MARKOV: a computer program for multi-state Markov models with covariables

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.

A tool to predict progression of non-alcoholic fatty liver disease in severely obese patients

BACKGROUND & AIMS

Severely obese patients are a growing population at risk of non-alcoholic fatty liver disease (NAFLD). Considering the increasing burden, a predictive tool of NAFLD progression would be of interest. Our objective was to provide a tool allowing general practitioners to identify and refer the patients most at risk, and specialists to estimate disease progression and adapt the therapeutic strategy.

METHODS

This predictive tool is based on a Markov model simulating steatosis, fibrosis and non-alcoholic steatohepatitis (NASH) evolution. This model was developped from data of 1801 severely obese, bariatric surgery candidates, with histological assessment, integrating duration of exposure to risk factors. It is then able to predict current disease severity in the absence of assessment, and future cirrhosis risk based on current stage.

RESULTS

The model quantifies the impact of sex, body-mass index at 20, diabetes, age of overweight onset, on progression. For example, for 40-year-old severely obese patients seen by the general practitioners: (a) non-diabetic woman overweight at 20, and (b) diabetic man overweight at 10, without disease assessment, the model predicts their current risk to have NASH or F3-F4: for (a) 5.7% and 0.6%, for (b) 16.1% and 10.0% respectively. If those patients have been diagnosed F2 by the specialist, the model predicts the 5-year cirrhosis risk: 1.8% in the absence of NASH and 6.0% in its presence for (a), 10.3% and 26.7% respectively, for (b).

CONCLUSIONS

This model provides a decision-making tool to predict the risk of liver disease that could help manage severely obese patients.

A Model to Identify Heavy Drinkers at High Risk for Liver Disease Progression

BACKGROUND & AIMS

Alcohol-related liver disease (ALD) causes chronic liver disease. We investigated how information on patients' drinking history and amount, stage of liver disease, and demographic feature can be used to determine risk of disease progression.

METHODS

We collected data from 2334 heavy drinkers (50 g/day or more) with persistently abnormal results from liver tests who had been admitted to a hepato-gastroenterology unit in France from January 1982 through December 1997; patients with a recorded duration of alcohol abuse were assigned to the development cohort (n=1599; 75% men) or the validation cohort (n=735; 75% men), based on presence of a liver biopsy. We collected data from both cohorts on patient history and disease stage at the time of hospitalization. For the development cohort, severity of the disease was scored by the METAVIR (due to the availability of liver histology reports); in the validation cohort only the presence of liver complications was assessed. We developed a model of ALD progression and occurrence of liver complications (hepatocellular carcinoma and/or liver decompensation) in association with exposure to alcohol, age at the onset of heavy drinking, amount of alcohol intake, sex and body mass index. The model was fitted to the development cohort and then evaluated in the validation cohort. We then tested the ability of the model to predict disease progression for any patient profile (baseline evaluation). Patients with a 5-y weighted risk of liver complications greater than 5% were considered at high risk for disease progression.

RESULTS

Model results are given for the following patient profiles: men and women, 40 y old, who started drinking at an age of 25 y, drank 150 g/day, and had a body mass index of 22 kg/m² according to the disease severity at baseline evaluation. For men with baseline F0-F2 fibrosis, the model estimated the probabilities of normal liver, steatosis, or steatohepatitis at baseline to be 31.8%, 61.5% and 6.7%, respectively. The 5-y weighted risk of liver complications was 1.9%, ranging from 0.2% for men with normal liver at baseline evaluation to 10.3% for patients with steatohepatitis at baseline. For women with baseline F0-F2 fibrosis, probabilities of normal liver, steatosis, or steatohepatitis at baseline were 25.1%, 66.5% and 8.4%, respectively; the 5-y weighted risk of liver complications was 3.2%, ranging from 0.5% for women with normal liver at baseline to 14.7% for patients with steatohepatitis at baseline. Based on the model, men with F3-F4 fibrosis at baseline have a 24.5% 5-y weighted risk of complications (ranging from 20.2% to 34.5%) and women have a 30.1% 5-y weighted risk of complications (ranging from 24.7% to 41.0%).

CONCLUSIONS

We developed a Markov model that integrates data on level and duration of alcohol use to identify patients at high risk of liver disease progression. This model might be used to adapt patient care pathways.

Cost-Effectiveness of Three Alternative Boosted Protease Inhibitor-Based Second-Line Regimens in HIV-Infected Patients in West and Central Africa

BACKGROUND

While dolutegravir has been added by WHO as a preferred second-line option for the treatment of HIV infection, boosted protease inhibitor (bPI)-based regimens are still needed as alternative second-line options. Identifying optimal bPI-based second-line combinations is essential, given associated high costs and funding constraints in low- and middle-income countries. We assessed the cost-effectiveness of three alternative bPI-based second-line regimens in Burkina Faso, Cameroon and Senegal.

METHODS

We used data collected over 2010-2015 in the 2LADY trial/post-trial cohort. Patients with first-line antiretroviral therapy (ART) failure were randomly assigned to tenofovir/emtricitabine + lopinavir/ritonavir (TDF/FTC LPV/r; arm A), abacavir + didanosine + lopinavir/ritonavir (arm B), or tenofovir/emtricitabine + darunavir/ritonavir (arm C). Costs (US dollars, 2016), quality-adjusted life-years (QALYs) and incremental cost-effectiveness ratios were computed for each country over 24 months of follow-up and extrapolated to 5 years using a simulated patient-level Markov model. We assessed uncertainty using cost-effectiveness acceptability curves, scenarios and prices threshold analysis.

RESULTS

In each country, over 24 months, arm A was significantly less costly than arms B and C (incremental costs ranging from US$410-$US721 and US$468-US$546 for B and C vs A, respectively) and offered similar health benefits (incremental QALY: - 0.138 to 0.023 and - 0.179 to 0.028, respectively). Over 5 years, arm A remained the least costly, health benefits not being significantly different between arms. Compared with arms B and C, in each study country, Arm A had a ≥ 95% probability of being cost-effective for a large range of cost-effectiveness thresholds, irrespective of the scenario considered.

CONCLUSIONS

Using TDF/FTC LPV/r as a bPI-based second-line regimen provided the best economic value in the three study countries.

TRIAL REGISTRATION

ClinicalTrials.gov Identifier: NCT00928187.

Telehealth practice recommendations for diabetic retinopathy, second edition

Ocular telemedicine and telehealth have the potential to decrease vision loss from DR. Planning, execution, and follow-up are key factors for success. Telemedicine is complex, requiring the services of expert teams working collaboratively to provide care matching the quality of conventional clinical settings. Improving access and outcomes, however, makes telemedicine a valuable tool for our diabetic patients. Programs that focus on patient needs, consider available resources, define clear goals, promote informed expectations, appropriately train personnel, and adhere to regulatory and statutory requirements have the highest chance of achieving success.

Transitions between tobacco and cannabis use among adolescents: a multi-state modeling of progression from onset to daily use

Use of a given substance may follow a stage process leading from onset to regular use, and use of one substance can be strongly associated with use of another. The aim of this study was to describe the transitions between tobacco and cannabis use. Data was derived from a French nationwide survey involving 29,393 teenagers. A homogenous Markov multi-state model (MSM) was fitted. The substance use pattern modeled was: no lifetime use→1 (2) substance(s) initiation→1 (2) daily substance(s) use, with pathways between tobacco and cannabis. The likelihood of first initiating tobacco appeared 17.6 times greater than the likelihood of initiating cannabis. Once a subject has experimented with one substance, the risk of another substance experiment was much greater. Transition intensity from tobacco initiation to daily use was 4.8 times higher than that from cannabis. Our results are compatible with a process mixing the gateway theory, the reverse gateway theory and the route of administration model, but do not explore a common liability to addictions, which could be explored by using a MSM on a prospective cohort with initial collection of some explanatory factors.

The mstate package for estimation and prediction in non- and semi-parametric multi-state and competing risks models

In recent years, multi-state models have been studied widely in survival analysis. Despite their clear advantages, their use in biomedical and other applications has been rather limited so far. An important reason for this is the lack of flexible and user-friendly software for multi-state models. This paper introduces a package in R, called 'mstate', for each of the steps of the analysis of multi-state models. It can be applied to non- and semi-parametric models. The package contains functions to facilitate data preparation and flexible estimation of different types of covariate effects in the context of Cox regression models, functions to estimate patient-specific transition intensities, dynamic prediction probabilities and their associated standard errors (both Greenwood and Aalen-type). Competing risks models can also be analyzed by means of mstate, as they are a special type of multi-state models. The package is available from the R homepage http://cran.r-project.org. We give a self-contained account of the underlying mathematical theory, including a new asymptotic result for the cumulative hazard function and new recursive formulas for the calculation of the estimated standard errors of the estimated transition probabilities, and we illustrate the use of the key functions of the mstate package by the analysis of a reversible multi-state model describing survival of liver cirrhosis patients.

Markov modelling of HIV infection evolution in the HAART era

The aim was to investigate the impact of the main prognostic factors on HIV evolution. A multi-state Markov model was applied in a cohort of 2126 patients to estimate impact of these factors on patients' clinical and immunological evolutions. Clinical progression and immunological deterioration shared most of their prognostic factors: male gender, intravenous drug use, weight loss, low haemoglobin level (<110 g/l), CD8 cell count (<500/mm(3)) and HIV viral load (>5 log(10) copies/ml). Highly active retroviral therapy reduced the risks of clinical progression and immune deterioration whatever patients' CD4 cell count. Risk reductions were 41-60% for protease inhibitor-based and 27-68% for non-nucleoside reverse transcriptase inhibitor-based regimens. Three-year transition probabilities showed that only patients with a CD4 cell count >or=350 CD4/mm(3) could in most cases maintain their immunity. This model provides 'real life' transition probabilities from one immunological stage to another, allowing decision analyses that could help determine the beneficial therapeutic strategies for HIV-infected patients.

Multi-state models for the analysis of time-to-event data

The experience of a patient in a survival study may be modelled as a process with two states and one possible transition from an "alive" state to a "dead" state. In some studies, however, the "alive" state may be partitioned into two or more intermediate (transient) states, each of which corresponding to a particular stage of the illness. In such studies, multi-state models can be used to model the movement of patients among the various states. In these models issues, of interest include the estimation of progression rates, assessing the effects of individual risk factors, survival rates or prognostic forecasting. In this article, we review modelling approaches for multi-state models, and we focus on the estimation of quantities such as the transition probabilities and survival probabilities. Differences between these approaches are discussed, focussing on possible advantages and disadvantages for each method. We also review the existing software currently available to fit the various models and present new software developed in the form of an R library to analyse such models. Different approaches and software are illustrated using data from the Stanford heart transplant study and data from a study on breast cancer conducted in Galicia, Spain.

tdc.msm: an R library for the analysis of multi-state survival data

The aim of this paper is to present an R library, called tdc.msm, developed to analyze multi-state survival data. In this library, the time-dependent regression model and multi-state models are included as two possible approaches for such data. For the multi-state modelling five different models are considered, allowing the user to choose between Markov and semi-Markov property, as well as to use homogeneous or non-homogeneous models. Specifically, the following multi-state models in continuous time were implemented: Cox Markov model; Cox semi-Markov model; homogeneous Markov model; non-homogeneous piecewise model and non-parametric Markov model. This software can be used to fit multi-state models with one initial state (e.g., illness diagnosis), a finite number of intermediate states, representing, for example, a change of treatment, and one absorbing state corresponding to a terminal event of interest. Graphical output includes survival estimates, transition probabilities estimates and smooth log hazard for continuous covariates.

Disability evolution in multiple sclerosis: how to deal with missing transition times in the Markov model?

Markov modeling of disability progression in multiple sclerosis requires knowledge of all times of transitions from a given level of disability to the next level, but such data are often missing. We address methodological challenges due to partly missing transition times. To estimate the effects of prognostic factors on the risk of transitions between three consecutive disability levels, two methods were used to deal with missing data. Listwise deletion limited the analysis to subjects with complete data. Multiple imputation of missing data revealed that data were missing at random (MAR mechanism) and imputed the missing transition times from the Weibull model. The results were then compared with the full data set with the actual times established through chart review. Multiple imputation estimates were systematically closer to those from the full data set than the listwise deletion estimates.

A population-based assessment of the prognostic value of the CD19 positive lymphocyte count in B-cell chronic lymphocytic leukemia using Cox and Markov models

No population-based study has assessed the prognostic impact on survival of the CD19 positive lymphocyte count, evaluated by immunophenotyping at diagnosis, in B-cell chronic lymphocytic leukemia (B-CLL). Aiming at addressing this issue, we investigated the clinical outcome of a well-defined population of B-CLL patients. Survival of B-CLL patients, diagnosed between 1990 and 1999 and recorded by the Registry of Hematological Malignancies of the Côte d'Or, was analysed applying Cox's regression model to the 237 included cases and to the 195 Binet stage A patients. To assess simultaneously the predictive value of each parameter on the risk of disease progression and on the risk of death, we completed this analysis by applying a three-states homogeneous Markov model to the whole study population. Analysis of the entire population showed that age (p < 0.001), Binet stage (p = 0.008) and CD19 positive lymphocyte count (p = 0.038) were three independent prognostic factors. However, in stage A patients, only progression into a more advanced stage, analysed as a time-dependent variable, and age had a clear impact on survival (p < 0.001 for both). Markov model revealed that an increased CD19 positive lymphocyte count increased the risk of disease progression in stage A patients (p = 0.002) but did not have direct impact on survival of either stage A patients with stable disease or stage B or C patients. An increased CD19 positive lymphocyte count at diagnosis is a marker of an increased risk of disease progression in stage A patients. Thus, it can be a useful tool for the clinical management of these patients.

A computer program to estimate the parameters of covariate dependent higher order Markov model

This paper presents a computer program developed in S-plus to estimate the parameters of covariate dependent higher order Markov Chain and related tests. The program can be applied for two states Markov Chain with any order and any number of covariates depending on the PC capabilities. The program provides the maximum likelihood estimates of the parameters, together with their estimated standard error, t-value and significance level. It also produces the test results for likelihood ratio and model chi-square. To illustrate the program we have used a longitudinal data set on maternal morbidity of rural women in Bangladesh. The occurrences of haemorrhage, convulsion, or fits at different follow-ups were used as outcome variable. Economic status, wanted pregnancy, ages at marriage, and education of women were used as covariates.

Modeling recurrence in colorectal cancer

OBJECTIVE

To assess the role of recurrence in prognosis of colon cancer, we investigated several methodologic issues, including application of classic survival analysis and Markov model.

STUDY DESIGN AND SETTING

The data were recorded by the Registry of Digestive Tumors of Côte d'Or, France, for 874 patients who had been treated by surgery between 1976 and 1984 and followed for up to 11 years. Survival analyses included the Cox proportional hazards model and its two generalizations that allow recurrence to be taken into account as a time-dependent covariate or as a competing outcome. The Markov model was used to analyze simultaneously recurrence and death.

RESULTS

The competing risks approach is not appropriate because censoring is indisputably informative. The Markov model and the Cox model, with recurrence as a time-dependent covariate, provided similar results, demonstrating the impact of age and gender on recurrence and revealing a reduction in the effect of site and stage on mortality.

CONCLUSION

A Markov multistate model seems to give new insights about the course of digestive cancer progression and into the role of recurrence in this process.

Inference for multi-state models from interval-censored data

Clinical statuses of subjects are often observed at a finite number of visits. This leads to interval-censored observations of times of transition from one state to another. The likelihood can still easily be written in terms of both transition probabilities and transition intensities. In homogeneous Markov models, transition probabilities can be expressed simply in terms of transition intensities, but this is not the case in more general multi-state models. In addition, inference in homogeneous Markov models is easy because these are parametric models. Non-parametric approaches to non-homogeneous Markov models may follow two paths: one is the completely non-parametric approach and can be seen as a generalisation of the Turnbull approach; the other implies a restriction to smooth intensities models. In particular, the penalized likelihood method has been applied to this problem. This paper gives a review of these topics.

MKVPCI: a computer program for Markov models with piecewise constant intensities and covariates

We present a computer program for fitting Markov models with piecewise constant intensities and for estimating the effect of covariates on transition intensities. The basic idea of the proposed approach is to introduce artificial time-dependent covariates in the data to represent the time dependence of the transition intensities, and to use a modified time-homogeneous Markov model to estimate the baseline transition intensities and the regression coefficients. The program provides the maximum likelihood estimates of the parameters together with their estimated standard errors, and allows testing various statistical hypotheses. To illustrate the use of the program, we present a three-state model for analyzing the smoking habits of school children.

DT-Planner: an environment for managing dynamic decision problems

The problem of formulating plans under uncertainty and coping with dynamic decision problems is a major task of both artificial intelligence and control theory applications in medicine. In this paper we will describe a software package, called DT-Planner, designed to represent and solve dynamic decision problems that can be modelled as Markov decision processes, by exploiting a novel graphical formalism, called influence view. An influence view is a directed acyclic graph that depicts the probabilistic relationships between the problem state variables in a generic time transition; additional variables, called event variables, may be added, in order to describe the conditional independencies between state variables. By using the specified conditional independence structure, an influence view may allow a parsimonious specification of a Markov decision process. DT-Planner lets the user specify and manage models through a user-friendly graphical interface, and implements efficient for policy determination algorithms. DT-Planner is written in C with Open Interface libraries and can be obtained, for non commercial use, via anonymous ftp without charge.