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ABSTRACT: 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.
Lifetime Data Analysis 12/2012; · 0.92 Impact Factor
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Chee-Seng Yee,
Caroline Gordon,
David A Isenberg,
Bridget Griffiths,
Lee-Suan Teh,
Ian N Bruce,
Yasmeen Ahmad,
Anisur Rahman,
Athiveeraramapandian Prabu,
Mohammed Akil,
Neil McHugh,
Christopher Edwards,
David D'Cruz,
Munther A Khamashta, Vernon T Farewell
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ABSTRACT: 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.
Rheumatology (Oxford, England) 08/2012; 51(11):2099-105. · 4.24 Impact Factor
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ABSTRACT: 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. Copyright © 2012 John Wiley & Sons, Ltd.
Statistics in Medicine 07/2012; · 1.88 Impact Factor
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ABSTRACT: 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.
Rheumatology (Oxford, England) 07/2012; 51(10):1877-80. · 4.24 Impact Factor
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ABSTRACT: We examined the association between responses on a screening questionnaire and objective performance on a computer-administered test of cognitive abilities in systemic lupus erythematosus (SLE).
The Cognitive Symptom Inventory (CSI) and Hospital Anxiety and Depression Scales (HADS) questionnaires were compared in patients with SLE or rheumatoid arthritis (RA). The Automated Neuropsychological Assessment Metrics (ANAM) was used to evaluate cognitive performance in patients with SLE. Efficiency of performance was measured by "throughput" (number of correct responses per minute) and "inverse efficiency" (response speed/proportion of correct responses). Linear regression was applied to log-transformed CSI scores to examine their associations with ANAM scores and other factors.
Patients with SLE (n = 68) or RA (n = 33) were similar in age, sex, ethnicity, and education status (p > 0.05). Patients with SLE had higher total CSI scores (33.6 ± 10.5 vs 29.4 ± 6.8, respectively; p = 0.041) and attention/concentration subscale CSI scores (15.7 ± 5.3 vs 13.3 ± 3.4; p = 0.016) compared to patients with RA. In patients with SLE there was a positive association between CSI scores and neuropsychiatric (NP) events at the time of testing (p = 0.0006), HADS anxiety (p < 0.0001), and depression (p < 0.0001) scores. After adjustment for age, education, disease duration, and NP events at the time of testing, there was no significant association (p > 0.05) between ANAM and CSI scores in patients with SLE. The results were similar using either "throughput" or "inverse efficiency" or the number of impaired ANAM subscales after adjustment for simple reaction time.
The CSI self-report questionnaire of cognitive symptoms does not reliably screen for efficiency of cognitive processing in patients with SLE. Rather, cognitive complaints reported in the CSI are influenced by the presence of anxiety and depression.
The Journal of Rheumatology 06/2012; 39(7):1371-7. · 3.69 Impact Factor
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ABSTRACT: To test the bidirectional hypothesis that depressive symptoms influence changes in pain over time, and pain influences changes in depressive symptoms.
A total of 394 patients attending the University of Toronto Psoriatic Arthritis clinic were followed over a mean period of 7.5 years with annual assessments, including number of swollen joints (SJC), Health Assessment Questionnaire (HAQ), and the Medical Outcomes Survey Short Form 36 (SF-36). Linear mixed-effects models were used to examine the cross- and lagged associations between the changes in HAQ pain and in the SF-36 mental component summary (MCS) score, adjusting for SJC and other covariates.
The strongest predictors of changes in pain, SJC, and depressive symptoms between visits were scores of the corresponding variables at the previous visit, with standardized regression coefficients exceeding 0.75 in absolute value. There was, however, evidence of a small, but consequential, bidirectional relationship (i.e., standardized regression coefficients <0.3) between depressive symptoms and pain. Both previous MCS scores and change in MCS scores were associated with change in pain between visits; conversely, previous pain scores and change in pain scores were associated with change in depressive symptoms between visits.
Even though cross-variable associations between pain and depressive symptoms exist, changes in pain and depressive symptoms appear to be strongly driven by their measurements at the previous visit. To optimize patient outcomes, a clinical approach that assesses and treats clinically significant depressive symptoms, as well as pain, is required.
Arthritis care & research. 01/2012; 64(5):758-65.
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ABSTRACT: 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.
Statistics in Medicine 12/2011; 30(30):3520-31. · 1.88 Impact Factor
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ABSTRACT: In psoriatic arthritis, permanent joint damage characterizes disease progression and represents a major debilitating aspect of the disease. Understanding the process of joint damage will assist in the treatment and disease management of patients. Multistate models provide a means to examine patterns of disease, such as symmetric joint damage. Additionally, the link between damage and the dynamic course of disease activity (represented by joint swelling and stress pain) at both the individual joint level and otherwise can be represented within a correlated multistate model framework. Correlation is reflected through the use of random effects for progressive models and robust variance estimation for non-progressive models. Such analyses, undertaken with data from a large psoriatic arthritis cohort, are discussed and the extent to which they permit causal reasoning is considered. For this, emphasis is given to the use of the Bradford Hill criteria for causation in observational studies and the concept of local (in)dependence to capture the dynamic nature of the relationships.
Applied Statistics 11/2011; 60(5):675-699. · 0.83 Impact Factor
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ABSTRACT: Two-part models are an attractive approach for analysing longitudinal semicontinuous data consisting of a mixture of true zeros and continuously distributed positive values. When the population-averaged (marginal) covariate effects are of interest, two-part models that provide straightforward interpretation of the marginal effects are desirable. Presently, the only available approaches for fitting two-part marginal models to longitudinal semicontinuous data are computationally difficult to implement. Therefore, there exists a need to develop two-part marginal models that can be easily implemented in practice. We propose a fully likelihood-based two-part marginal model that satisfies this need by using the bridge distribution for the random effect in the binary part of an underlying two-part mixed model; and its maximum likelihood estimation can be routinely implemented via standard statistical software such as the SAS NLMIXED procedure. We illustrate the usage of this new model by investigating the marginal effects of pre-specified genetic markers on physical functioning, as measured by the Health Assessment Questionnaire, in a cohort of psoriatic arthritis patients from the University of Toronto Psoriatic Arthritis Clinic. An added benefit of our proposed marginal model when compared to a two-part mixed model is the robustness in regression parameter estimation when departure from the true random effects structure occurs. This is demonstrated through simulation.
Statistical Methods in Medical Research 08/2011; · 2.44 Impact Factor
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ABSTRACT: 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.
Biostatistics 01/2011; 12(1):102-11. · 2.14 Impact Factor
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Chee-Seng Yee, Vernon T Farewell,
David A Isenberg,
Bridget Griffiths,
Lee-Suan Teh,
Ian N Bruce,
Yasmeen Ahmad,
Anisur Rahman,
Athiveeraramapandian Prabu,
Mohammed Akil,
Neil McHugh,
Christopher Edwards,
David D'Cruz,
Munther A Khamashta,
Caroline Gordon
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ABSTRACT: 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.
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.
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).
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.
Rheumatology (Oxford, England) 01/2011; 50(5):982-8. · 4.24 Impact Factor
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ABSTRACT: To develop a recommended measure of response for use in psoriatic arthritis (PsA) clinical trials and observational cohort studies reflecting joint involvement.
Previously, we used data from phase III randomized placebo-controlled trials of anti-tumor necrosis factor (TNF) agents to determine models, based primarily on statistical considerations but with some clinical input when necessary, that best distinguish drug-treated from placebo-treated patients. For the same data, we examine response criteria currently used for PsA and logistic regression models based on the individual components of these response criteria. Comparison with our previously developed models, based primarily on statistical consideration, is made.
A simplified score, the PsA Joint Activity Index (PsAJAI), based on components of the ACR30, performed better than the ACR20 and PsARC, and comparable to our previously developed models. The PsAJAI is a weighted sum of 30% improvement in core measures with weights of 2 given to the joint count measure, the C-reactive protein laboratory measure, and the physician global assessment of disease activity measure. Weights of 1 should be given to the remaining 30% improvement measures including pain, patient global assessment of disease activity, and the Health Assessment Questionnaire.
We recommend the PsAJAI be used as an outcome measure for assessing joint disease response in PsA clinical trials.
The Journal of Rheumatology 10/2010; 37(12):2559-65. · 3.69 Impact Factor
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ABSTRACT: 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.
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.
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.
Both joint tenderness and swelling are important predictors of joint damage in PsA.
Annals of the rheumatic diseases 10/2010; 70(2):305-8. · 8.11 Impact Factor
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ABSTRACT: To develop statistical models, based on the analysis of data from phase III randomized placebo-controlled trials of tumor necrosis factor-alpha (TNF-alpha) inhibitors over a 24-week period, that may inform the definition of response measures for clinical trials in psoriatic arthritis (PsA).
Data from phase III randomized controlled trials with anti-TNF agents were used. A training set using baseline and 24-week data from 2 trials was used to derive the models, which were then tested on a dataset using baseline and interim data from the third trial, and baseline and interim data from the first 2 trials. Logistic regression, tree analysis, and factor analysis were considered in the development of the models. Receiver-operating characteristic curves were constructed and area under the curve (AUC) calculated to assess performance of the models.
Two models were derived. One was based on differences between baseline and last-visit values, which identified the current 68 tender joint count (TJC68), baseline and change in C-reactive protein (CRP), and the measure with the highest difference among the patient and physician global assessment of disease activity (GDA), patient assessment of pain and the Health Assessment Questionnaire (HAQ). The second model was based on percentage change from baseline and included TJC68, CRP, physician GDA, patient global assessment of arthritis pain, and HAQ. Both models provided high AUC of at least 0.8 for both the training and testing sets.
Models for discriminating joint disease response patterns in PsA were derived from data from randomized controlled trials. These models can now be used to inform further consideration of response measures for trials.
The Journal of Rheumatology 09/2010; 37(9):1892-7. · 3.69 Impact Factor
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ABSTRACT: To describe the longitudinal course of fatigue in psoriatic arthritis (PsA).
Our study included 390 patients who attended the University of Toronto Psoriatic Arthritis Clinic between 1998 and 2006 and who completed 2 or more administrations of the modified Fatigue Severity Scale (mFSS) at yearly intervals. Clinical data were used that corresponded to visits in which mFSS was administered. We used linear mixed effects models to examine the relationships of disease-related and nondisease-related variables with mFSS scores across multiple clinic visits, and linear regression models to investigate the association between change in mFSS scores (DeltamFSS) and changes in covariates between visits.
Clinical measures of disease activity were related to fatigue over time; however, these relationships disappeared in the context of patient-reported physical disability and pain. Patient-reported measures of physical disability, pain, and psychological distress were most closely related to higher mFSS scores (greater fatigue) across clinic assessments. Fatigue was found to vary over time, at least when assessed at yearly intervals. In general, measures of clinical and functional status at the current visit were more predictive of DeltamFSS in between previous and current visits than change scores in these measures between visits. Comorbid fibromyalgia or hypertension were also associated with greater fatigue across multiple visits and with change in fatigue between visits.
A combination of factors is associated with fatigue in PsA. The full effect of comorbidities on fatigue warrants further study to better understand the effective management of fatigue in PsA.
The Journal of Rheumatology 09/2010; 37(9):1878-84. · 3.69 Impact Factor
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ABSTRACT: To determine the association between folate pathway gene polymorphisms and the effectiveness, toxicity, and drug survival of methotrexate (MTX) in psoriatic arthritis (PsA).
Data were obtained from a longitudinal cohort of PsA patients evaluated according to a standard protocol. Data on duration of drug therapy, dose, side effects, and reasons for discontinuation are systematically recorded. Patients treated with MTX after clinic admission who had > or = 3 swollen joints prior to initiating MTX therapy were selected for evaluation of effectiveness. Response to MTX treatment was assessed at 6 months. Data from all patients treated in the clinic with MTX were used in evaluation of toxicity and drug survival. The following single-nucleotide polymorphisms (SNP) were measured using the Sequenom platform: MTHFR 677C>T (rs1801133), MTHFR 1298A>C (rs1801131), DHFR -473T>C (rs1650697), DHFR 35289A>G (rs1232027), and RFC 80G>A (rs1051266). Fisher's exact test, logistic regression, and Cox proportional hazard analyses were used to determine association.
Two hundred eighty-one patients were identified from the database. All patients were included in the analysis for side effects and drug survival, and 119 patients were included in the effectiveness analysis. The minor A allele of DHFR gene at +35289 was the only SNP demonstrating association with response to MTX therapy (OR 2.99, p = 0.02). Patients homozygous for the minor allele of MTHFR 677C/T (677TT) had more liver toxicity (Fisher exact test, p = 0.04).
Polymorphisms of the DHFR gene may be associated with MTX efficacy. MTHFR 677TT may have a relationship with MTX-induced liver toxicity in PsA.
The Journal of Rheumatology 07/2010; 37(7):1508-12. · 3.69 Impact Factor
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ABSTRACT: With specific reference to studies of growth hormone therapies, this chapter re-examines some basic principles in clinical research and considers some of the more complex aspects of trial design. The statistical structure which underpins trial design is characterized with specific attention given to samples size, subgroup analyses, multicentre trials and the role and implementation of randomization. Topics related to outcomes in studies of growth hormone therapy are discussed, including the possible value of surrogate responses, longitudinal outcomes and their analysis, and multiple outcomes. Additional design issues addressed are multiarmed trials, factorial designs and study monitoring. Brief comments are offered on the interpretation of negative trials and on non-inferiority trials.
Endocrine development 01/2010; 18:1-22.
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ABSTRACT: To evaluate changes in symptoms, spinal mobility, and radiographic features in patients with axial psoriatic arthritis (AxPsA).
Patients with AxPsA were identified from the University of Toronto Psoriatic Arthritis clinic database. Axial symptoms, metrology, and radiographic features at study entry were compared to 5-year and 10-year followup assessments. Data were analyzed using continuity adjusted McNemar's test, an exact binomial test, or logistic regression.
Of 297 patients (mean age 42.5 yrs, PsA duration 8 yrs) in the study, 56% had axial symptoms, 43% had radiographic evidence of sacroiliitis, and 13% had syndesmophytes at entry. The number of patients with neck/back pain, neck/back stiffness, and clinical sacroiliitis declined significantly at both 5- and 10-year followup periods. There was a significant increase in the number of patients with restricted cervical spinal mobility at both 5- and 10-year visits and significant reduction in lateral flexion at both timepoints. At 5 (10) years, of those without sacroiliitis at baseline, 36.6% (51.7%) developed at least grade 2 sacroiliitis; 46.5% (52.0%) of those who presented with grade 2 progressed to a higher grade; and 15.6% (25.0%) with grade 3 progressed to grade 4 sacroiliitis. Of the patients without cervical/thoracic/lumbar syndesmophytes at study entry, 11%/16%/14% (14%/21%/20%) developed syndesmophytes in these regions at 5 (10) year followup. Similar results were obtained when analyses were restricted to patients satisfying radiographic criteria alone.
Over a 10-year period, patients with AxPsA had improvement in neck and back pain, but lateral spinal flexion and cervical mobility deteriorated.
The Journal of Rheumatology 11/2009; 36(12):2744-50. · 3.69 Impact Factor
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ABSTRACT: Joint damage in psoriatic arthritis can be measured by clinical and radiological methods, the former being done more frequently during longitudinal follow-up of patients. Motivated by the need to compare findings based on the different methods with different observation patterns, we consider longitudinal data where the outcome variable is a cumulative total of counts that can be unobserved when other, informative, explanatory variables are recorded. We demonstrate how to calculate the likelihood for such data when it is assumed that the increment in the cumulative total follows a discrete distribution with a location parameter that depends on a linear function of explanatory variables. An approach to the incorporation of informative observation is suggested. We present analyses based on an observational database from a psoriatic arthritis clinic. Although the use of the new statistical methodology has relatively little effect in this example, simulation studies indicate that the method can provide substantial improvements in bias and coverage in some situations where there is an important time varying explanatory variable.
Applied Statistics 07/2009; 58(3):369-382. · 0.83 Impact Factor
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Statistical Methods in Medical Research 03/2009; 18(1):107-8; discussion 108-9. · 2.44 Impact Factor
