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.

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.

Estimation of state occupancy probabilities in multistate models with dependent intermittent observation, with application to HIV viral rebounds

In follow-up studies on chronic disease cohorts, individuals are often observed at irregular visit times that may be related to their previous disease history and other factors. This can produce bias in standard methods of estimation. Working in the context of multistate models, we consider a method of nonparametric estimation for state occupancy probabilities that adjusts for dependent follow-up through the use of inverse-intensity-of-visit weighted estimating functions and smoothing. The methodology is applied to the estimation of viral rebound probabilities in the Canadian Observational Cohort on HIV-positive persons. Copyright © 2016 John Wiley & Sons, Ltd.

A joint modelling approach for multistate processes subject to resolution and under intermittent observations

Multistate processes provide a convenient framework when interest lies in characterising the transition intensities between a set of defined states. If, however, there is an unobserved event of interest (not known if and when the event occurs), which when it occurs stops future transitions in the multistate process from occurring, then drawing inference from the joint multistate and event process can be problematic. In health studies, a particular example of this could be resolution, where a resolved patient can no longer experience any further symptoms, and this is explored here for illustration. A multistate model that includes the state space of the original multistate process but partitions the state representing absent symptoms into a latent absorbing resolved state and a temporary transient state of absent symptoms is proposed. The expanded state space explicitly distinguishes between resolved and temporary spells of absent symptoms through disjoint states and allows the uncertainty of not knowing if resolution has occurred to be easily captured when constructing the likelihood; observations of absent symptoms can be considered to be temporary or having resulted from resolution. The proposed methodology is illustrated on a psoriatic arthritis data set where the outcome of interest is a set of intermittently observed disability scores. Estimated probabilities of resolving are also obtained from the model. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Joint modelling of longitudinal and multi-state processes: application to clinical progressions in prostate cancer

Joint modelling of longitudinal and survival data is increasingly used in clinical trials on cancer. In prostate cancer for example, these models permit to account for the link between longitudinal measures of prostate-specific antigen (PSA) and time of clinical recurrence when studying the risk of relapse. In practice, multiple types of relapse may occur successively. Distinguishing these transitions between health states would allow to evaluate, for example, how PSA trajectory and classical covariates impact the risk of dying after a distant recurrence post-radiotherapy, or to predict the risk of one specific type of clinical recurrence post-radiotherapy, from the PSA history. In this context, we present a joint model for a longitudinal process and a multi-state process, which is divided into two sub-models: a linear mixed sub-model for longitudinal data and a multi-state sub-model with proportional hazards for transition times, both linked by a function of shared random effects. Parameters of this joint multi-state model are estimated within the maximum likelihood framework using an EM algorithm coupled with a quasi-Newton algorithm in case of slow convergence. It is implemented under R, by combining and extending mstate and JM packages. The estimation program is validated by simulations and applied on pooled data from two cohorts of men with localized prostate cancer. Thanks to the classical covariates available at baseline and the repeated PSA measurements, we are able to assess the biomarker's trajectory, define the risks of transitions between health states and quantify the impact of the PSA dynamics on each transition intensity. Copyright © 2016 John Wiley & Sons, Ltd.

Recurrent event data analysis with intermittently observed time-varying covariates

Although recurrent event data analysis is a rapidly evolving area of research, rigorous studies on estimation of the effects of intermittently observed time-varying covariates on the risk of recurrent events have been lacking. Existing methods for analyzing recurrent event data usually require that the covariate processes are observed throughout the entire follow-up period. However, covariates are often observed periodically rather than continuously. We propose a novel semiparametric estimator for the regression parameters in the popular proportional rate model. The proposed estimator is based on an estimated score function where we kernel smooth the mean covariate process. We show that the proposed semiparametric estimator is asymptotically unbiased, normally distributed, and derives the asymptotic variance. Simulation studies are conducted to compare the performance of the proposed estimator and the simple methods carrying forward the last covariates. The different methods are applied to an observational study designed to assess the effect of group A streptococcus on pharyngitis among school children in India. Copyright © 2016 John Wiley & Sons, Ltd.

State selection in Markov models for panel data with application to psoriatic arthritis

Markov multistate models in continuous-time are commonly used to understand the progression over time of disease or the effect of treatments and covariates on patient outcomes. The states in multistate models are related to categorisations of the disease status, but there is often uncertainty about the number of categories to use and how to define them. Many categorisations, and therefore multistate models with different states, may be possible. Different multistate models can show differences in the effects of covariates or in the time to events, such as death, hospitalisation, or disease progression. Furthermore, different categorisations contain different quantities of information, so that the corresponding likelihoods are on different scales, and standard, likelihood-based model comparison is not applicable. We adapt a recently developed modification of Akaike's criterion, and a cross-validatory criterion, to compare the predictive ability of multistate models on the information which they share. All the models we consider are fitted to data consisting of observations of the process at arbitrary times, often called 'panel' data. We develop an implementation of these criteria through Hidden Markov models and apply them to the comparison of multistate models for the Health Assessment Questionnaire score in psoriatic arthritis. This procedure is straightforward to implement in the R package 'msm'.

The effect of different remission definitions on identification of predictors of both point and sustained remission in rheumatoid arthritis treated with anti-TNF therapy

OBJECTIVE

Predictors of remission in rheumatoid arthritis (RA) have been defined in cross-sectional analyses using the 28-joint Disease Activity Score (DAS28), but not with newer composite disease activity measures or using the more clinically relevant state of sustained remission. We have evaluated predictors of remission using cross-sectional and longitudinal durations of disease state, and by applying additional definitions of remission [American College of Rheumatology/European League Against Rheumatism Boolean, Simplified Disease Activity Index (SDAI), and Clinical Disease Activity Index (CDAI)].

METHODS

Individuals in the Alberta Biologics Pharmacosurveillance Program were classified for the presence of remission (point and/or sustained > 1 yr) by each of the 4 definitions. Multivariate models were constructed including all available variables in the dataset and refined to optimize model fit and predictive ability to calculate OR for remission.

RESULTS

Nonsmoking status independently predicted point remission by all definitions (OR range 1.20-2.71). Minority ethnicity decreased odds of remission by DAS28 (OR 0.13) and CDAI (OR 0.09) definitions. Male sex was associated with DAS28 remission (OR 2.85), whereas higher baseline physician global (OR 0.67) and erythrocyte sedimentation rate values (OR 0.98) decreased odds of DAS28 remission. Higher baseline patient global score (OR 0.77) and swollen joint counts (OR 0.93) were negative predictors for CDAI remission. Higher baseline Health Assessment Questionnaire (OR 0.62) reduced odds for remission by the SDAI definition, and educational attainment increased these odds (OR 2.13). Sustained remission was negatively predicted by baseline physician global for the DAS28 (OR 0.80), and higher tender joint count (OR 0.96) for the CDAI.

CONCLUSION

We demonstrate the influence of duration of remission state and remission definition on defining independent predictors for remission in RA requiring anti-tumor necrosis factor therapy. These predictors offer improved applicability for modern rheumatology practice.

The versatility of multi-state models for the analysis of longitudinal data with unobservable features

Multi-state models provide a convenient statistical framework for a wide variety of medical applications characterized by multiple events and longitudinal data. We illustrate this through four examples. The potential value of the incorporation of unobserved or partially observed states is highlighted. In addition, joint modelling of multiple processes is illustrated with application to potentially informative loss to follow-up, mis-measured or missclassified data and causal inference.

Application of seemingly unrelated regression in medical data with intermittently observed time-dependent covariates

Background. In many studies with longitudinal data, time-dependent covariates can only be measured intermittently (not at all observation times), and this presents difficulties for standard statistical analyses. This situation is common in medical studies, and methods that deal with this challenge would be useful. Methods. In this study, we performed the seemingly unrelated regression (SUR) based models, with respect to each observation time in longitudinal data with intermittently observed time-dependent covariates and further compared these models with mixed-effect regression models (MRMs) under three classic imputation procedures. Simulation studies were performed to compare the sample size properties of the estimated coefficients for different modeling choices. Results. In general, the proposed models in the presence of intermittently observed time-dependent covariates showed a good performance. However, when we considered only the observed values of the covariate without any imputations, the resulted biases were greater. The performances of the proposed SUR-based models in comparison with MRM using classic imputation methods were nearly similar with approximately equal amounts of bias and MSE. Conclusion. The simulation study suggests that the SUR-based models work as efficiently as MRM in the case of intermittently observed time-dependent covariates. Thus, it can be used as an alternative to MRM.