Random effects models for complex designs.

Plaid designs are characterised by having one set of treatments applied to rows and another set of treatments applied to columns. In a 2003 publication, Farewell and Herzberg presented an analysis of variance structure for such designs. They presented an example of a study in which medical practitioners, trained in different ways, evaluated a series of videos of patients obtained under a variety of conditions. However, their analysis did not take full account of all error terms. In this paper, a more comprehensive analysis of this study is presented, informed by the recognition that the study can also be regarded as a two-phase design. The development of random effects models is outlined and the potential importance of block-treatment interactions is highlighted. The use of a variety of techniques is shown to lead to a better understanding of the study. Examination of the variance components involved in the expected mean squares is demonstrated to have particular value in identifying appropriate error terms for F-tests derived from an analysis of variance table. A package such as ASReml can also be used provided an appropriate error structure is specified. The methods presented can be applied to the design and analysis of other complex studies in which participants supply multiple measurements under a variety of conditions.

Two-Part and Related Regression Models for Longitudinal Data.

Statistical models that involve a two-part mixture distribution are applicable in a variety of situations. Frequently, the two parts are a model for the binary response variable and a model for the outcome variable that is conditioned on the binary response. Two common examples are zero-inflated or hurdle models for count data and two-part models for semicontinuous data. Recently, there has been particular interest in the use of these models for the analysis of repeated measures of an outcome variable over time. The aim of this review is to consider motivations for the use of such models in this context and to highlight the central issues that arise with their use. We examine two-part models for semicontinuous and zero-heavy count data, and we also consider models for count data with a two-part random effects distribution.

Differential major histocompatibility complex class I chain-related A allele associations with skin and joint manifestations of psoriatic disease.

About 30% of patients with psoriasis have psoriatic arthritis (PsA), an inflammatory arthritis that can affect both axial and peripheral joints. Major histocompatibility complex class I chain-related A (MICA) alleles have previously been shown to be associated with PsA; however it is unclear whether there is a differential association of MICA alleles with skin and joint manifestations of PsA. Here, we describe a case-control study that aims to validate previously reported MICA allele associations with PsA and determine whether MICA alleles differentiate patients with PsA from those with psoriasis without PsA. Two hundred forty-nine unrelated Caucasian PsA patients, 243 psoriasis patients without arthritis, and 248 healthy controls were genotyped for 55 MICA alleles using PCR-SSP, and for human leucocyte antigen (HLA)-B and HLA-C alleles by PCR-SSO reverse line blot. Allele frequencies were calculated and logistic regressions were performed, adjusting for HLA-B and HLA-C alleles previously shown to be associated with psoriasis and/or PsA. Several MICA alleles were associated with psoriatic disease, PsA, and psoriasis compared with controls, and PsA compared with psoriasis in univariate analyses. Haplotype analysis showed evidence of strong linkage disequilibrium (LD) between PsA and psoriasis risk alleles of HLA-C, HLA-B, and MICA. After adjusting for significant HLA-B and HLA-C alleles in multivariate analyses, MICA*016 remained significantly associated with psoriasis [odds ratio (OR) = 5.5, P = 0.008]. MICA*00801 homozygosity was associated with susceptibility to PsA when compared with patients with psoriasis alone (OR = 2.26, P = 0.009). We conclude that most MICA allele associations with psoriasis and PsA are dependent on LD with HLA-B and HLA-C risk alleles. Independent of HLA, only MICA*016 influences the risk of developing psoriasis without arthritis, and homozygosity for MICA*00801 increases the risk of developing PsA in patients with psoriasis.

One-stage parametric meta-analysis of time-to-event outcomes.

Methodology for the meta-analysis of individual patient data with survival end-points is proposed. Motivated by questions about the reliance on hazard ratios as summary measures of treatment effects, a parametric approach is considered and percentile ratios are introduced as an alternative to hazard ratios. The generalized log-gamma model, which includes many common time-to-event distributions as special cases, is discussed in detail. Likelihood inference for percentile ratios is outlined. The proposed methodology is used for a meta-analysis of glioma data that was one of the studies which motivated this work. A simulation study exploring the validity of the proposed methodology is available electronically.

Multi-state Markov models for disease progression in the presence of informative examination times: an application to hepatitis C.

In many chronic diseases it is important to understand the rate at which patients progress from infection through a series of defined disease states to a clinical outcome, e.g. cirrhosis in hepatitis C virus (HCV)-infected individuals or AIDS in HIV-infected individuals. Typically data are obtained from longitudinal studies, which often are observational in nature, and where disease state is observed only at selected examinations throughout follow-up. Transition times between disease states are therefore interval censored. Multi-state Markov models are commonly used to analyze such data, but rely on the assumption that the examination times are non-informative, and hence the examination process is ignorable in a likelihood-based analysis. In this paper we develop a Markov model that relaxes this assumption through the premise that the examination process is ignorable only after conditioning on a more regularly observed auxiliary variable. This situation arises in a study of HCV disease progression, where liver biopsies (the examinations) are sparse, irregular, and potentially informative with respect to the transition times. We use additional information on liver function tests (LFTs), commonly collected throughout follow-up, to inform current disease state and to assume an ignorable examination process. The model developed has a similar structure to a hidden Markov model and accommodates both the series of LFT measurements and the partially latent series of disease states. We show through simulation how this model compares with the commonly used ignorable Markov model, and a Markov model that assumes the examination process is non-ignorable.

Development and initial validation of a screening questionnaire for psoriatic arthritis: the Toronto Psoriatic Arthritis Screen (ToPAS).

OBJECTIVE: To develop and validate a psoriatic arthritis (PsA) screening questionnaire: the Toronto Psoriatic Arthritis Screen (ToPAS). METHODS: The ToPAS was developed through review of items seen in patients with PsA and evaluation by patients with PsA and patients with other rheumatological conditions, and was administered to consecutive consenting patients attending five clinics: PsA, psoriasis, general dermatology, general rheumatology (excluding PsA patients) and family medicine. All patients were assessed by a rheumatologist according to a standard protocol. A three-step analysis strategy was adopted: a stepwise logistic regression to identify the questions most important in discriminating between those with and without PsA; a logistic model was fitted to three clinically relevant domains for PsA: skin, joints and nails; and a simpler weighting of each of the domains used in step 2. Receiver operating characteristic (ROC) curves were obtained based on these various models. RESULTS: In all, there were 134 patients from the PsA clinic, 123 with psoriasis, 118 from dermatology, 135 from rheumatology and 178 from family medicine. A simplified discriminatory score based on the skin, joint and nail domains gave results comparable to other methods with an observed overall sensitivity and specificity, based on a single cut point, of 86.8% and 93.1%. When the patients with PsA were compared with each of the other four patient groups individually, the sensitivity and specificity of the ToPAS were: psoriasis 89.1%, 86.3%; dermatology 91.9%, 95.2%; rheumatology 92.6%, 85.7%; and family medicine 90.4%, 100%. CONCLUSION: Our simplified index is very good at classifying those who are not diagnosed with PsA and those who are diagnosed with PsA.

Cardiovascular morbidity in psoriatic arthritis.

BACKGROUND: Increasing evidence for cardiovascular mortality among patients with psoriasis and psoriatic arthritis (PsA) has accumulated, together with evidence for increased prevalence of risk factors for cardiovascular disease (CVD). OBJECTIVES: To describe cardiovascular morbidity in PsA, determine its prevalence and identify risk factors for its development. METHODS: At the University of Toronto, patients were followed up prospectively according to a standard protocol, including disease-related features and comorbidities. Patients with CVD, including myocardial infarction (MI), angina, hypertension and cerebrovascular accident (CVA), were identified. The prevalence of CVD morbidities in these patients was compared with data from the Canadian Community Health Survey through standardised prevalence ratios (SPRs). Cox relative risk regression analysis was used to analyse risk factors. RESULTS: At the time of analysis, 648 patients were registered in the database. After clinic entry, 122 developed hypertension, 38 had an MI and 5, 21 and 11 had CVA, angina and congestive heart failure (CHF), respectively. 155 patients had at least one of these conditions. The SPRs for MI (2.57; 95% CI 1.73 to 3.80), angina (1.97; 95% CI 1.24 to 3.12) and hypertension (1.90; 95% CI 1.59 to 2.27) were statistically significant, whereas the SPRs for CHF (1.19; 95% CI 0.50 to 2.86) and CVA (0.91; 95% CI 0.34 to 2.43) were not. Factors associated with CVD included diabetes, hyperlipidaemia and high Psoriasis Area and Severity Index scores. CONCLUSION: Patients with PsA are at increased risk of cardiovascular morbidities compared with the general population. In addition to known risk factors for CVD, severe psoriasis is an important predictor in patients with PsA.

Occurrence and correlates of fatigue in psoriatic arthritis.

OBJECTIVE: To determine the relationship between fatigue and disease-related and psychosocial variables in psoriatic arthritis (PsA). METHOD: 499 patients attending the University of Toronto PsA Clinic were administered the modified fatigue severity scale (mFSS). At the time of mFSS administration, clinical and laboratory measures of disease activity and damage were recorded. Linear regression models were used to examine the cross-sectional relationship between disease-related and psychosocial variables and mFSS scores. RESULTS: At least moderate fatigue occurred in 49.5% of patients and severe fatigue in 28.7%. Univariately the vast majority of variables were significantly associated with mFSS scores. The final multivariate model was composed of female sex, the medical outcome survey short form 36 (SF-36) pain and mental health scales, the number of fibromyalgia tender points, the health assessment questionnaire (HAQ) and "ever used" methotrexate, and explained 54.5% of the variation in mFSS scores. The SF-36 mental health scale played the largest role in the multivariate model, uniquely accounting for 6.6% of the variation in the fatigue severity scale. The disease-related factors significant at the univariate level did not achieve statistical significance in the context of HAQ and pain measures. CONCLUSION: Fatigue is a common symptom in PsA, and is associated, in a multivariate model, with pain, female sex, physical functional disability, medication status and psychological distress. Fatigue appears to provide some information that does not overlap with the core set of outcome domains in PsA.

Dynamic modelling in a study of surgical error management.

We demonstrate the use of dynamic longitudinal models to investigate error management in cardiac surgery. Case study data were collected from a multicentre study of the neonatal arterial switch operation (ASO). Information on two types of negative events, or 'errors', observed during surgery, major and minor events, was extracted from case studies. Each event was judged to be recovered from (compensated) or not (uncompensated). The aim of the study was to model compensation given the occurrence of past events within a case. Two models were developed, one for the probability of compensating for a major event and a second model for the probability of compensating for a minor event. Analyses based on dynamic logistic regression models suggest that the total number of preceding minor events, irrespective of compensation status, is negatively related with the ability to compensate for major events. The alternative use of random effects models is investigated for comparison purposes.

A multi-state model for joint modelling of terminal and non-terminal events with application to Whitehall II.

Serious coronary heart disease (CHD) is a primary outcome in the Whitehall II study, a large epidemiological study of British civil servants. Both fatal (F) and non-fatal (NF) CHD events are of interest and while essentially complete information is available on F events, the observation of NF events is subject to potentially informative censoring. A multi-state model with an unobserved state is introduced for the joint modelling of F and NF events. Two model-based assumptions ensure identifiability of the model and a parameter is introduced to allow sensitivity analyses concerning the assumption linked to informative censoring. Weibull transition rates, which include dependence on explanatory variables, are used in the analysis of Whitehall II data with a particular focus on the relationship between civil service grade and CHD events.

Clinical and radiological damage in psoriatic arthritis.

BACKGROUND: Psoriatic arthritis may progress to joint damage. Joint damage may be assessed clinically, by identifying deformed, fused, or flail joints, or radiologically, by recording erosions, joint space narrowing, ankylosis, lysis, or surgery. The relation between clinical and radiological damage is unclear. OBJECTIVE: To study the ordering of clinical and radiological damage detection, and the clinical features associated with the type of damage detected first. METHODS: The University of Toronto psoriatic arthritis database was used to relate clinical and radiological damage in the hand joints in 655 patients followed prospectively between 1978 and 2003. Generalised estimating equations were used to fit logistic regression models to identify factors that predict classification of damage by radiographic assessment first. RESULTS: The majority of the joints were not informative, as they either had evidence of damage by both methods at entry, or remained undamaged. Of the remainder, 81% of the joints showed radiological damage first and 19% had clinical damage first. Development of radiological damage first was related to previous detection of swollen joints, and was inversely related to duration of arthritis. CONCLUSIONS: Radiological damage is often detected before clinical damage is observed. Clinical inflammation often precedes the detection of radiological damage.

A statistical analysis of the interrelationships between disease activity in different systems in systemic lupus erythematosus.

OBJECTIVES: To develop models for disease activity in patients with systemic lupus erythematosus (SLE) and to examine the hypothesis that possible subsets exist within the disease, notably renal disease and little else, mucocutaneous and musculoskeletal disease in isolation and more multisystem disease. METHODS: Four hundred and forty patients with SLE were followed for a period of 10 yr. Socio-demographic data were obtained at the first visit with disease activity being recorded at subsequent visits and damage scores at 6-monthly intervals. Prognostic factors for active disease in each of the mucocutaneous, musculoskeletal and renal systems were examined statistically. The results were then validated using data collected over 5 yr on a further 295 SLE patients from a different centre. RESULTS: Logistic regression analyses indicated that for all three systems studied a patient known to have an involvement in that system is more likely to present with active disease in that same system than a patient with no known prior involvement. Patients with a higher frequency of clinic visits with active disease in a system are more likely to represent with active disease than those with fewer visits. The results suggest that renal disease is most likely to occur on its own. Associations between activity in the mucocutaneous and musculoskeletal systems support the suggestion that patients with musculoskeletal and mucocutaneous disease alone represent a possible subset of SLE. None of the associations identified were modified by the medication a patient received. CONCLUSIONS: Previous disease history and involvement of other systems determine a patient's chance of developing further episodes of active disease in SLE.

SARS incubation and quarantine times: when is an exposed individual known to be disease free?

The setting of a quarantine time for an emerging infectious disease will depend on current knowledge concerning incubation times. Methods for the analysis of information on incubation times are investigated with a particular focus on inference regarding a possible maximum incubation time, after which an exposed individual would be known to be disease free. Data from the Hong Kong SARS epidemic are used for illustration. The incorporation of interval-censored data is considered and comparison is made with percentile estimation. Results suggest that a wide class of models for incubation times should be considered because the apparent informativeness of a likelihood depends on the choice and generalizability of a model. There will usually remain a probability of releasing from quarantine some infected individuals and the impact of early release will depend on the size of the epidemic.

Regression analysis of overdispersed correlated count data with subject specific covariates.

A robust likelihood approach for the analysis of overdispersed correlated count data that takes into account cluster varying covariates is proposed. We emphasise two characteristics of the proposed method: That the correlation structure satisfies the constraints on the second moments and that the estimation of the correlation structure guarantees consistent estimates of the regression coefficients. In addition we extend the mean specification to include within- and between-cluster effects. The method is illustrated through the analysis of data from two studies. In the first study, cross-sectional count data from a randomised controlled trial are analysed to evaluate the efficacy of a communication skills training programme. The second study involves longitudinal count data which represent counts of damaged hand joints in patients with psoriatic arthritis. Motivated by this study, we generalize our model to accommodate for a subpopulation of patients who are not susceptible to the development of damaged hand joints.

Association of SEEK1 and psoriatic arthritis in two distinct Canadian populations.

OBJECTIVE: To examine the relationship between SNP +39604 in SEEK1 and psoriatic arthritis (PsA) in two distinct Canadian populations. METHODS: 103 patients with PsA and 105 ethnically matched controls from Newfoundland and 202 patients with PsA and 100 controls from Ontario were studied. Patients and controls were genotyped for SNP +39604 of SEEK1 by time of flight mass spectrometry, using the Sequenom platform. Genomic DNA was amplified by the Dynal RELI SSO HLA-Cw* typing kit for HLA-C typing. RESULTS: The frequency of the minor SEEK1(T) allele in subjects with PsA and controls was 48.5% and 32.4%, respectively (odds ratio (OR) = 2.0; p = 0.017), in the Newfoundland population and 46.5% and 38.0%, respectively (OR = 1.4; p = 0.16), in the Ontario population. Although SEEK1 is associated with PsA, particularly in the Newfoundland population, multivariate analysis showed that SEEK1 does not seem to be a further susceptibility factor if the HLA-Cw*0602 status is already known. No association was noted between SEEK1(T) allele and onset of psoriasis, PsA, or arthritis pattern. CONCLUSION: SEEK1 is associated with PsA in the Newfoundland founder population. This association is probably due to linkage disequilibrium between SEEK1 and HLA-Cw*0602 in this population.

A risk-adjusted Sets method for monitoring adverse medical outcomes.

The Sets method has been advocated in previous work as a method for monitoring adverse medical outcomes where the adverse event rate is low. Here, a risk-adjusted version of the refined Sets method is presented and an example is given to demonstrate its advantage over the unadjusted method. The method is suitable for any risk distribution and does not assume that changes in risk will be small. A graphical representation, referred to as the Grass plot, of the original and risk-adjusted methods is also given.

CARD15: a pleiotropic autoimmune gene that confers susceptibility to psoriatic arthritis.

A recent genomewide scan in psoriatic arthritis (PsA) revealed a susceptibility locus at 16q. This region overlaps CARD15, a susceptibility gene in Crohn disease. The possibility of a common susceptibility gene between PsA and Crohn disease is further supported by epidemiological studies that note an increased incidence of psoriasis in subjects with Crohn. We screened 187 patients with PsA and 136 healthy controls, all from Newfoundland, for the three common, independent sequence variants of CARD15 (R702W, leu1007fsinsC, and G908R), which were detected by polymerase chain reaction by use of allele-specific primers and visualized through gel electrophoresis. In total, 53/187 (28.3%) probands with PsA had at least one variant of the CARD15 gene, compared with 16/136 (11.8%) controls (odds ratio 2.97; 95% confidence interval 1.61-5.47; P=.0005). Allele frequencies of R702W, leu1007fsinsC, and G908R were 10.43%, 3.21%, and 1.61%, respectively, in patients with PsA, compared with 3.31%, 2.57%, and 0.37%, respectively, in the control patients. CARD15 conferred susceptibility to PsA independent of HLA-Cw*0602. Thus, CARD15 represents a pleiotropic autoimmune gene and is the first non-MHC gene to be associated with PsA.

Use of risk-adjusted CUSUM and RSPRT charts for monitoring in medical contexts.

In this paper we discuss the use of charts derived from the sequential probability ratio test (SPRT): the cumulative sum (CUSUM) chart, RSPRT (resetting SPRT), and FIR (fast initial response) CUSUM. The theoretical development of the methods is described and some considerations one might address when designing a chart, explored, including the approximation of average run lengths (ARLs), the importance of detecting improvements in a process as well as detecting deterioration and estimation of the process parameter following a signal. Two examples are used to demonstrate the practical issues of quality control in the medical setting, the first a running example and the second a fully worked example at the end of the paper. The first example relates to 30-day mortality for patients of a single cardiac surgeon over the period 1994-1998, the second to patient deaths in the practice of a single GP, Harold Shipman. The charts' performances relative to each other are shown to be sensitive to the definition of the 'out of control' state of the process being monitored. In light of this, it is stressed that a suitable means by which to compare charts is chosen in any specific application.