The Analysis of Longitudinal Ordinal Response Data in Continuous Time

Developing a clinical-environmental-genotypic prognostic index for relapsing-onset multiple sclerosis and clinically isolated syndrome

Our inability to reliably predict disease outcomes in multiple sclerosis remains an issue for clinicians and clinical trialists. This study aims to create, from available clinical, genetic and environmental factors; a clinical–environmental–genotypic prognostic index to predict the probability of new relapses and disability worsening. The analyses cohort included prospectively assessed multiple sclerosis cases (N = 253) with 2858 repeated observations measured over 10 years. N = 219 had been diagnosed as relapsing-onset, while N = 34 remained as clinically isolated syndrome by the 10th-year review. Genotype data were available for 199 genetic variants associated with multiple sclerosis risk. Penalized Cox regression models were used to select potential genetic variants and predict risk for relapses and/or worsening of disability. Multivariable Cox regression models with backward elimination were then used to construct clinical–environmental, genetic and clinical–environmental–genotypic prognostic index, respectively. Robust time-course predictions were obtained by Landmarking. To validate our models, Weibull calibration models were used, and the Chi-square statistics, Harrell’s C-index and pseudo-R² were used to compare models. The predictive performance at diagnosis was evaluated using the Kullback–Leibler and Brier (dynamic) prediction error (reduction) curves. The combined index (clinical–environmental–genotypic) predicted a quadratic time-dynamic disease course in terms of worsening (HR = 2.74, CI: 2.00–3.76; pseudo-R²=0.64; C-index = 0.76), relapses (HR = 2.16, CI: 1.74–2.68; pseudo-R² = 0.91; C-index = 0.85), or both (HR = 3.32, CI: 1.88–5.86; pseudo-R² = 0.72; C-index = 0.77). The Kullback–Leibler and Brier curves suggested that for short-term prognosis (≤5 years from diagnosis), the clinical–environmental components of disease were more relevant, whereas the genetic components reduced the prediction errors only in the long-term (≥5 years from diagnosis). The combined components performed slightly better than the individual ones, although their prognostic sensitivities were largely modulated by the clinical–environmental components. We have created a clinical–environmental–genotypic prognostic index using relevant clinical, environmental, and genetic predictors, and obtained robust dynamic predictions for the probability of developing new relapses and worsening of symptoms in multiple sclerosis. Our prognostic index provides reliable information that is relevant for long-term prognostication and may be used as a selection criterion and risk stratification tool for clinical trials. Further work to investigate component interactions is required and to validate the index in independent data sets.

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.

Model diagnostics for multi-state models

Multi-state models are a popular method of describing medical processes that can be represented as discrete states or stages. They have particular use when the data are panel-observed, meaning they consist of discrete snapshots of disease status at irregular time points which may be unique to each patient. However, due to the difficulty of inference in more complicated cases, strong assumptions such as the Markov property, patient homogeneity and time homogeneity are applied. It is important that the validity of these assumptions is tested. A review of methods for diagnosing model fit for panel-observed continuous-time Markov and misclassification-type hidden Markov models is given, with illustrative application to a dataset on cardiac allograft vasculopathy progression in post-heart transplant patients.

Applications of continuous time hidden Markov models to the study of misclassified disease outcomes

Disease progression in prospective clinical and epidemiological studies is often conceptualized in terms of transitions between disease states. Analysis of data from such studies can be complicated by a number of factors, including the presence of individuals in various prevalent disease states and with unknown prior disease history, interval censored observations of state transitions and misclassified measurements of disease states. We present an approach where the disease states are modelled as the hidden states of a continuous time hidden Markov model using the imperfect measurements of the disease state as observations. Covariate effects on transitions between disease states are incorporated using a generalized regression framework. Parameter estimation and inference are based on maximum likelihood methods and rely on an EM algorithm. In addition, techniques for model assessment are proposed. Applications to two binary disease outcomes are presented: the oral lesion hairy leukoplakia in a cohort of HIV infected men and cervical human papillomavirus (HPV) infection in a cohort of young women. Estimated transition rates and misclassification probabilities for the hairy leukoplakia data agree well with clinical observations on the persistence and diagnosis of this lesion, lending credibility to the interpretation of hidden states as representing the actual disease states. By contrast, interpretation of the results for the HPV data are more problematic, illustrating that successful application of the hidden Markov model may be highly dependent on the degree to which the assumptions of the model are satisfied.

Longitudinal data analysis (repeated measures) in clinical trials

Longitudinal data is often collected in clinical trials to examine the effect of treatment on the disease process over time. This paper reviews and summarizes much of the methodological research on longitudinal data analysis from the perspective of clinical trials. We discuss methodology for analysing Gaussian and discrete longitudinal data and show how these methods can be applied to clinical trials data. We illustrate these methods with five examples of clinical trials with longitudinal outcomes. We also discuss issues of particular concern in clinical trials including sequential monitoring and adjustments for missing data. A review of current software for analysing longitudinal data is also provided. Published in 1999 by John Wiley & Sons, Ltd. This article is a US Government work and is the public domain in the United States.

Comprehensive analysis of risk factors for acquisition of Pseudomonas aeruginosa in young children with cystic fibrosis

The objective of this study was to identify risk factors of significance for acquisition of Pseudomonas aeruginosa by children with cystic fibrosis (CF). Our working hypothesis is that exposure of infants and young children with CF to older, infected patients increases their risk for acquiring this organism. A special opportunity arose to study this question in detail, as we have been performing a randomized clinical trial of neonatal screening for CF throughout the state of Wisconsin during the period of 1985-1994. Patients were selected for this study based on either early identification through screening or diagnosis by standard methods. A longitudinal protocol employed at Wisconsin's two CF Centers includes routine cultures of respiratory secretions and collection of clinical, demographic, and activity information on patients and their families. Previous observations in our trial revealed that one center at an old hospital in an urban location showed a significantly shorter time to acquisition of P. aeruginosa for CF patients followed there. To study the center effect further, we performed statistical analyses using survival curves and stepwise regression analysis of all life history covariates available. The results of these analyses showed that the statistically significant correlations involve the following risk factors: 1) center and old hospital (r=0.42); 2) center and original physician (r=0.61); 3) center and exposure to pseudomonas-positive patients (r=0.29); and 4) population density and urban location (r=0.49). The final statistical model demonstrated that increased risk due to aerosol use (odds ratio=3.45, P=0.014) and a protective effect associated with education of the mother (odds ratio=0.81, P=0.024) were the most significant factors for acquisition of P. aeruginosa. The previously observed center effect was confined to the 1985-1990 interval at the old hospital (odds ratio=4.43, P < 0.001). We conclude that multiple factors are involved in increasing the risk of young children with CF to acquire P. aeruginosa, and that the observed center effect can best be explained by a combination of factors. These results suggest that facilities and methods used to care for young children with CF can significantly influence their likelihood of acquiring pseudomonas in the respiratory tract.