulnerability in the country. Moreover, factors such as education, urbanization, having a job, fertilizer usage in cropping, sanitation, and farming livestock and crops have a significant influence on reducing a household's probability of being at higher food insecurity levels (insecurity and vulnerability), whereas shocks occurrence and small land size ownership have worsened it.

Conclusion

Chronically food insecure zones showed a strong cluster in the northern and south-western areas of the country, even though higher levels of household food insecurity in Ethiopia have shown a declining trend over the years. Therefore, in these areas, interventions addressing spatial structure factors, particularly urbanization, education, early marriage control, and job creation, along with controlling conflict and drought effect by food aid and selected coping strategies, and performing integrated farming by conserving land and the environment of zones can help to reduce a household's probability of being at higher food insecurity levels.

A Bayesian multivariate spatial approach for illness-death survival models

Illness-death models are a class of stochastic models inside the multi-state framework. In those models, individuals are allowed to move over time between different states related to illness and death. They are of special interest when working with non-terminal diseases, as they not only consider the competing risk of death but also allow us to study the progression from illness to death. The intensity of each transition can be modelled including both fixed and random effects of covariates. In particular, spatially structured random effects or their multivariate versions can be used to assess spatial differences between regions and among transitions. We propose a Bayesian methodological framework based on an illness-death model with a multivariate Leroux prior for the random effects. We apply this model to a cohort study regarding progression after an osteoporotic hip fracture in elderly patients. From this spatial illness-death model, we assess the geographical variation in risks, cumulative incidences and transition probabilities related to recurrent hip fracture and death. Bayesian inference is done via the integrated nested Laplace approximation.

A review of multistate modelling approaches in monitoring disease progression: Bayesian estimation using the Kolmogorov-Chapman forward equations

There are numerous fields of science in which multistate models are used, including biomedical research and health economics. In biomedical studies, these stochastic continuous-time models are used to describe the time-to-event life history of an individual through a flexible framework for longitudinal data. The multistate framework can describe more than one possible time-to-event outcome for a single individual. The standard estimation quantities in multistate models are transition probabilities and transition rates which can be mapped through the Kolmogorov-Chapman forward equations from the Bayesian estimation perspective. Most multistate models assume the Markov property and time homogeneity; however, if these assumptions are violated, an extension to non-Markovian and time-varying transition rates is possible. This manuscript extends reviews in various types of multistate models, assumptions, methods of estimation and data features compatible with fitting multistate models. We highlight the contrast between the frequentist (maximum likelihood estimation) and the Bayesian estimation approaches in the multistate modeling framework and point out where the latter is advantageous. A partially observed and aggregated dataset from the Zimbabwe national ART program was used to illustrate the use of Kolmogorov-Chapman forward equations. The transition rates from a three-stage reversible multistate model based on viral load measurements in WinBUGS were reported.

Validation of the Chinese Version of the Patient's Communication Perceived Self-Efficacy Scale (PCSS) in Outpatients After Total Hip Replacement

BACKGROUND

Among older people in the world, older patients' communication has become a public health issue of vital importance. Such communication could be improved by different interventions. However, a means of measuring patient's communication confidence in these measures has not been established in China. This study is aimed at translating and introducing the Patient's Communication Self-Efficacy Scale for communication between doctors and patients after total hip replacement.

METHOD

(1) A questionnaire was completed after a consultation by 167 patients (mean age = 70.04 years; SD: 6.3 years; females/males: 94/73). Translation of the original English version PCSS into the Chinese; (2) Validation of the final Chinese version of the PCSS. Measurement indexes included item generation, reliability testing, construct validity and test-retest reliability. To actualize the above test, we used SPSS 19.0 software and LISREL 8.7. We build the Bayesian Network Model of the Chinese version of the PCSS and determined predictive variables.

RESULT

Confirmatory factor analysis showed that the Chinese version of the PCSS has fit a three-dimensional model. Meanwhile, the Chinese version of the PCSS has high internal consistency (Cronbach's α coefficient 0.929) and test-retest reliability (Kappa coefficient 0.761). Analysis using Bayesian networks shows that the important predictors are education (0.4207), PEPPI 3(0.3951), and PCSS 1(0.1139). The connections between PCSS 3 and other variables do not indicate causality, conditional dependencies or inter-relatedness.

CONCLUSION

This is the first study to validate the Chinese version of the PCSS in outpatients after total hip replacement. Our results confirmed that the Chinese version of the scale has high internal consistency, construct validity and test-retest reliability. And the patient-doctor interaction and education are important predictors of patient's communication self-efficacy.

General tests of the Markov property in multi-state models

Multi-state models for event history analysis most commonly assume the process is Markov. This article considers tests of the Markov assumption that are applicable to general multi-state models. Two approaches using existing methodology are considered; a simple method based on including time of entry into each state as a covariate in Cox models for the transition intensities and a method involving detecting a shared frailty through a stratified Commenges–Andersen test. In addition, using the principle that under a Markov process the future rate of transitions of the process at times $t > s$ should not be influenced by the state occupied at time $s$, a new class of general tests is developed by considering summaries from families of log-rank statistics where patients are grouped by the state occupied at varying initial time $s$. An extended form of the test applicable to models that are Markov conditional on observed covariates is also derived. The null distribution of the proposed test statistics are approximated by using wild bootstrap sampling. The approaches are compared in simulation and applied to a dataset on sleeping behavior. The most powerful test depends on the particular departure from a Markov process, although the Cox-based method maintained good power in a wide range of scenarios. The proposed class of log-rank statistic based tests are most useful in situations where the non-Markov behavior does not persist, or is not uniform in nature across patient time.

Estimation and inference for semi-competing risks based on data from a nested case-control study

In semi-competing risks, the occurrence of some non-terminal event is subject to a terminal event, usually death. While existing methods for semi-competing risks data analysis assume complete information on all relevant covariates, data on at least one covariate are often not readily available in practice. In this setting, for standard univariate time-to-event analyses, researchers may choose from several strategies for sub-sampling patients on whom to collect complete data, including the nested case-control study design. Here, we consider a semi-competing risks analysis through the reuse of data from an existing nested case-control study for which risk sets were formed based on either the non-terminal or the terminal event. Additionally, we introduce the supplemented nested case-control design in which detailed data are collected on additional events of the other type. We propose estimation with respect to a frailty illness-death model through maximum weighted likelihood, specifying the baseline hazard functions either parametrically or semi-parametrically via B-splines. Two standard error estimators are proposed: (i) a computationally simple sandwich estimator and (ii) an estimator based on a perturbation resampling procedure. We derive the asymptotic properties of the proposed methods and evaluate their small-sample properties via simulation. The designs/methods are illustrated with an investigation of risk factors for acute graft-versus-host disease among N = 8838 patients undergoing hematopoietic stem cell transplantation, for which death is a significant competing risk.

A Bayesian semiparametric Markov regression model for juvenile dermatomyositis

Juvenile dermatomyositis (JDM) is a rare autoimmune disease that may lead to serious complications, even to death. We develop a 2-state Markov regression model in a Bayesian framework to characterise disease progression in JDM over time and gain a better understanding of the factors influencing disease risk. The transition probabilities between disease and remission state (and vice versa) are a function of time-homogeneous and time-varying covariates. These latter types of covariates are introduced in the model through a latent health state function, which describes patient-specific health over time and accounts for variability among patients. We assume a nonparametric prior based on the Dirichlet process to model the health state function and the baseline transition intensities between disease and remission state and vice versa. The Dirichlet process induces a clustering of the patients in homogeneous risk groups. To highlight clinical variables that most affect the transition probabilities, we perform variable selection using spike and slab prior distributions. Posterior inference is performed through Markov chain Monte Carlo methods. Data were made available from the UK JDM Cohort and Biomarker Study and Repository, hosted at the UCL Institute of Child Health.

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.

Non-parametric regression in clustered multistate current status data with informative cluster size

Datasets examining periodontal disease records current (disease) status information of tooth-sites, whose stochastic behavior can be attributed to a multistate system with state occupation determined at a single inspection time. In addition, the tooth-sites remain clustered within a subject, and the number of available tooth-sites may be representative of the true PD status of that subject, leading to an 'informative cluster size' scenario. To provide insulation against incorrect model assumptions, we propose a nonparametric regression framework to estimate state occupation probabilities at a given time and state exit/entry distributions, utilizing weighted monotonic regression and smoothing techniques. We demonstrate the superior performance of our proposed weighted estimators over the un-weighted counterparts via. a simulation study, and illustrate the methodology using a dataset on periodontal disease.

Hierarchical models for semi-competing risks data with application to quality of end-of-life care for pancreatic cancer

Readmission following discharge from an initial hospitalization is a key marker of quality of health care in the United States. For the most part, readmission has been studied among patients with 'acute' health conditions, such as pneumonia and heart failure, with analyses based on a logistic-Normal generalized linear mixed model (Normand et al., 1997). Naïve application of this model to the study of readmission among patients with 'advanced' health conditions such as pancreatic cancer, however, is problematic because it ignores death as a competing risk. A more appropriate analysis is to imbed such a study within the semi-competing risks framework. To our knowledge, however, no comprehensive statistical methods have been developed for cluster-correlated semi-competing risks data. To resolve this gap in the literature we propose a novel hierarchical modeling framework for the analysis of cluster-correlated semi-competing risks data that permits parametric or non-parametric specifications for a range of components giving analysts substantial flexibility as they consider their own analyses. Estimation and inference is performed within the Bayesian paradigm since it facilitates the straightforward characterization of (posterior) uncertainty for all model parameters, including hospital-specific random effects. Model comparison and choice is performed via the deviance information criterion and the log-pseudo marginal likelihood statistic, both of which are based on a partially marginalized likelihood. An efficient computational scheme, based on the Metropolis-Hastings-Green algorithm, is developed and had been implemented in the SemiCompRisks R package. A comprehensive simulation study shows that the proposed framework performs very well in a range of data scenarios, and outperforms competitor analysis strategies. The proposed framework is motivated by and illustrated with an on-going study of the risk of readmission among Medicare beneficiaries diagnosed with pancreatic cancer. Using data on n=5,298 patients at J=112 hospitals in the six New England states between 2000-2009, key scientific questions we consider include the role of patient-level risk factors on the risk of readmission and the extent of variation in risk across hospitals not explained by differences in patient case-mix.

Time-dependent ROC methodology to evaluate the predictive accuracy of semiparametric multi-state models in the presence of competing risks: An application to peritoneal dialysis programme

Abstract:

The evaluation of peritoneal dialysis (PD) programmes requires the use of statistical methods that suit the complexity of such programmes. Multi-state regression models taking competing risks into account are a good example of suitable approaches. In this work, multi-state structured additive regression (STAR) models combined with penalized splines (P-splines) are proposed to evaluate peritoneal dialysis programmes. These models are very flexible since they may consider smooth estimates of baseline transition intensities and the inclusion of time-varying and smooth covariate effects at each transition. A key issue in survival analysis is the quantification of the time-dependent predictive accuracy of a given regression model, which is typically assessed using receiver operating characteristic (ROC)’based methodologies. The main objective of the present study is to adapt the concept of time-dependent ROC curve, and their corresponding area under the curve (AUC), to a multi-state competing risks framework. All statistical methodologies discussed in this work were applied to PD survival data. Using a multi-state competing risks framework, this study explored the effects of major clinical covariates on survival such as age, sex, diabetes and previous renal replacement therapy. Such multi-state model was composed of one transient state (peritonitis) and several absorbing states (death, transfer to haemodialysis and renal transplantation). The application of STAR models combined with time-dependent ROC curves revealed important conclusions not previously reported in the nephrology literature when using standard statistical methodologies. For practical application, all the statistical methods proposed in this article were implemented in R and we wrote and made available a script named as NestedCompRisks.

Structured fusion lasso penalized multi-state models

Multi-state models generalize survival or duration time analysis to the estimation of transition-specific hazard rate functions for multiple transitions. When each of the transition-specific risk functions is parametrized with several distinct covariate effect coefficients, this leads to a model of potentially high dimension. To decrease the parameter space dimensionality and to work out a clear image of the underlying multi-state model structure, one can either aim at setting some coefficients to zero or to make coefficients for the same covariate but two different transitions equal. The first issue can be approached by penalizing the absolute values of the covariate coefficients as in lasso regularization. If, instead, absolute differences between coefficients of the same covariate on different transitions are penalized, this leads to sparse competing risk relations within a multi-state model, that is, equality of covariate effect coefficients. In this paper, a new estimation approach providing sparse multi-state modelling by the aforementioned principles is established, based on the estimation of multi-state models and a simultaneous penalization of the L₁ -norm of covariate coefficients and their differences in a structured way. The new multi-state modelling approach is illustrated on peritoneal dialysis study data and implemented in the R package penMSM. Copyright © 2016 John Wiley & Sons, Ltd.

Semi-Competing Risks Data Analysis: Accounting for Death as a Competing Risk When the Outcome of Interest Is Nonterminal

Hospital readmission is a key marker of quality of health care. Notwithstanding its widespread use, however, it remains controversial in part because statistical methods used to analyze readmission, primarily logistic regression and related models, may not appropriately account for patients who die before experiencing a readmission event within the time frame of interest. Toward resolving this, we describe and illustrate the semi-competing risks framework, which refers to the general setting where scientific interest lies with some nonterminal event (eg, readmission), the occurrence of which is subject to a terminal event (eg, death). Although several statistical analysis methods have been proposed for semi-competing risks data, we describe in detail the use of illness-death models primarily because of their relation to well-known methods for survival analysis and the availability of software. We also describe and consider in detail several existing approaches that could, in principle, be used to analyze semi-competing risks data, including composite end point and competing risks analyses. Throughout we illustrate the ideas and methods using data on N=49 763 Medicare beneficiaries hospitalized between 2011 and 2013 with a principle discharge diagnosis of heart failure.

Modeling sleep fragmentation in sleep hypnograms: An instance of fast, scalable discrete-state, discrete-time analyses

Methods are introduced for the analysis of large sets of sleep study data (hypnograms) using a 5-state 20-transition-type structure defined by the American Academy of Sleep Medicine. Application of these methods to the hypnograms of 5598 subjects from the Sleep Heart Health Study provide: the first analysis of sleep hypnogram data of such size and complexity in a community cohort with a range of sleep-disordered breathing severity; introduce a novel approach to compare 5-state (20-transition-type) to 3-state (6-transition-type) sleep structures to assess information loss from combining sleep state categories; extend current approaches of multivariate survival data analysis to clustered, recurrent event discrete-state discrete-time processes; and provide scalable solutions for data analyses required by the case study. The analysis provides detailed new insights into the association between sleep-disordered breathing and sleep architecture. The example data and both R and SAS code are included in online supplementary materials.

Bayesian path specific frailty models for multi-state survival data with applications

Multi-state models can be viewed as generalizations of both the standard and competing risks models for survival data. Models for multi-state data have been the theme of many recent published works. Motivated by bone marrow transplant data, we propose a Bayesian model using the gap times between two successive events in a path of events experienced by a subject. Path specific frailties are introduced to capture the dependence structure of the gap times in the paths with two or more states. Under improper prior distributions for the parameters, we establish propriety of the posterior distribution. An efficient Gibbs sampling algorithm is developed for drawing samples from the posterior distribution. An extensive simulation study is carried out to examine the empirical performance of the proposed approach. A bone marrow transplant data set is analyzed in detail to further demonstrate the proposed methodology.

Nosocomial Infection, Length of Stay, and Time-Dependent Bias

Nosocomial pneumonia and its impact on length of stay are major healthcare concerns. From an epidemiological perspective, nosocomial pneumonia is a time-dependent event. Any statistical analysis that does not explicitly model this time dependency will be biased. The bias is not redeemed by adjusting for baseline information.

Bayesian Semi-parametric Analysis of Semi-competing Risks Data: Investigating Hospital Readmission after a Pancreatic Cancer Diagnosis

In the U.S., the Centers for Medicare and Medicaid Services uses 30-day readmission, following hospitalization, as a proxy outcome to monitor quality of care. These efforts generally focus on treatable health conditions, such as pneumonia and heart failure. Expanding quality of care systems to monitor conditions for which treatment options are limited or non-existent, such as pancreatic cancer, is challenging because of the non-trivial force of mortality; 30-day mortality for pancreatic cancer is approximately 30%. In the statistical literature, data that arise when the observation of the time to some non-terminal event is subject to some terminal event are referred to as 'semi-competing risks data'. Given such data, scientific interest may lie in at least one of three areas: (i) estimation/inference for regression parameters, (ii) characterization of dependence between the two events, and (iii) prediction given a covariate profile. Existing statistical methods focus almost exclusively on the first of these; methods are sparse or non-existent, however, when interest lies with understanding dependence and performing prediction. In this paper we propose a Bayesian semi-parametric regression framework for analyzing semi-competing risks data that permits the simultaneous investigation of all three of the aforementioned scientific goals. Characterization of the induced posterior and posterior predictive distributions is achieved via an efficient Metropolis-Hastings-Green algorithm, which has been implemented in an R package. The proposed framework is applied to data on 16,051 individuals diagnosed with pancreatic cancer between 2005-2008, obtained from Medicare Part A. We found that increased risk for readmission is associated with a high comorbidity index, a long hospital stay at initial hospitalization, non-white race, male, and discharge to home care.

Mortality of patients infected with HIV in the intensive care unit (2005 through 2010): significant role of chronic hepatitis C and severe sepsis

INTRODUCTION

The combination antiretroviral therapy (cART) has led to decreased opportunistic infections and hospital admissions in human immunodeficiency virus (HIV)-infected patients, but the intensive care unit (ICU) admission rate remains constant (or even increased in some instances) during the cART era. Hepatitis C virus (HCV) infection is associated with an increased risk for hospital admission and/or mortality (particularly those related to severe liver disease) compared with the general population. The aim of this study was to assess the mortality among HIV-infected patients in ICU, and to evaluate the impact of HIV/HCV coinfection and severe sepsis on ICU mortality.

METHODS

We carried out a retrospective study based on patients admitted to ICU who were recorded in the Minimum Basic Data Set (2005 through 2010) in Spain. HIV-infected patients (All-HIV-group (n = 1,891)) were divided into two groups: HIV-monoinfected patients (HIV group (n = 1,191)) and HIV/HCV-coinfected patients (HIV/HCV group (n = 700)). A control group (HIV(-)/HCV(-)) was also included (n = 7,496).

RESULTS

All-HIV group had higher frequencies of severe sepsis (57.7% versus 39.4%; P < 0.001) than did the control group. Overall, ICU mortality in patients with severe sepsis was much more frequent than that in patients without severe sepsis (other causes) at days 30 and 90 in HIV-infected patients and the control group (P < 0.001). Moreover, the all-HIV group in the presence or absence of severe sepsis had a higher percentage of death than did the control group at days 7 (P < 0.001), 30 (P < 0.001) and 90 (P < 0.001). Besides, the HIV/HCV group had a higher percentage of death, both in patients with severe sepsis and in patients without severe sepsis compared with the HIV group at days 7 (P < 0.001) and 30 (P < 0.001), whereas no differences were found at day 90. In a bayesian competing-risk model, the HIV/HCV group had a higher mortality risk (adjusted hazard ratio (aHR) = 1.44 (95% CI = 1.30 to 1.59) and aHR = 1.57 (95% CI = 1.38 to 1.78) for patients with and without severe sepsis, respectively).

CONCLUSIONS

HIV infection was related to a higher frequency of severe sepsis and death among patients admitted to the ICU. Besides, HIV/HCV coinfection contributed to an increased risk of death in both the presence and the absence of severe sepsis.

Multi-state models for colon cancer recurrence and death with a cured fraction

In cancer clinical trials, patients often experience a recurrence of disease prior to the outcome of interest, overall survival. Additionally, for many cancers, there is a cured fraction of the population who will never experience a recurrence. There is often interest in how different covariates affect the probability of being cured of disease and the time to recurrence, time to death, and time to death after recurrence. We propose a multi-state Markov model with an incorporated cured fraction to jointly model recurrence and death in colon cancer. A Bayesian estimation strategy is used to obtain parameter estimates. The model can be used to assess how individual covariates affect the probability of being cured and each of the transition rates. Checks for the adequacy of the model fit and for the functional forms of covariates are explored. The methods are applied to data from 12 randomized trials in colon cancer, where we show common effects of specific covariates across the trials.

Combining hidden Markov models for comparing the dynamics of multiple sleep electroencephalograms

In this manuscript, we consider methods for the analysis of populations of electroencephalogram signals during sleep for the study of sleep disorders using hidden Markov models (HMMs). Notably, we propose an easily implemented method for simultaneously modeling multiple time series that involve large amounts of data. We apply these methods to study sleep-disordered breathing (SDB) in the Sleep Heart Health Study (SHHS), a landmark study of SDB and cardiovascular consequences. We use the entire, longitudinally collected, SHHS cohort to develop HMM population parameters, which we then apply to obtain subject-specific Markovian predictions. From these predictions, we create several indices of interest, such as transition frequencies between latent states. Our HMM analysis of electroencephalogram signals uncovers interesting findings regarding differences in brain activity during sleep between those with and without SDB. These findings include stability of the percent time spent in HMM latent states across matched diseased and non-diseased groups and differences in the rate of transitioning.

Factors involved in health-related transitions after curative resection for pancreatic cancer. 10-years experience: a multi state model

BACKGROUND

Pancreatic cancer is one of the least common tumours, nevertheless it is one of the most lethal. This lethality is mainly due to the fact that the vast majority of patients are diagnosed in an advanced stage. The purpose of this study was to investigate how different covariates affect the transition to death or discharge with and without complications after pancreatic resection.

METHODS

We analyse the impact of different factors on transitions after pancreatic resection based on a multi state model.

RESULTS

Transitions of interest include the transition to death/discharge with/without complications after pancreatic resection. We consider presence of comorbidities, higher age (>60), gender-male, lower hospital volume (<10 cases per year), type of surgery, localization of tumour and transfusion received as covariates with a potentially negative effect on the transition intensities to death with or without complications.

CONCLUSIONS

The multi-state model allows for a very detailed analysis of the impact of covariates on each transition, since effects of covariates may change depending on the current state of the patient, thus helping surgeons and patients throughout the surgical process and counselling patients if needed.

Bayesian analysis of a disability model for lung cancer survival

Bayesian reasoning, survival analysis and multi-state models are used to assess survival times for Stage IV non-small-cell lung cancer patients and the evolution of the disease over time. Bayesian estimation is done using minimum informative priors for the Weibull regression survival model, leading to an automatic inferential procedure. Markov chain Monte Carlo methods have been used for approximating posterior distributions and the Bayesian information criterion has been considered for covariate selection. In particular, the posterior distribution of the transition probabilities, resulting from the multi-state model, constitutes a very interesting tool which could be useful to help oncologists and patients make efficient and effective decisions.

Mixed effect Poisson log-linear models for clinical and epidemiological sleep hypnogram data

Bayesian Poisson log-linear multilevel models scalable to epidemiological studies are proposed to investigate population variability in sleep state transition rates. Hierarchical random effects are used to account for pairings of subjects and repeated measures within those subjects, as comparing diseased with non-diseased subjects while minimizing bias is of importance. Essentially, non-parametric piecewise constant hazards are estimated and smoothed, allowing for time-varying covariates and segment of the night comparisons. The Bayesian Poisson regression is justified through a re-derivation of a classical algebraic likelihood equivalence of Poisson regression with a log(time) offset and survival regression assuming exponentially distributed survival times. Such re-derivation allows synthesis of two methods currently used to analyze sleep transition phenomena: stratified multi-state proportional hazards models and log-linear generalized estimating equations (GEE) models for transition counts. An example data set from the Sleep Heart Health Study is analyzed. Supplementary material includes the analyzed data set as well as the code for a reproducible analysis.

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).

Flexible hazard ratio curves for continuous predictors in multi-state models

Multi-state models (MSMs) are very useful for describing complicated event history data. These models may be considered as a generalization of survival analysis where survival is the ultimate outcome of interest but where intermediate (transient) states are identified. One major goal in clinical applications of MSMs is to study the relationship between the different covariates and disease evolution. Usually, MSMs are assumed to be parametric, and the effects of continuous predictors on log-hazards are modelled linearly. In practice, however, the effect of a given continuous predictor can be unknown, and its form may be different in all transitions. In this paper,we propose a P-spline approach that allows for non-linear relationships between continuous predictors and survival in the multi-state framework. To better understand the effects at each transition, results are expressed in terms of hazard ratio curves, taking a specific covariate value as reference. Confidence bands for these curves are also derived. The proposed methodology was applied to a database on breast cancer, using a progressive three-state model. This application revealed hitherto unreported effects: whereas DNA index is only an important non-linear predictor of recurrence, the percentage of cells in phase S is a significant predictor of both recurrence and mortality.

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.