A case-study in the clinical epidemiology of psoriatic arthritis: multistate models and causal arguments

Power and sample size for multistate model analysis of longitudinal discrete outcomes in disease prevention trials

For clinical trials where participants pass through a number of discrete health states resulting in longitudinal measures over time, there are several potential primary estimands for the treatment effect. Incidence or time to a particular health state are commonly used outcomes but the choice of health state may not be obvious and these estimands do not make full use of the longitudinal assessments. Multistate models have been developed for some diseases and conditions with the purpose of understanding their natural history and have been used for secondary analysis to understand mechanisms of action of treatments. There is little published on the use of multistate models as the primary analysis method and potential implications on design features, such as assessment schedules. We illustrate methods via analysis of data from a motivating example; a Phase III clinical trial of pressure ulcer prevention strategies. We clarify some of the possible estimands that might be considered and we show, via a simulation study, that under some circumstances the sample size could be reduced by half using a multistate model based analysis, without adversely affecting the power of the trial.

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.

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.

Correlated multistate models for multiple processes: an application to renal disease progression in systemic lupus erythematosus

Bidirectional changes over time in the estimated glomerular filtration rate and in urine protein content are of interest for the treatment and management of patients with lupus nephritis. Although these processes may be modelled by separate multistate models, the processes are likely to be correlated within patients. Motivated by the lupus nephritis application, we develop a new multistate modelling framework where subject-specific random effects are introduced to account for the correlations both between the processes and within patients over time. Models are fitted by using bespoke code in standard statistical software. A variety of forms for the random effects are introduced and evaluated by using the data from the Systemic Lupus International Collaborating Clinics.

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.

Clinical and Demographic Characteristics of Erosion-free and Erosion-present Status in Psoriatic Arthritis in a Cohort Study

OBJECTIVE

Psoriatic arthritis (PsA) has been recognized as a severe erosive disease. However, some patients do not develop erosions. We aimed to determine the prevalence, characteristics, and predictors of erosion-free patients (EFP) as compared with erosion-present patients (EPP) among patients with PsA followed prospectively.

METHODS

This is a retrospective analysis conducted on patients from the Toronto PsA cohort. Patients with at least 10 years of followup and radiographs were analyzed. Radiographs were scored with the modified Steinbrocker method. Baseline (first visit to clinic) characteristics were used to predict the development of erosions with logistic regression models. To examine the effect of time-varying covariates, Cox regression models were fit for the time to development of erosions from baseline.

RESULTS

Among 290 patients, 12.4% were EFP and 87.6% were EPP over the study period. The mean time to development of erosion in the EPP over the course of followup was 6.8 ± 6.1 years. EFP were diagnosed with psoriasis at a younger age compared with EPP. In both models, actively inflamed joints and clinically damaged joints were predictive of the development of erosion, whereas a longer duration of psoriasis at baseline decreased the odds of developing erosion. EPP had a higher percentage of unemployment as compared with EFP at baseline and followup visits.

CONCLUSION

Among patients with PsA followed for at least 10 years, 12.4% never develop erosions. The clinical and radiographic findings can ultimately assist in the stratification of a patient's prognosis regarding the development of erosions.

Estimation and assessment of markov multistate models with intermittent observations on individuals

Multistate models provide important methods of analysis for many life history processes, and this is an area where John Klein made numerous contributions. When individuals in a study group are observed continuously so that all transitions between states, and their times, are known, estimation and model checking is fairly straightforward. However, individuals in many studies are observed intermittently, and only the states occupied at the observation times are known. We review methods of estimation and assessment for Markov models in this situation. Numerical studies that show the effects of inter-observation times are provided, and new methods for assessing fit are given. An illustration involving viral load dynamics for HIV-positive persons is presented.

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.

Mixture distributions in multi-state modelling: some considerations in a study of psoriatic arthritis

In many studies, interest lies in determining whether members of the study population will undergo a particular event of interest. Such scenarios are often termed ‘mover–stayer’ scenarios, and interest lies in modelling two sub-populations of ‘movers’ (those who have a propensity to undergo the event of interest) and ‘stayers’ (those who do not). In general, mover–stayer scenarios within data sets are accounted for through the use of mixture distributions, and in this paper, we investigate the use of various random effects distributions for this purpose. Using data from the University of Toronto psoriatic arthritis clinic, we present a multi-state model to describe the progression of clinical damage in hand joints of patients with psoriatic arthritis. We consider the use of mover–stayer gamma, inverse Gaussian and compound Poisson distributions to account for both the correlation amongst joint locations and the possible mover–stayer situation with regard to clinical hand joint damage. We compare the fits obtained from these models and discuss the extent to which a mover–stayer scenario exists in these data. Furthermore, we fit a mover–stayer model that allows a dependence of the probability of a patient being a stayer on a patient-level explanatory variable.