The BILAG-2004 index is associated with development of new damage in SLE.

OBJECTIVE: To determine whether BILAG-2004 index is associated with the development of damage in a cohort of SLE patients. Mortality and development of damage were examined. METHODS: This was a multicentre longitudinal study. Patients were recruited within 12 months of achieving fourth ACR classification criterion for SLE. Data were collected on disease activity, damage, SLE-specific drug exposure, cardiovascular risk factors, antiphospholipid syndrome status and death at every visit. This study ran from 1 January 2005 to 31 December 2017. Descriptive statistics were used to analyse mortality and development of new damage. Poisson regression was used to examine potential explanatory variables for development of new damage. RESULTS: A total of 273 SLE patients were recruited with total follow-up of 1767 patient-years (median 73.4 months). There were 6348 assessments with disease activity scores available for analysis. During follow-up, 13 deaths and 114 new damage items (in 83 patients) occurred. The incidence rate for development of damage was higher in the first 3 years before stabilizing at a lower rate. Overall rate for damage accrual was 61.1 per 1000 person-years (95% CI: 50.6, 73.8). Analysis showed that active disease scores according to BILAG-2004 index (systems scores of A or B, counts of systems with A and BILAG-2004 numerical score) were associated with development of new damage. Low disease activity (LDA) states [BILAG-2004 LDA and BILAG Systems Tally (BST) persistent LDA] were inversely associated with development of damage. CONCLUSIONS: BILAG-2004 index is associated with new damage. BILAG-2004 LDA and BST persistent LDA can be considered as treatment targets.

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.

Trivariate mover-stayer counting process models for investigating joint damage in psoriatic arthritis.

In psoriatic arthritis, many patients do not develop permanent joint damage even after a prolonged follow-up. This has led several authors to consider the possibility of a subpopulation of stayers (those who do not have the propensity to experience the event of interest), as opposed to assuming the entire population consist of movers (those who have the propensity to experience the event of interest). In addition, it is recognised that the damaged joints process may act very differently across different joint areas, particularly the hands, feet and large joints. From a clinical perspective, interest lies in identifying possible relationships between the damaged joints processes in these joint areas for the movers and estimating the proportion of stayers in these joint areas, if they exist. For this purpose, this paper proposes a novel trivariate mover-stayer model consisting of mover-stayer truncated negative binomial margins, and patient-level dynamic covariates and random effects in the models for the movers and stayers, respectively. The model is then extended to have a two-level mover-stayer structure for its margins so that the nature of the stayer property can be investigated. A particularly attractive feature of the proposed models is that only an optimisation routine is required in their model fitting procedures. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Dirichlet negative multinomial regression for overdispersed correlated count data.

A generic random effects formulation for the Dirichlet negative multinomial distribution is developed together with a convenient regression parameterization. A simulation study indicates that, even when somewhat misspecified, regression models based on the Dirichlet negative multinomial distribution have smaller median absolute error than generalized estimating equations, with a particularly pronounced improvement when correlation between observations in a cluster is high. Estimation of explanatory variable effects and sources of variation is illustrated for a study of clinical trial recruitment.

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.

A multistate model for events defined by prolonged observation.

Time-to-event and similar analyses can be problematic if the event of interest is operationally defined by some condition being true for a prolonged period of time. A particular example of this, remission in psoriatic arthritis, is considered in detail for illustration. A 3-state model is proposed for characterizing the transition rates into and out of remission. Remission is linked to an initial and subsequent state for the purpose of introducing the condition that remission must be of some duration to be clinically meaningful. The model is compared with alternative approaches that have been used in such situations. These involve 2-state models where the duration of remission is allowed for through different definitions for the time of entry into remission. Both definitions are linked to prolonged observation of a particular clinical state.

The BILAG2004-Pregnancy index is reliable for assessment of disease activity in pregnant SLE patients.

OBJECTIVE: To assess the inter-rater reliability of the BILAG2004-Pregnancy index for assessment of SLE disease activity in pregnancy. METHODS: Pregnant SLE patients were recruited from four centres and assessed separately by two raters/physicians in routine clinical practice. Disease activity was determined using the BILAG2004-Pregnancy index. Reliability was assessed using level of agreement, κ-statistics and analysis of disagreement. Major disagreement was defined as a score difference of A and C/D/E or B and D/E between the two raters, and minor disagreement was a score difference of A and B or B and C between raters. RESULTS: A total of 30 patients (63.3% Caucasian, 13.3% Afro-Caribbean, 16.7% South Asian) were recruited. The majority of patients had low-level disease activity according to the local rater's assessment, and there was no grade A activity, with grade B activity present in the following systems: mucocutaneous (nine patients), musculoskeletal (two patients), cardiorespiratory (one patient) and renal (one patient). The distribution of disease activity was similar to the external rater's assessment. Good levels of agreement (>70%) were achieved in all systems. κ-statistics were not appropriate for use in the gastrointestinal, ophthalmic, constitutional and neuropsychiatric systems, as there was minimal variation between patients but good levels of agreement otherwise. There were three major disagreements (0.1 per patient, all differences between B and D/E) and five minor disagreements (0.17 per patient). CONCLUSION: The BILAG2004-Pregnancy index is reliable for assessment of disease activity in pregnant SLE patients.

The BILAG-2004 systems tally--a novel way of representing the BILAG-2004 index scores longitudinally.

OBJECTIVE: This was an exploratory analysis to develop a new way of representing BILAG-2004 system scores longitudinally that would be clinically meaningful and easier to analyse in comparison with multiple categorical variables. METHODS: Data from a multicentre longitudinal study of SLE patients (the BILAG-2004 index and therapy collected at every visit) were used. External responsiveness analysis of the index suggested the possibility of using counts of systems with specified transitions in scores as a basis to analyse the system scores. Exploratory analyses with multinomial logistic regression were used to examine the appropriateness of this new method of analysing BILAG-2004 system scores. Receiver operating characteristic (ROC) curve analysis was used to assess the performance of this approach. RESULTS: There were 1414 observations from 347 patients. A novel method was devised based on counts of systems with defined transitions in score (BILAG-2004 systems tally, BST). It has six components (systems with major deterioration, systems with minor deterioration, systems with persistent significant activity, systems with major improvement, systems with minor improvement and systems with persistent minimal or no activity). This was further simplified (simplified BST, sBST) into three components (systems with active/worsening disease, systems with improving disease and systems with persistent minimal or no activity). Both versions had expected associations with change in therapy. ROC curve analyses demonstrated that both versions had similar good performance characteristics (areas under the curve >0.80) in predicting increase in therapy. CONCLUSION: The BST and sBST provide alternative approaches to representing BILAG-2004 disease activity longitudinally. Further validation of their use is required.

Comparison of Responsiveness of British Isles Lupus Assessment Group 2004 Index, Systemic Lupus Erythematosus Disease Activity Index 2000, and British Isles Lupus Assessment Group 2004 Systems Tally.

OBJECTIVE: To compare the responsiveness of the British Isles Lupus Assessment Group 2004 index (BILAG-2004) and the Systemic Lupus Erythematosus Disease Activity Index 2000 (SLEDAI-2K) disease activity indices and to determine whether there was any added value in combining BILAG-2004, BILAG-2004 system tally (BST), or simplified BST (sBST) with SLEDAI-2K. METHODS: This was a multicenter longitudinal study of SLE patients. Data were collected on BILAG-2004, SLEDAI-2K, and therapy on consecutive assessments in routine practice. The external responsiveness of the indices was assessed by determining the relationship between change in disease activity and change in therapy between 2 consecutive visits. Comparison of indices and their derivatives was performed by assessing the main effects of the indices using logistic regression. Receiver operating characteristic curves analysis was used to describe the performance of these indices individually and in various combinations, and comparisons of area under the curve were performed. RESULTS: There were 1,414 observations from 347 patients. Both BILAG-2004 and SLEDAI-2K maintained an independent relationship with change in therapy when compared. There was some improvement in responsiveness when continuous SLEDAI-2K variables (change in score and score of previous visit) were combined with BILAG-2004 system scores. Dichotomization of BILAG-2004 or SLEDAI-2K resulted in poorer performance. BST and sBST had similar responsiveness as the combination of SLEDAI-2K variables and BILAG-2004 system scores. There was little benefit in combining SLEDAI-2K with BST or sBST. CONCLUSION: The BILAG-2004 index had comparable responsiveness to SLEDAI-2K. There was some benefit in combining both indices. Dichotomization of BILAG-2004 and SLEDAI-2K leads to suboptimal performance. BST and sBST performed well on their own; sBST is recommended for its simplicity and clinical meaningfulness.

Inflammation in an individual joint predicts damage to that joint in psoriatic arthritis.

OBJECTIVE: The authors have previously reported on the relationship between activity and subsequent damage at the patient level for patients with psoriatic arthritis (PsA). The aim of this study was to identify key predictors of damage to individual joints in the hands and feet of patients with PsA, in particular those that capture previous activity. METHODS: Data from patients followed prospectively at the University of Toronto PsA clinic between 1978 and 2006 were available for analysis. Logistic regression was used to relate the probability of a joint developing damage, within a specified time interval after the most recent clinic visit, to potential predictor variables. The predictor variables considered encompassed the history of disease activity of the joint and elsewhere, previous damage and the timing of clinical assessments. RESULTS: 511 patients with no hand damage at clinic entry and 552 patients with no foot damage at clinic entry were included in the analysis of the hand and foot joints, respectively. The analysis of the hand and foot joints demonstrated that the activity (tenderness and/or swelling) history of the specific joint is associated with subsequent damage. For the joints of the feet, activity observations elsewhere in the same foot, and in particular the same toe, were also shown to be associated with subsequent damage. CONCLUSIONS: Both joint tenderness and swelling are important predictors of joint damage in PsA.

The use of Systemic Lupus Erythematosus Disease Activity Index-2000 to define active disease and minimal clinically meaningful change based on data from a large cohort of systemic lupus erythematosus patients.

OBJECTIVES: To examine SLEDAI-2000 cut-off scores for definition of active SLE and to determine the sensitivity to change of SLEDAI-2000 for the assessment of SLE disease activity and minimal clinically meaningful changes in score. METHODS: Data from two multi-centre studies were used in the analysis: in a cross-sectional and a longitudinal fashion. At every assessment, data were collected on SLEDAI-2000 and treatment. The cross-sectional analysis with receiver operating characteristic (ROC) curves was used to examine the appropriate SLEDAI-2000 score to define active disease and increase in therapy was the reference standard. In the longitudinal analysis, sensitivity to change of SLEDAI-2000 was assessed with multinomial logistic regression. ROC curves analysis was used to examine possible cut-points in score changes associated with change in therapy, and mean changes were estimated. RESULTS: In the cross-sectional analysis, the most appropriate cut-off scores for active disease were 3 or 4. In the longitudinal analysis, the best model for predicting treatment increase was with the change in SLEDAI-2000 score and the score from the previous visit as continuous variables. The use of cut-points was less predictive of treatment change than the use of continuous score. The mean difference in the change in SLEDAI-2000 scores, adjusted for prior score, between patients with treatment increase and those without was 2.64 (95% CI 2.16, 3.14). CONCLUSIONS: An appropriate SLEDAI-2000 score to define active disease is 3 or 4. SLEDAI-2000 index is sensitive to change. The use of SLEDAI-2000 as a continuous outcome is recommended for comparative purposes.

Intermittent observation of time-dependent explanatory variables: a multistate modelling approach.

Motivated by investigations of factors related to various patient-reported outcome measures in psoriatic arthritis patients, after controlling for the effect of disease activity on these outcomes, we outline an approach for dealing with a rapidly fluctuating explanatory variable in a multistate model. On the basis of a representation of this variable as an ordinal classification, we suggest the use of an expanded multistate model. We examine the bias in estimating effects associated with other variables via simulation for different modelling choices. We present an analysis of a motivating data set on physical functional disability in psoriatic arthritis patients.

Bias in 2-part mixed models for longitudinal semicontinuous data.

Semicontinuous data in the form of a mixture of zeros and continuously distributed positive values frequently arise in biomedical research. Two-part mixed models with correlated random effects are an attractive approach to characterize the complex structure of longitudinal semicontinuous data. In practice, however, an independence assumption about random effects in these models may often be made for convenience and computational feasibility. In this article, we show that bias can be induced for regression coefficients when random effects are truly correlated but misspecified as independent in a 2-part mixed model. Paralleling work on bias under nonignorable missingness within a shared parameter model, we derive and investigate the asymptotic bias in selected settings for misspecified 2-part mixed models. The performance of these models in practice is further evaluated using Monte Carlo simulations. Additionally, the potential bias is investigated when artificial zeros, due to left censoring from some detection or measuring limit, are incorporated. To illustrate, we fit different 2-part mixed models to the data from the University of Toronto Psoriatic Arthritis Clinic, the aim being to examine whether there are differential effects of disease activity and damage on physical functioning as measured by the health assessment questionnaire scores over the course of psoriatic arthritis. Some practical issues on variance component estimation revealed through this data analysis are considered.

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.

Exploring the existence of a stayer population with mover-stayer counting process models: application to joint damage in psoriatic arthritis.

Many psoriatic arthritis patients do not progress to permanent joint damage in any of the 28 hand joints, even under prolonged follow-up. This has led several researchers to fit models that estimate the proportion of stayers (those who do not have the propensity to experience the event of interest) and to characterize the rate of developing damaged joints in the movers (those who have the propensity to experience the event of interest). However, when fitted to the same data, the paper demonstrates that the choice of model for the movers can lead to widely varying conclusions on a stayer population, thus implying that, if interest lies in a stayer population, a single analysis should not generally be adopted. The aim of the paper is to provide greater understanding regarding estimation of a stayer population by comparing the inferences, performance and features of multiple fitted models to real and simulated data sets. The models for the movers are based on Poisson processes with patient level random effects and/or dynamic covariates, which are used to induce within-patient correlation, and observation level random effects are used to account for time varying unobserved heterogeneity. The gamma, inverse Gaussian and compound Poisson distributions are considered for the random effects.

Study design.

A brief survey is provided of common designs for medical studies and important issues in their implementation. The designs discussed include those for laboratory studies, clinical trials, cohort studies, case-control and related studies, and diagnostic studies.

A corrected formulation for marginal inference derived from two-part mixed models for longitudinal semi-continuous data.

For semi-continuous data which are a mixture of true zeros and continuously distributed positive values, the use of two-part mixed models provides a convenient modelling framework. However, deriving population-averaged (marginal) effects from such models is not always straightforward. Su et al. presented a model that provided convenient estimation of marginal effects for the logistic component of the two-part model but the specification of marginal effects for the continuous part of the model presented in that paper was based on an incorrect formulation. We present a corrected formulation and additionally explore the use of the two-part model for inferences on the overall marginal mean, which may be of more practical relevance in our application and more generally.

On Modelling Minimal Disease Activity.

OBJECTIVE: To explore methods for statistical modelling of minimal disease activity (MDA) based on data from intermittent clinic visits. METHODS: The analysis was based on a 2-state model. Comparisons were made between analyses based on "complete case" data from visits at which MDA status was known, and the use of hidden model methodology that incorporated information from visits at which only some MDA defining criteria could be established. Analyses were based on an observational psoriatic arthritis cohort. RESULTS: With data from 856 patients and 7,024 clinic visits, analysis was based on virtually all visits, although only 62.6% provided enough information to determine MDA status. Estimated mean times for an episode of MDA varied from 4.18 years to 3.10 years, with smaller estimates derived from the hidden 2-state model analysis. Over a 10-year period, the estimated expected times spent in MDA episodes of longer than 1 year was 3.90 to 4.22, and the probability of having such an MDA episode was estimated to be 0.85 to 0.91, with longer times and greater probabilities seen with the hidden 2-state model analysis. CONCLUSION: A 2-state model provides a useful framework for the analysis of MDA. Use of data from visits at which MDA status can not be determined provide more precision, and notable differences are seen in estimated quantities related to MDA episodes based on complete case and hidden 2-state model analyses. The possibility of bias, as well as loss of precision, should be recognized when complete case analyses are used.