The Analysis of Panel Data under a Markov Assumption

Transition between [R]- and [S]-stereoisomers without bond breaking

The fifty-year old proposal of a nondissociative racemization reaction of a tetracoordinated tetrahedral center from one enantiomer to another via a planar transition state by Hoffmann and coworkers has been explored by many research groups over the past five decades. A number of stable molecules with planar tetracoordinated and higher-coordinated centers have been designed and experimentally realized; however, there has not been a single example of a molecular system that can possibly undergo such racemization. Here we show examples of molecular species that undergo inversion of stereochemistry around tetrahedral centers (Si, Al- and P+) either via a planar transition state or an intermediate state using quantum mechanical, ab initio quasi-classical dynamics calculations, and Born-Oppenheimer molecular dynamics (BOMD) simulations. This work is expected to provide potential leads for future studies on this fundamental phenomenon in chemistry.

An Individualized, Interactive, and Advance Care Planning Intervention Promotes Transitions in Prognostic Awareness States Among Terminally Ill Cancer Patients in Their Last Six Months-A Secondary Analysis of a Randomized Controlled Trial

CONTEXT/OBJECTIVES

To examine whether an advance care planning intervention randomized controlled trial facilitates terminally ill cancer patients' transitions to accurate prognostic awareness (PA) and the time spent in the accurate PA state in patients' last six months.

METHODS

Participants (N = 460) were randomized 1:1 to experimental (interactive intervention tailored to participants' readiness for advance care planning/prognostic information) and control (symptom management education) arms with similar formats. PA was categorized into four states: 1) unknown and not wanting to know; 2) unknown but wanting to know; 3) inaccurate awareness; and 4) accurate awareness. Intervention effectiveness in the two outcomes was evaluated by intention-to-treat analysis with multistate Markov modeling (effect size ≥0.2 as minimal clinically important difference).

RESULTS

The final sample constituted 188 and 184 experimental arm and control arm participants who died and were repeatedly assessed, respectively. Experimental arm participants in States 1-3 had a higher probability of shifting to accurate PA (23.0%-35.4% vs. 15.2%-26.2%) than control arm participants, and all effect sizes met the minimal clinically important difference criterion (effect sizes 0.22-0.49). In their last six months, experimental arm participants spent more time in States 3 and 4 (0.18 vs. 0.08 and 2.94 vs. 2.38 months, respectively) but less time in States 1 and 2 (2.70 vs. 3.19 and 0.18 vs. 0.36 months, respectively) (effect sizes 0.11-0.19).

CONCLUSION

Our intervention meaningfully facilitated participants' transition toward accurate PA and more time spent in the accurate PA state (State 4). Our intervention can help health care professionals foster cancer patients' accurate PA earlier in the terminal illness trajectory to make informed end-of-life care decisions tailored to their readiness for prognostic information.

A multistate joint model for interval-censored event-history data subject to within-unit clustering and informative missingness, with application to neurocysticercosis research

We propose a multistate joint model to analyze interval-censored event-history data subject to within-unit clustering and nonignorable missing data. The model is motivated by a study of the neurocysticercosis (NC) cyst evolution at the cyst-level, taking into account the multiple cysts phases with intermittent missing data and loss to follow-up, as well as the intra-brain clustering of observations made on a predefined data collection schedule. Of particular interest in this study is the description of the process leading to cyst resolution, and whether this process varies by antiparasitic treatment. The model uses shared random effects to account for within-brain correlation and to explain the hidden heterogeneity governing the missing data mechanism. We developed a likelihood-based method using a Monte Carlo EM algorithm for the inference. The practical utility of the methods is illustrated using data from a randomized controlled trial on the effect of antiparasitic treatment with albendazole on NC cysts among patients from six hospitals in Ecuador. Simulation results demonstrate that the proposed methods perform well in the finite sample and misspecified models that ignore the data complexities could lead to substantial biases.

Modeling Viral Suppression, Viral Rebound and State-Specific Duration of HIV Patients with CD4 Count Adjustment: Parametric Multistate Frailty Model Approach

INTRODUCTION

Combination antiretroviral therapy has become the standard care of human immunodeficiency virus (HIV)-infected patients and has further led to a dramatically decreased progression probability to acquired immune deficiency syndrome (AIDS) for patients under such a therapy. However, responses of the patients to this therapy have recorded heterogeneous complexity and high dynamism. In this paper, we simultaneously model long-term viral suppression, viral rebound, and state-specific duration of HIV-infected patients.

METHODS

Full-parametric and semi-parametric Markov multistate models were applied to assess the effects of covariates namely TB co-infection, educational status, marital status, age, quality of life (QoL) scores, white and red blood cell parameters, and liver enzyme abnormality on long-term viral suppression, viral rebound and state-specific duration for HIV-infected individuals before and after treatment. Furthermore, two models, one including and another excluding the effect of the frailty, were presented and compared in this study.

RESULTS

Results from the diagnostic plots, Akaike information criterion (AIC) and likelihood ratio test showed that the Weibull multistate frailty model fitted significantly better than the exponential and semi-parametric multistate models. Viral rebound was found to be significantly associated with many sex partners, higher eosinophils count, younger age, lower educational level, higher monocyte counts, having abnormal neutrophils count, and higher liver enzyme abnormality. Furthermore, viral suppression was also found to be significantly associated with higher QoL scores, and having a stable sex partner. The analysis result also showed that patients with a stable sex partner, higher educational levels, higher QoL scores, lower eosinophils count, lower monocyte counts, and higher RBC indices were more likely to spend more time in undetectable viral load state.

CONCLUSIONS

To achieve and maintain the UNAIDS 90% suppression targets, additional interventions are required to optimize antiretroviral therapy outcomes, specifically targeting those with poor clinical characteristics, lower education, younger age, and those with many sex partners. From a methodological perspective, the parametric multistate approach with frailty is a flexible approach for modeling time-varying variables, allowing for dealing with heterogeneity between the sequence of transitions, as well as allowing for a reasonable degree of flexibility with a few additional parameters, which then aids in gaining a better insight into how factors change over time.

Bayesian latent multi-state modeling for nonequidistant longitudinal electronic health records

Large amounts of longitudinal health records are now available for dynamic monitoring of the underlying processes governing the observations. However, the health status progression across time is not typically observed directly: records are observed only when a subject interacts with the system, yielding irregular and often sparse observations. This suggests that the observed trajectories should be modeled via a latent continuous-time process potentially as a function of time-varying covariates. We develop a continuous-time hidden Markov model to analyze longitudinal data accounting for irregular visits and different types of observations. By employing a specific missing data likelihood formulation, we can construct an efficient computational algorithm. We focus on Bayesian inference for the model: this is facilitated by an expectation-maximization algorithm and Markov chain Monte Carlo methods. Simulation studies demonstrate that these approaches can be implemented efficiently for large data sets in a fully Bayesian setting. We apply this model to a real cohort where patients suffer from chronic obstructive pulmonary disease with the outcome being the number of drugs taken, using health care utilization indicators and patient characteristics as covariates.

Seasonal influenza vaccination among people with diabetes: influence of patients' characteristics and healthcare use on behavioral changes

Annual seasonal influenza vaccination (SIV) is recommended for people with diabetes, but vaccine coverage remains low. We estimated the probabilities of stopping or starting SIV, their correlates, and the expected time spent in the vaccinated state over 10 seasons for different patient profiles. We set up a retrospective cohort study of patients with diabetes in 2006 (n = 16,026), identified in a representative sample of beneficiaries of the French National Health Insurance Fund. We followed them up over 10 seasons (2005/06–2015/16). We used a Markov model to estimate transition probabilities and a proportional hazards model to study covariates. Between two consecutive seasons, the probabilities of starting (0.17) or stopping (0.09) SIV were lower than those of remaining vaccinated (0.91) or unvaccinated (0.83). Men, older patients, those with type 1 diabetes, treated diabetes or more comorbidities, frequent contacts with doctors, and with any hospital stay for diabetes or influenza during the last year were more likely to start and/or less likely to stop SIV. The mean expected number of seasons with SIV uptake over 10 seasons (range: 2.6–7.9) was lowest for women <65 years with untreated diabetes and highest for men ≥65 years with type 1 diabetes. Contacts with doctors and some clinical events may play a key role in SIV adoption. Healthcare workers have a crucial role in reducing missed opportunities for SIV. The existence of empirical patient profiles with different patterns of SIV uptake should encourage their use of tailored educational approaches about SIV to address patients’ vaccine hesitancy.

Multistate Markov Model to Predict the Prognosis of High-Risk Human Papillomavirus-Related Cervical Lesions

Cervical intraepithelial neoplasia (CIN) has a natural history of bidirectional transition between different states. Therefore, conventional statistical models assuming a unidirectional disease progression may oversimplify CIN fate. We applied a continuous-time multistate Markov model to predict this CIN fate by addressing the probability of transitions between multiple states according to the genotypes of high-risk human papillomavirus (HPV). This retrospective cohort comprised 6022 observations in 737 patients (195 normal, 259 CIN1, and 283 CIN2 patients at the time of entry in the cohort). Patients were followed up or treated at the University of Tokyo Hospital between 2008 and 2015. Our model captured the prevalence trend satisfactory, particularly for up to two years. The estimated probabilities for 2-year transition to CIN3 or more were the highest in HPV 16-positive patients (13%, 30%, and 42% from normal, CIN1, and CIN2, respectively) compared with those in the other genotype-positive patients (3.1%-9.6%, 7.6%-16%, and 21%-32% from normal, CIN1, and CIN2, respectively). Approximately 40% of HPV 52- or 58-related CINs remained at CIN1 and CIN2. The Markov model highlights the differences in transition and progression patterns between high-risk HPV-related CINs. HPV genotype-based management may be desirable for patients with cervical lesions.

Enhancing NMR derived ensembles with kinetics on multiple timescales

Nuclear magnetic resonance (NMR) has the unique advantage of elucidating the structure and dynamics of biomolecules in solution at physiological temperatures, where they are in constant movement on timescales from picoseconds to milliseconds. Such motions have been shown to be critical for enzyme catalysis, allosteric regulation, and molecular recognition. With NMR being particularly sensitive to these timescales, detailed information about the kinetics can be acquired. However, nearly all methods of NMR-based biomolecular structure determination neglect kinetics, which introduces a large approximation to the underlying physics, limiting both structural resolution and the ability to accurately determine molecular flexibility. Here we present the Kinetic Ensemble approach that uses a hierarchy of interconversion rates between a set of ensemble members to rigorously calculate Nuclear Overhauser Effect (NOE) intensities. It can be used to simultaneously refine both temporal and structural coordinates. By generalizing ideas from the extended model free approach, the method can analyze the amplitudes and kinetics of motions anywhere along the backbone or side chains. Furthermore, analysis of a large set of crystal structures suggests that NOE data contains a surprising amount of high-resolution information that is better modeled using our approach. The Kinetic Ensemble approach provides the means to unify numerous types of experiments under a single quantitative framework and more fully characterize and exploit kinetically distinct protein states. While we apply the approach here to the protein ubiquitin and cross validate it with previously derived datasets, the approach can be applied to any protein for which NOE data is available.

Sampling-based Markov regression model for multistate disease progression: Applications to population-based cancer screening program

To develop personalized screening and surveillance strategies, the information required to superimpose state-specific covariates into the multi-step progression of disease natural history often relies on the entire population-based screening data, which are costly and infeasible particularly when a new biomarker is proposed. Following Prentice's case-cohort concept, a non-standard case-cohort design from a previous study has been adapted for constructing multistate disease natural history with two-stage sampling. Nonetheless, the use of data only from first screens may invoke length-bias and fail to consider the test sensitivity. Therefore, a new sampling-based Markov regression model and its variants are proposed to accommodate additional subsequent follow-up data on various detection modes to construct state-specific covariate-based multistate disease natural history with accuracy and efficiency. Computer simulation algorithms for determining the required sample size and the sampling fraction of each detection mode were developed either through power function or the capacity of screening program. The former is illustrated with breast cancer screening data from which the effect size and the required sample size regarding the effect of BRCA on multistate outcome of breast cancer were estimated. The latter is applied to population-based colorectal cancer screening data to identify the optimal sampling fraction of each detection mode.

Independence conditions and the analysis of life history studies with intermittent observation

Multistate models provide a powerful framework for the analysis of life history processes when the goal is to characterize transition intensities, transition probabilities, state occupancy probabilities, and covariate effects thereon. Data on such processes are often only available at random visit times occurring over a finite period. We formulate a joint multistate model for the life history process, the recurrent visit process, and a random loss to follow-up time at which the visit process terminates. This joint model is helpful when discussing the independence conditions necessary to justify the use of standard likelihoods involving the life history model alone and provides a basis for analyses that accommodate dependence. We consider settings with disease-driven visits and routinely scheduled visits and develop likelihoods that accommodate partial information on the types of visits. Simulation studies suggest that suitably constructed joint models can yield consistent estimates of parameters of interest even under dependent visit processes, providing the models are correctly specified; identifiability and estimability issues are also discussed. An application is given to a cohort of individuals attending a rheumatology clinic where interest lies in progression of joint damage.

The frequency of testing for glycated haemoglobin, HbA1c, is linked to the probability of achieving target levels in patients with suboptimally controlled diabetes mellitus

Background We previously showed, in patients with diabetes, that >50% of monitoring tests for glycated haemoglobin (HbA1c) are outside recommended intervals and that this is linked to diabetes control. Here, we examined the effect of tests/year on achievement of commonly utilised HbA1c targets and on HbA1c changes over time. Methods Data on 20,690 adults with diabetes with a baseline HbA1c of >53 mmol/mol (7%) were extracted from Clinical Biochemistry Laboratory records at three UK hospitals. We examined the effect of HbA1c tests/year on (i) the probability of achieving targets of ≤53 mmol/mol (7%) and ≤48 mmol/mol (6.5%) in a year using multi-state modelling and (ii) the changes in mean HbA1c using a linear mixed-effects model. Results The probabilities of achieving ≤53 mmol/mol (7%) and ≤48 mmol/mol (6.5%) targets within 1 year were 0.20 (95% confidence interval: 0.19-0.21) and 0.10 (0.09-0.10), respectively. Compared with four tests/year, having one test or more than four tests/year were associated with lower likelihoods of achieving either target; two to three tests/year gave similar likelihoods to four tests/year. Mean HbA1c levels were higher in patients who had one test/year compared to those with four tests/year (mean difference: 2.64 mmol/mol [0.24%], p<0.001). Conclusions We showed that ≥80% of patients with suboptimal control are not achieving commonly recommended HbA1c targets within 1 year, highlighting the major challenge facing healthcare services. We also demonstrated that, although appropriate monitoring frequency is important, testing every 6 months is as effective as quarterly testing, supporting international recommendations. We suggest that the importance HbA1c monitoring frequency is being insufficiently recognised in diabetes management.

High risk and probability of progression to osteoporosis at 10 years in HIV-infected individuals: the role of PIs

Background

Osteoporotic fractures still remain very infrequent and physicians rarely evaluate bone health. We wanted to assess the magnitude of this problem in the near future by determining the risk and likelihood of progression to osteoporosis.

Methods

We estimated the risk of progression to osteopenia/osteoporosis among HIV-infected patients with at least 2 DXA scans (3726 scans from 875 patients). Time-non-homogeneous bidirectional multistate models based on three states (normal bone mineral density, osteopenia and osteoporosis) were used to model the progression of bone mineral density as a function of age and to study the association between the risk of bone loss and antiretroviral use.

Results

The HRs associated with age (>45 versus ≤45 years) were: (i) from normal bone mineral density to osteopenia, 0.71 (95% CI 0.45-1.11) for men and 1.06 (95% CI 0.55-2.05) for women; and (ii) from osteopenia to osteoporosis, 0.83 (95% CI 0.51-1.35) for men and 0.99 (95% CI 0.38-2.56) for women. The transition probabilities from osteopenia to osteoporosis over 10 years among men aged 30 and 50 years were 14.9% (95% CI 10.5%-20.4%) and 19% (95% CI 14.3%-24.3%), respectively; and for women, 6.9% (95% CI 3.1%-14.4%) and 30.1% (95% CI 19.8%-41.8%), respectively. An increased osteoporosis risk was observed for PIs and PIs + tenofovir disoproxil fumarate; darunavir was associated with a higher risk of osteoporosis among men (HR 3.9; 95% CI 2-7.5) and women (HR 4.5; 95% CI 1.4-14.7); and atazanavir was associated with a higher risk of osteoporosis among women (HR 4.2; 95% CI 1.3-14).

Conclusions

Our results highlight the importance of monitoring bone mineral density given the high probability of progression to osteopenia/osteoporosis, especially in women. In the future, changes in antiretrovirals other than tenofovir, such as PIs, should be recommended to reduce the risk of fracture.

Continuous-Time Latent Markov Factor Analysis for Exploring Measurement Model Changes Across Time

Abstract. Drawing valid inferences about daily or long-term dynamics of psychological constructs (e.g., depression) requires the measurement model (indicating which constructs are measured by which items) to be invariant within persons over time. However, it might be affected by time- or situation-specific artifacts (e.g., response styles) or substantive changes in item interpretation. To efficiently evaluate longitudinal measurement invariance, and violations thereof, we proposed Latent Markov factor analysis (LMFA), which clusters observations based on their measurement model into separate states, indicating which measures are validly comparable. LMFA is, however, tailored to “discrete-time” data, where measurement intervals are equal, which is often not the case in longitudinal data. In this paper, we extend LMFA to accommodate unequally spaced intervals. The so-called “continuous-time” (CT) approach considers the measurements as snapshots of continuously evolving processes. A simulation study compares CT-LMFA parameter estimation to its discrete-time counterpart and a depression data application shows the advantages of CT-LMFA.

Partially hidden multi-state modelling of a prolonged disease state defined by a composite outcome

For rheumatic diseases, Minimal Disease Activity (MDA) is usually defined as a composite outcome which is a function of several individual outcomes describing symptoms or quality of life. There is ever increasing interest in MDA but relatively little has been done to characterise the pattern of MDA over time. Motivated by the aim of improving the modelling of MDA in psoriatic arthritis, the use of a two-state model to estimate characteristics of the MDA process is illustrated when there is particular interest in prolonged periods of MDA. Because not all outcomes necessary to define MDA are measured at all clinic visits, a partially hidden multi-state model with latent states is used. The defining outcomes are modelled as conditionally independent given these latent states, enabling information from all visits, even those with missing data on some variables, to be used. Data from the Toronto Psoriatic Arthritis Clinic are analysed to demonstrate improvements in accuracy and precision from the inclusion of data from visits with incomplete information on MDA. An additional benefit of this model is that it can be extended to incorporate explanatory variables, which allows process characteristics to be compared between groups. In the example, the effect of explanatory variables, modelled through the use of relative risks, is also summarised in a potentially more clinically meaningful manner by comparing times in states, and probabilities of visiting states, between patient groups.

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.

Score tests based on a finite mixture model of Markov processes under intermittent observation

A mixture model is described, which accommodates different Markov processes governing disease progression in a finite set of latent classes. We give special attention to the setting in which individuals are examined intermittently and transition times are consequently interval censored. A score test is developed to identify genetic markers associated with class membership. Simulation studies are conducted to validate the algorithm, assess the finite sample properties of the estimators, and assess the frequency properties of the score tests. A permutation test is recommended for settings when there is concern that the asymptotic approximation to the score test is poor. An application involving progression in joint damage in psoriatic arthritis (PsA) provides illustration and identifies human leukocyte antigen markers associated with unilateral and bilateral sacroiliac damage in individuals with PsA.

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 parametric multistate modelling of employment history

A multistate model is used to describe employment history. Transition-specific rates are defined using generalized gamma distributions and Gompertz distributions. This flexible parametric modelling of the rate of change is combined with latent classes for unobserved propensity to change jobs. The propensity is described by two latent classes which can be interpreted as consisting of movers and stayers. The modelling is illustrated by analysing longitudinal data from the German Life History Study.

Approximate Bayesian inference for discretely observed continuous-time multi-state models

Inference for continuous time multi-state models presents considerable computational difficulties when the process is only observed at discrete time points with no additional information about the state transitions. In fact, for general multi-state Markov model, evaluation of the likelihood function is possible only via intensive numerical approximations. Moreover, in real applications, transitions between states may depend on the time since entry into the current state, and semi-Markov models, where the likelihood function is not available in closed form, should be fitted to the data. Approximate Bayesian Computation (ABC) methods, which make use only of comparisons between simulated and observed summary statistics, represent a solution to intractable likelihood problems and provide alternative algorithms when the likelihood calculation is computationally too costly. In this article we investigate the potentiality of ABC techniques for multi-state models both to obtain the posterior distributions of the model parameters and to compare Markov and semi-Markov models. In addition, we will also exploit ABC methods to estimate and compare hidden Markov and semi-Markov models when observed states are subject to classification errors. We illustrate the performance of the ABC methodology both with simulated data and with a real data example.

Semiparametric Regression Analysis of Panel Count Data: A Practical Review

Panel count data arise in many applications when the event history of a recurrent event process is only examined at a sequence of discrete time points. In spite of the recent methodological developments, the availability of their software implementations has been rather limited. Focusing on a practical setting where the effects of some time-independent covariates on the recurrent events are of primary interest, we review semiparametric regression modelling approaches for panel count data that have been implemented in R package spef. The methods are grouped into two categories depending on whether the examination times are associated with the recurrent event process after conditioning on covariates. The reviewed methods are illustrated with a subset of the data from a skin cancer clinical trial.

Multistate recursively imputed survival trees for time-to-event data analysis: an application to AIDS and mortality post-HIV infection data

BACKGROUND

This study aimed to introduce recursively imputed survival trees into multistate survival models (MSRIST) to analyze these types of data and to identify the prognostic factors influencing the disease progression in patients with intermediate events. The proposed method is fully nonparametric and can be used for estimating transition probabilities.

METHODS

A general algorithm was provided for analyzing multi-state data with a focus on the illness-death and progressive multi-state models. The model considered both beyond Markov and Non-Markov settings. We also proposed a multi-state random survival method (MSRSF) and compared their performance with the classical multi-state Cox model. We applied the proposed method to a dataset related to HIV/AIDS patients based on a retrospective cohort study extracted in Tehran from April 2004 to March 2014 consist of 2473 HIV-infected patients.

RESULTS

The results showed that MSRIST outperformed the classical multistate method using Cox Model and MSRSF in terms of integrated Brier score and concordance index over 500 repetitions. We also identified a set of important risk factors as well as their interactions on different states of HIV and AIDS progression.

CONCLUSIONS

There are different strategies for modelling the intermediate event. We adapted two newly developed data mining technique (RSF and RIST) for multistate models (MSRSF and MSRIST) to identify important risk factors in different stages of the diseases. The methods can capture any complex relationship between variables and can be used as a useful tool for identifying important risk factors in different states of this disease.

Estimation of annual probabilities of changing disability levels in Australians with relapsing-remitting multiple sclerosis

BACKGROUND

Transition probabilities are the engine within many health economics decision models. However, the probabilities of progression of disability due to multiple sclerosis (MS) have not previously been estimated in Australia.

OBJECTIVES

To estimate annual probabilities of changing disability levels in Australians with relapsing-remitting MS (RRMS).

METHODS

Combining data from Ausimmune/Ausimmune Longitudinal (2003-2011) and Tasmanian MS Longitudinal (2002-2005) studies (n = 330), annual transition probabilities were obtained between no/mild (Expanded Disability Status Scale (EDSS) levels 0-3.5), moderate (EDSS 4-6.0) and severe (EDSS 6.5-9.5) disability.

RESULTS

From no/mild disability, 6.4% (95% confidence interval (CI): 4.7-8.4) and 0.1% (0.0-0.2) progressed to moderate and severe disability annually, respectively. From moderate disability, 6.9% (1.0-11.4) improved (to no/mild state) and 2.6% (1.1-4.5) worsened. From severe disability, 0.0% improved to moderate and no/mild disability. Male sex, age at onset, longer disease duration, not using immunotherapies greater than 3 months and a history of relapse were related to higher probabilities of worsening.

CONCLUSION

We have estimated probabilities of changing disability levels in Australians with RRMS. Probabilities differed between various subgroups, but due to small sample sizes, results should be interpreted with caution. Our findings will be helpful in predicting long-term disease outcomes and in health economic evaluations of MS.

Quantifying the association between progression-free survival and overall survival in oncology trials using Kendall's τ

This paper considers methods for estimating the association between progression-free and overall survival in oncology trials. Copula-based, nonparametric, and illness-death model-based methods are reviewed. In addition, the approach based on an underlying illness-death model is generalized to allow general parametric models. The performance of these methods, in terms of bias and efficiency, is investigated through simulation and also illustrated using data from a clinical trial of treatments for colon cancer. The simulations suggest that the illness-death model-based method provides good estimates of Kendall's τ across several scenarios. In some situations, copula-based methods perform well but their performance is sensitive to the choice of copula. The Clayton copula is most appropriate in scenarios, which might realistically reflect an oncology trial, but the use of copula models in practice is questionable.

Bayesian measurement-error-driven hidden Markov regression model for calibrating the effect of covariates on multistate outcomes: Application to androgenetic alopecia

Multistate Markov regression models used for quantifying the effect size of state‐specific covariates pertaining to the dynamics of multistate outcomes have gained popularity. However, the measurements of multistate outcome are prone to the errors of classification, particularly when a population‐based survey/research is involved with proxy measurements of outcome due to cost consideration. Such a misclassification may affect the effect size of relevant covariates such as odds ratio used in the field of epidemiology. We proposed a Bayesian measurement‐error‐driven hidden Markov regression model for calibrating these biased estimates with and without a 2‐stage validation design. A simulation algorithm was developed to assess various scenarios of underestimation and overestimation given nondifferential misclassification (independent of covariates) and differential misclassification (dependent on covariates). We applied our proposed method to the community‐based survey of androgenetic alopecia and found that the effect size of the majority of covariate was inflated after calibration regardless of which type of misclassification. Our proposed Bayesian measurement‐error‐driven hidden Markov regression model is practicable and effective in calibrating the effects of covariates on multistate outcome, but the prior distribution on measurement errors accrued from 2‐stage validation design is strongly recommended.

Prediction of transfer among multiple states of blood pressure based on Markov model: an 18-year cohort study

OBJECTIVE

This study aimed to identify the rules of transition between normotension, prehypertension and hypertension states and to establish a prediction model for the incidence of prehypertension and hypertension.

METHODS

Data from the China Health and Nutrition Survey from 1991 to 2009 were used as training data to develop the model. Data of the year 2011 were used for model validation. The multistate Markov model was developed using the msm package in R software.

RESULTS

A total of 5265 participants were included at baseline, with an average follow-up of 8.05 ± 5.27 years and 17 640 observations. The ratio of men to women was 1 : 1.17, and the mean age was 37.54 ± 13.80 years. Within 10 years, in men, from normotension, the average probability to prehypertension and hypertension are 34.5 and 35.25%, respectively; from prehypertension, the average probability of recovering to normotension and developing to hypertension are 17.78 and 43.85%, respectively. In women, the average probabilities are 27.49, 28.09, 29.11 and 39.05%. Fat consumption increasing was found to be a protective factor, with 4.5% lower rate of transferring from normotension to prehypertension for a quarter percentage increasing. The model showed a very good prediction ability within 10 years and provided good prediction of blood pressure in the 2011 cohort (χ = 0.781, P = 0.676).

CONCLUSION

The multistate Markov model can be a useful tool to identify the rules of transition among multiple states of blood pressure and predict well prevalence of the normotension, prehypertension and hypertension in cohort populations.

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.

Regularized continuous-time Markov Model via elastic net

Continuous-time Markov models are commonly used to analyze longitudinal transitions between multiple disease states in panel data, where participants' disease states are only observed at multiple time points, and the exact state paths between observations are unknown. However, when covariate effects are incorporated and allowed to vary for different transitions, the number of potential parameters to estimate can become large even when the number of covariates is moderate, and traditional maximum likelihood estimation and subset model selection procedures can easily become unstable due to overfitting. We propose a novel regularized continuous-time Markov model with the elastic net penalty, which is capable of simultaneous variable selection and estimation for large number of parameters. We derive an efficient coordinate descent algorithm to solve the penalized optimization problem, which is fully automatic and data driven. We further consider an extension where one of the states is death, and time of death is exactly known but the state path leading to death is unknown. The proposed method is extensively evaluated in a simulation study, and demonstrated in an application to real-world data on airflow limitation state transitions.

Clustered multistate models with observation level random effects, mover-stayer effects and dynamic covariates: modelling transition intensities and sojourn times in a study of psoriatic arthritis

In psoriatic arthritis, it is important to understand the joint activity (represented by swelling and pain) and damage processes because both are related to severe physical disability. The paper aims to provide a comprehensive investigation into both processes occurring over time, in particular their relationship, by specifying a joint multistate model at the individual hand joint level, which also accounts for many of their important features. As there are multiple hand joints, such an analysis will be based on the use of clustered multistate models. Here we consider an observation level random-effects structure with dynamic covariates and allow for the possibility that a subpopulation of patients is at minimal risk of damage. Such an analysis is found to provide further understanding of the activity-damage relationship beyond that provided by previous analyses. Consideration is also given to the modelling of mean sojourn times and jump probabilities. In particular, a novel model parameterization which allows easily interpretable covariate effects to act on these quantities is proposed.

Time-homogeneous Markov process for HIV/AIDS progression under a combination treatment therapy: cohort study, South Africa

BACKGROUND

As HIV enters the human body, its main target is the CD4 cell which it turns into a factory that produces millions of other HIV particles. These HIV particles target new CD4 cells resulting in the progression of HIV infection to AIDS. A continuous depletion of CD4 cells results in opportunistic infections, for example tuberculosis (TB). The purpose of this study is to model and describe the progression of HIV/AIDS disease in an individual on antiretroviral therapy (ART) follow up using a continuous time homogeneous Markov process. A cohort of 319 HIV infected patients on ART follow up at a Wellness Clinic in Bela Bela, South Africa is used in this study. Though Markov models based on CD4 cell counts is a common approach in HIV/AIDS modelling, this paper is unique clinically in that tuberculosis (TB) co-infection is included as a covariate.

METHODS

The method partitions the HIV infection period into five CD4-cell count intervals followed by the end points; death, and withdrawal from study. The effectiveness of treatment is analysed by comparing the forward transitions with the backward transitions. The effects of reaction to treatment, TB co-infection, gender and age on the transition rates are also examined. The developed models give very good fit to the data.

RESULTS

The results show that the strongest predictor of transition from a state of CD4 cell count greater than 750 to a state of CD4 between 500 and 750 is a negative reaction to drug therapy. Development of TB during the course of treatment is the greatest predictor of transitions to states of lower CD4 cell count. Transitions from good states to bad states are higher on male patients than their female counterparts. Patients in the cohort spend a greater proportion of their total follow-up time in higher CD4 states.

CONCLUSION

From some of these findings we conclude that there is need to monitor adverse reaction to drugs more frequently, screen HIV/AIDS patients for any signs and symptoms of TB and check for factors that may explain gender differences further.

Optimal screening schedules for disease progression with application to diabetic retinopathy

Clinical management of chronic diseases requires periodic evaluations. Subjects transition between various levels of severity of a disease over time, one of which may trigger an intervention that requires treatment. For example, in diabetic retinopathy, patients with type 1 diabetes are evaluated yearly for either the onset of proliferative diabetic retinopathy (PDR) or clinically significant macular edema (CSME) that would require immediate treatment to preserve vision. Herein, we investigate methods for the selection of personalized cost-effective screening schedules and compare them with a fixed visit schedule (e.g., annually) in terms of both cost and performance. The approach is illustrated using the progression of retinopathy in the DCCT/EDIC study.

Semiparametric estimation of the accelerated mean model with panel count data under informative examination times

Panel count data arise when the number of recurrent events experienced by each subject is observed intermittently at discrete examination times. The examination time process can be informative about the underlying recurrent event process even after conditioning on covariates. We consider a semiparametric accelerated mean model for the recurrent event process and allow the two processes to be correlated through a shared frailty. The regression parameters have a simple marginal interpretation of modifying the time scale of the cumulative mean function of the event process. A novel estimation procedure for the regression parameters and the baseline rate function is proposed based on a conditioning technique. In contrast to existing methods, the proposed method is robust in the sense that it requires neither the strong Poisson-type assumption for the underlying recurrent event process nor a parametric assumption on the distribution of the unobserved frailty. Moreover, the distribution of the examination time process is left unspecified, allowing for arbitrary dependence between the two processes. Asymptotic consistency of the estimator is established, and the variance of the estimator is estimated by a model-based smoothed bootstrap procedure. Numerical studies demonstrated that the proposed point estimator and variance estimator perform well with practical sample sizes. The methods are applied to data from a skin cancer chemoprevention trial.

A state transition framework for patient-level modeling of engagement and retention in HIV care using longitudinal cohort data

The human immunodeficiency virus (HIV) care cascade is a conceptual model used to outline the benchmarks that reflects effectiveness of HIV care in the whole HIV care continuum. The models can be used to identify barriers contributing to poor outcomes along each benchmark in the cascade such as disengagement from care or death. Recently, the HIV care cascade has been widely applied to monitor progress towards HIV prevention and care goals in an attempt to develop strategies to improve health outcomes along the care continuum. Yet, there are challenges in quantifying successes and gaps in HIV care using the cascade models that are partly due to the lack of analytic approaches. The availability of large cohort data presents an opportunity to develop a coherent statistical framework for analysis of the HIV care cascade. Motivated by data from the Academic Model Providing Access to Healthcare, which has provided HIV care to nearly 200,000 individuals in Western Kenya since 2001, we developed a state transition framework that can characterize patient-level movements through the multiple stages of the HIV care cascade. We describe how to transform large observational data into an analyzable format. We then illustrate the state transition framework via multistate modeling to quantify dynamics in retention aspects of care. The proposed modeling approach identifies the transition probabilities of moving through each stage in the care cascade. In addition, this approach allows regression-based estimation to characterize effects of (time-varying) predictors of within and between state transitions such as retention, disengagement, re-entry into care, transfer-out, and mortality. Copyright © 2017 John Wiley & Sons, Ltd.

Estimation of overdiagnosis in breast cancer screening using a non-homogeneous multi-state model: A simulation study

Objectives

Overdiagnosis is regarded as a harm of screening. We aimed to develop a non-homogeneous multi-state model to consider the age-specific transition rates for estimation of overdiagnosis, to validate the model by a simulation study where the true frequency of overdiagnosis can be calculated, and to compare our estimate with the cumulative incidence method.

Methods

We constructed a four-state model to describe the natural history of breast cancer. The latent disease progression and the observed states for each individual were simulated in a trial with biennial screening of women aged 51–69 and a control group of the same size without screening. We performed 100 repetitions of the simulation with one million women to evaluate the performance of estimates. A sensitivity analysis with reduced number of controls was performed to imitate the data from the service screening programme.

Results

Based on the 100 repetitions, the mean value of the true frequency of overdiagnosis was 12.5% and the average estimates by the cumulative incidence method and the multi-state model were 12.9% (interquartile range: 2.46%) and 13.4% (interquartile range: 2.16%), respectively. The multi-state model had a greater bias of overdiagnosis than the cumulative incidence method, but the variation in the estimates was smaller. When the number of unscreened group was reduced, the variation of multi-state model estimates increased.

Conclusions

The multi-state model produces a proper estimate of overdiagnosis and the results are comparable with the cumulative incidence method. The multi-state model can be used in the estimation of overdiagnosis, and might be useful for the ongoing service screening programmes.

A stochastic estimation procedure for intermittently-observed semi-Markov multistate models with back transitions

Multistate models provide an important method for analyzing a wide range of life history processes including disease progression and patient recovery following medical intervention. Panel data consisting of the states occupied by an individual at a series of discrete time points are often used to estimate transition intensities of the underlying continuous-time process. When transition intensities depend on the time elapsed in the current state and back transitions between states are possible, this intermittent observation process presents difficulties in estimation due to intractability of the likelihood function. In this manuscript, we present an iterative stochastic expectation-maximization algorithm that relies on a simulation-based approximation to the likelihood function and implement this algorithm using rejection sampling. In a simulation study, we demonstrate the feasibility and performance of the proposed procedure. We then demonstrate application of the algorithm to a study of dementia, the Nun Study, consisting of intermittently-observed elderly subjects in one of four possible states corresponding to intact cognition, impaired cognition, dementia, and death. We show that the proposed stochastic expectation-maximization algorithm substantially reduces bias in model parameter estimates compared to an alternative approach used in the literature, minimal path estimation. We conclude that in estimating intermittently observed semi-Markov models, the proposed approach is a computationally feasible and accurate estimation procedure that leads to substantial improvements in back transition estimates.

Individualised variable-interval risk-based screening for sight-threatening diabetic retinopathy: the Liverpool Risk Calculation Engine

AIMS/HYPOTHESIS

Individualised variable-interval risk-based screening offers better targeting and improved cost-effectiveness in screening for diabetic retinopathy. We developed a generalisable risk calculation engine (RCE) to assign personalised intervals linked to local population characteristics, and explored differences in assignment compared with current practice.

METHODS

Data from 5 years of photographic screening and primary care for people with diabetes, screen negative at the first of > 1 episode, were combined in a purpose-built near-real-time warehouse. Covariates were selected from a dataset created using mixed qualitative/quantitative methods. Markov modelling predicted progression to screen-positive (referable diabetic retinopathy) against the local cohort history. Retinopathy grade informed baseline risk and multiple imputation dealt with missing data. Acceptable intervals (6, 12, 24 months) and risk threshold (2.5%) were established with patients and professional end users.

RESULTS

Data were from 11,806 people with diabetes (46,525 episodes, 388 screen-positive). Covariates with sufficient predictive value were: duration of known disease, HbA1c, age, systolic BP and total cholesterol. Corrected AUC (95% CIs) were: 6 months 0.88 (0.83, 0.93), 12 months 0.90 (0.87, 0.93) and 24 months 0.91 (0.87, 0.94). Sensitivities/specificities for a 2.5% risk were: 6 months 0.61, 0.93, 12 months 0.67, 0.90 and 24 months 0.82, 0.81. Implementing individualised RCE-based intervals would reduce the proportion of people becoming screen-positive before the allocated screening date by > 50% and the number of episodes by 30%.

CONCLUSIONS/INTERPRETATION

The Liverpool RCE shows sufficient performance for a local introduction into practice before wider implementation, subject to external validation. This approach offers potential enhancements of screening in improved local applicability, targeting and cost-effectiveness.

Protein-peptide association kinetics beyond the seconds timescale from atomistic simulations

Understanding and control of structures and rates involved in protein ligand binding are essential for drug design. Unfortunately, atomistic molecular dynamics (MD) simulations cannot directly sample the excessively long residence and rearrangement times of tightly binding complexes. Here we exploit the recently developed multi-ensemble Markov model framework to compute full protein-peptide kinetics of the oncoprotein fragment 25-109Mdm2 and the nano-molar inhibitor peptide PMI. Using this system, we report, for the first time, direct estimates of kinetics beyond the seconds timescale using simulations of an all-atom MD model, with high accuracy and precision. These results only require explicit simulations on the sub-milliseconds timescale and are tested against existing mutagenesis data and our own experimental measurements of the dissociation and association rates. The full kinetic model reveals an overall downhill but rugged binding funnel with multiple pathways. The overall strong binding arises from a variety of conformations with different hydrophobic contact surfaces that interconvert on the milliseconds timescale.

The Use of Multistate Models to Examine Associations of Stress and Adherence With Transitions Among HIV Care States Observed in a Clinical HIV Cohort

BACKGROUND

The "cascade of care" is a framework for quantifying the trajectory of people with HIV along the continuum of HIV care. We extended this framework to recognize that individuals may transition back and forth between states of care and to identify factors associated with movement among states of care over time, with particular focus on stress, depression, and adherence.

METHODS

The Ontario HIV Treatment Network Cohort Study is a multisite HIV clinical cohort. We analyzed data from participants who had initiated antiretroviral therapy, achieved virologic suppression, completed ≥1 study questionnaire including psychosocial data, and had ≥1 viral load (VL) result within 2 years of a questionnaire. Follow-up time from the first suppressed VL was divided into 6-month intervals and classified into 1 of 3 states for HIV care retention: (1) suppressed VL (VL <50 copies/mL), (2) unsuppressed VL (VL >50 copies/mL), and (3) unobserved. Multistate models were used to determine the association of transitioning between states and time-updated demographic and clinical characteristics.

RESULTS

In total, 1842 participants were included. After multivariable adjustment, poor adherence [hazard ratio (HR) 1.88, 95% confidence interval (CI): 1.19 to 2.98) and stress (HR = 1.38; 95% CI: 1.04 to 1.83) were associated with transitions from suppressed to unsuppressed VL. Similarly, low adherence (HR = 1.52; 95% CI: 1.14 to 2.04) and stress (HR = 1.25; 95%: 1.03, 1.51) were associated with transitions from suppressed to unobserved states.

CONCLUSIONS

Higher levels of stress and low adherence are associated with transitions to less favorable states of care. Interventions to manage stress and facilitate adherence may improve engagement in HIV care.

Bayesian variable selection for multistate Markov models with interval-censored data in an ecological momentary assessment study of smoking cessation

The application of sophisticated analytical methods to intensive longitudinal data, collected with ecological momentary assessments (EMA), has helped researchers better understand smoking behaviors after a quit attempt. Unfortunately, the wealth of information captured with EMAs is typically underutilized in practice. Thus, novel methods are needed to extract this information in exploratory research studies. One of the main objectives of intensive longitudinal data analysis is identifying relations between risk factors and outcomes of interest. Our goal is to develop and apply expectation maximization variable selection for Bayesian multistate Markov models with interval-censored data to generate new insights into the relation between potential risk factors and transitions between smoking states. Through simulation, we demonstrate the effectiveness of our method in identifying associated risk factors and its ability to outperform the LASSO in a special case. Additionally, we use the expectation conditional-maximization algorithm to simplify estimation, a deterministic annealing variant to reduce the algorithm's dependence on starting values, and Louis's method to estimate unknown parameter uncertainty. We then apply our method to intensive longitudinal data collected with EMA to identify risk factors associated with transitions between smoking states after a quit attempt in a cohort of socioeconomically disadvantaged smokers who were interested in quitting.

Joint analysis of panel count data with an informative observation process and a dependent terminal event

Panel count data occur in many clinical and observational studies, and in many situations, the observation process may be informative and also there may exist a terminal event such as death which stops the follow-up. In this article, we propose a new joint model for the analysis of panel count data in the presence of both an informative observation process and a dependent terminal event via two latent variables. For the inference on the proposed models, a class of estimating equations is developed and the resulting estimators are shown to be consistent and asymptotically normal. In addition, a lack-of-fit test is provided for assessing the adequacy of the models. Simulation studies suggest that the proposed approach works well for practical situations. A real example from a bladder cancer clinical trial is used to illustrate the proposed methods.

phydms: software for phylogenetic analyses informed by deep mutational scanning

It has recently become possible to experimentally measure the effects of all amino-acid point mutations to proteins using deep mutational scanning. These experimental measurements can inform site-specific phylogenetic substitution models of gene evolution in nature. Here we describe software that efficiently performs analyses with such substitution models. This software, phydms, can be used to compare the results of deep mutational scanning experiments to the selection on genes in nature. Given a phylogenetic tree topology inferred with another program, phydms enables rigorous comparison of how well different experiments on the same gene capture actual natural selection. It also enables re-scaling of deep mutational scanning data to account for differences in the stringency of selection in the lab and nature. Finally, phydms can identify sites that are evolving differently in nature than expected from experiments in the lab. As data from deep mutational scanning experiments become increasingly widespread, phydms will facilitate quantitative comparison of the experimental results to the actual selection pressures shaping evolution in nature.

Transitions in Prognostic Awareness Among Terminally Ill Cancer Patients in Their Last 6 Months of Life Examined by Multi-State Markov Modeling

BACKGROUND

Developing accurate prognostic awareness, a cornerstone of preference-based end-of-life (EOL) care decision-making, is a dynamic process involving more prognostic-awareness states than knowing or not knowing. Understanding the transition probabilities and time spent in each prognostic-awareness state can help clinicians identify trigger points for facilitating transitions toward accurate prognostic awareness. We examined transition probabilities in distinct prognostic-awareness states between consecutive time points in 247 cancer patients' last 6 months and estimated the time spent in each state.

METHODS

Prognostic awareness was categorized into four states: (a) unknown and not wanting to know, state 1; (b) unknown but wanting to know, state 2; (c) inaccurate awareness, state 3; and (d) accurate awareness, state 4. Transitional probabilities were examined by multistate Markov modeling.

RESULTS

Initially, 59.5% of patients had accurate prognostic awareness, whereas the probabilities of being in states 1-3 were 8.1%, 17.4%, and 15.0%, respectively. Patients' prognostic awareness generally remained unchanged (probabilities of remaining in the same state: 45.5%-92.9%). If prognostic awareness changed, it tended to shift toward higher prognostic-awareness states (probabilities of shifting to state 4 were 23.2%-36.6% for patients initially in states 1-3, followed by probabilities of shifting to state 3 for those in states 1 and 2 [9.8%-10.1%]). Patients were estimated to spend 1.29, 0.42, 0.68, and 3.61 months in states 1-4, respectively, in their last 6 months.

CONCLUSION

Terminally ill cancer patients' prognostic awareness generally remained unchanged, with a tendency to become more aware of their prognosis. Health care professionals should facilitate patients' transitions toward accurate prognostic awareness in a timely manner to promote preference-based EOL decisions.

IMPLICATIONS FOR PRACTICE

Terminally ill Taiwanese cancer patients' prognostic awareness generally remained stable, with a tendency toward developing higher states of awareness. Health care professionals should appropriately assess patients' readiness for prognostic information and respect patients' reluctance to confront their poor prognosis if they are not ready to know, but sensitively coach them to cultivate their accurate prognostic awareness, provide desired and understandable prognostic information for those who are ready to know, and give direct and honest prognostic information to clarify any misunderstandings for those with inaccurate awareness, thus ensuring that they develop accurate and realistic prognostic knowledge in time to make end-of-life care decisions.