Review of methods for handling confounding by cluster and informative cluster size in clustered data.

Clustered data are common in medical research. Typically, one is interested in a regression model for the association between an outcome and covariates. Two complications that can arise when analysing clustered data are informative cluster size (ICS) and confounding by cluster (CBC). ICS and CBC mean that the outcome of a member given its covariates is associated with, respectively, the number of members in the cluster and the covariate values of other members in the cluster. Standard generalised linear mixed models for cluster-specific inference and standard generalised estimating equations for population-average inference assume, in general, the absence of ICS and CBC. Modifications of these approaches have been proposed to account for CBC or ICS. This article is a review of these methods. We express their assumptions in a common format, thus providing greater clarity about the assumptions that methods proposed for handling CBC make about ICS and vice versa, and about when different methods can be used in practice. We report relative efficiencies of methods where available, describe how methods are related, identify a previously unreported equivalence between two key methods, and propose some simple additional methods. Unnecessarily using a method that allows for ICS/CBC has an efficiency cost when ICS and CBC are absent. We review tools for identifying ICS/CBC. A strategy for analysis when CBC and ICS are suspected is demonstrated by examining the association between socio-economic deprivation and preterm neonatal death in Scotland

Methods for observed-cluster inference when cluster size is informative: a review and clarifications.

Clustered data commonly arise in epidemiology. We assume each cluster member has an outcome Y and covariates X. When there are missing data in Y, the distribution of Y given X in all cluster members ("complete clusters") may be different from the distribution just in members with observed Y ("observed clusters"). Often the former is of interest, but when data are missing because in a fundamental sense Y does not exist (e.g., quality of life for a person who has died), the latter may be more meaningful (quality of life conditional on being alive). Weighted and doubly weighted generalized estimating equations and shared random-effects models have been proposed for observed-cluster inference when cluster size is informative, that is, the distribution of Y given X in observed clusters depends on observed cluster size. We show these methods can be seen as actually giving inference for complete clusters and may not also give observed-cluster inference. This is true even if observed clusters are complete in themselves rather than being the observed part of larger complete clusters: here methods may describe imaginary complete clusters rather than the observed clusters. We show under which conditions shared random-effects models proposed for observed-cluster inference do actually describe members with observed Y. A psoriatic arthritis dataset is used to illustrate the danger of misinterpreting estimates from shared random-effects models.SRS is funded by MRC grants U1052 60558 and MC_US_A030_0015, AJC and MP by MRC grant G0600657

A note on obtaining correct marginal predictions from a random intercepts model for binary outcomes.

BACKGROUND: Clustered data with binary outcomes are often analysed using random intercepts models or generalised estimating equations (GEE) resulting in cluster-specific or 'population-average' inference, respectively. METHODS: When a random effects model is fitted to clustered data, predictions may be produced for a member of an existing cluster by using estimates of the fixed effects (regression coefficients) and the random effect for the cluster (conditional risk calculation), or for a member of a new cluster (marginal risk calculation). We focus on the second. Marginal risk calculation from a random effects model is obtained by integrating over the distribution of random effects. However, in practice marginal risks are often obtained, incorrectly, using only estimates of the fixed effects (i.e. by effectively setting the random effects to zero). We compare these two approaches to marginal risk calculation in terms of model calibration. RESULTS: In simulation studies, it has been seen that use of the incorrect marginal risk calculation from random effects models results in poorly calibrated overall marginal predictions (calibration slope <1 and calibration in the large ≠ 0) with mis-calibration becoming worse with higher degrees of clustering. We clarify that this was due to the incorrect calculation of marginal predictions from a random intercepts model and explain intuitively why this approach is incorrect. We show via simulation that the correct calculation of marginal risks from a random intercepts model results in predictions with excellent calibration. CONCLUSION: The logistic random intercepts model can be used to obtain valid marginal predictions by integrating over the distribution of random effects

Health-Related Quality of Life in Adults With Classical Infratentorial Superficial Siderosis: A Cross-sectional Study

BACKGROUND AND OBJECTIVES: Infratentorial superficial siderosis (iSS) is a rare but disabling neurological condition characterised by progressive hearing loss, balance and mobility problems. The functional decline in these neurological domains with iSS progression is likely to adversely impact health-related quality of life (HRQoL). We studied HRQoL of adults with iSS using two common generic HRQoL measures (Health Utilities Index Mark III (HUI3) and EuroQoL EQ5D (5 Level) to determine the most impacted domains and evaluate the association between HRQoL scores and disease duration. METHODS: This observational study was an anonymous online survey. Following institutional Research Ethics Committee approval, we contacted dedicated international organisations, charities and patient-groups identified through online searches, social media and collaborative networks, to distribute the study information and study link, inviting their members diagnosed with iSS to participate. Participation required access to a digital device connected to the internet, confirmation of eligibility (aged ≥18 years and previously diagnosed with iSS) and informed consent to participate in the survey, which included study-specific questions (demographics, iSS, hearing) and HRQoL questionnaires. Survey responses were captured by the Research Electronic Data Capture (REDCap) survey software and analysed using the SPSS statistical package. Linear regression analysis was performed to investigate the association between HRQoL scores and disease duration. RESULTS: Of fifty participants,60% were male; the median (interquartile range, IQR) age was 60 (15) years. The median (IQR) multi-attribute scores for HUI3 and EQ5D were 0.36 (0.53) and 0.64 (0.33), respectively. The most frequently affected domains (moderate or worse category) were hearing (64%), and pain (48%) for HUI3, and mobility (54%) and pain (50%) for EQ5D. There was a weak association between disease duration and multi-attribute scores for HUI3 (R=0.353; adjusted R2=0.096; b=-0.008; p=0.047) but not EQ5D. DISCUSSION: Our findings demonstrate low HRQoL scores which capture low functional status in several domains typically affected in iSS, suggesting that iSS has a major adverse impact on quality of life in multiple functional domains. Measures of HRQoL in iSS should be included in clinical and research settings, including treatment trials

Analysis of Randomised Trials Including Multiple Births When Birth Size Is Informative.

BACKGROUND: Informative birth size occurs when the average outcome depends on the number of infants per birth. Although analysis methods have been proposed for handling informative birth size, their performance is not well understood. Our aim was to evaluate the performance of these methods and to provide recommendations for their application in randomised trials including infants from single and multiple births. METHODS: Three generalised estimating equation (GEE) approaches were considered for estimating the effect of treatment on a continuous or binary outcome: cluster weighted GEEs, which produce treatment effects with a mother-level interpretation when birth size is informative; standard GEEs with an independence working correlation structure, which produce treatment effects with an infant-level interpretation when birth size is informative; and standard GEEs with an exchangeable working correlation structure, which do not account for informative birth size. The methods were compared through simulation and analysis of an example dataset. RESULTS: Treatment effect estimates were affected by informative birth size in the simulation study when the effect of treatment in singletons differed from that in multiples (i.e. in the presence of a treatment group by multiple birth interaction). The strength of evidence supporting the effectiveness of treatment varied between methods in the example dataset. CONCLUSIONS: Informative birth size is always a possibility in randomised trials including infants from both single and multiple births, and analysis methods should be pre-specified with this in mind. We recommend estimating treatment effects using standard GEEs with an independence working correlation structure to give an infant-level interpretation.Australian National Health and Medical Research Council. Grant Number: #ID 1052388 United Kingdom Medical Research Council. Grant Number: ID U1052 6055

A cost-effectiveness analysis of hypertrophic cardiomyopathy sudden cardiac death risk algorithms for implantable cardioverter defibrillator decision-making

AIMS: To conduct a contemporary cost-effectiveness analysis examining the use of implantable cardioverter defibrillators (ICD) for primary prevention in patients with hypertrophic cardiomyopathy (HCM). METHODS: A discrete-time Markov model was used to determine the cost-effectiveness of different ICD decision-making rules for implantation. Several scenarios were investigated including the reference scenario of implantation rates according to observed real world practice. A 12-year time horizon with an annual cycle length was used. Transition probabilities used in the model were obtained using Bayesian analysis. The study has been reported according to the Consolidated Health Economic Evaluation Reporting Standards (CHEERS) checklist. RESULTS: Using a 5-year SCD risk threshold of 6% was cheaper than current practice and has marginally better total quality adjusted life years (QALYs). This is the most cost-effective of the options considered, with an incremental cost effectiveness ratio of £834 per QALY. Sensitivity analyses highlighted that this decision is largely driven by what health related quality of life (HRQL) is attributed to ICD patients and time horizon. CONCLUSION: We present a timely new perspective on HCM ICD cost-effectiveness, using methods reflecting real-world practice. While we have shown that a 6% 5-year SCD risk cut-off provides the best cohort stratification to aid ICD decision-making, this will also be influenced by the particular values of costs and HRQL for subgroups or at a local level. The process of explicitly demonstrating the main factors which drive conclusions from such an analysis will help to inform shared decision-making in this complex area for all stakeholders concerned

Estimation of required sample size for external validation of risk models for binary outcomes

Risk-prediction models for health outcomes are used in practice as part of clinical decision-making, and it is essential that their performance be externally validated. An important aspect in the design of a validation study is choosing an adequate sample size. In this paper, we investigate the sample size requirements for validation studies with binary outcomes to estimate measures of predictive performance (C-statistic for discrimination and calibration slope and calibration in the large). We aim for sufficient precision in the estimated measures. In addition, we investigate the sample size to achieve sufficient power to detect a difference from a target value. Under normality assumptions on the distribution of the linear predictor, we obtain simple estimators for sample size calculations based on the measures above. Simulation studies show that the estimators perform well for common values of the C-statistic and outcome prevalence when the linear predictor is marginally Normal. Their performance deteriorates only slightly when the normality assumptions are violated. We also propose estimators which do not require normality assumptions but require specification of the marginal distribution of the linear predictor and require the use of numerical integration. These estimators were also seen to perform very well under marginal normality. Our sample size equations require a specified standard error (SE) and the anticipated C-statistic and outcome prevalence. The sample size requirement varies according to the prognostic strength of the model, outcome prevalence, choice of the performance measure and study objective. For example, to achieve an SE < 0.025 for the C-statistic, 60–170 events are required if the true C-statistic and outcome prevalence are between 0.64–0.85 and 0.05–0.3, respectively. For the calibration slope and calibration in the large, achieving SE < 0.15 would require 40–280 and 50–100 events, respectively. Our estimators may also be used for survival outcomes when the proportion of censored observations is high

Effect of trimetazidine dihydrochloride therapy on exercise capacity in patients with nonobstructive hypertrophic cardiomyopathy: A randomized clinical trial

Importance: Hypertrophic cardiomyopathy causes limiting symptoms in patients, mediated partly through inefficient myocardial energy use. There is conflicting evidence for therapy with inhibitors of myocardial fatty acid metabolism in patients with nonobstructive hypertrophic cardiomyopathy. Objective: To determine the effect of oral therapy with trimetazidine, a direct inhibitor of fatty acid β-oxidation, on exercise capacity in patients with symptomatic nonobstructive hypertrophic cardiomyopathy. Design, Setting, and Participants: This randomized, placebo-controlled, double-blind clinical trial at The Heart Hospital, University College London Hospitals, London, United Kingdom was performed between May 31, 2012, and September 8, 2014. The trial included 51 drug-refractory symptomatic (New York Heart Association class ≥2) patients aged 24 to 74 years with a maximum left ventricular outflow tract gradient 50 mm Hg or lower and a peak oxygen consumption during exercise of 80% or less predicted value for age and sex. Statistical analysis was performed from March 1, 2016 through July 4, 2018. Interventions: Participants were randomly assigned to trimetazidine, 20 mg, 3 times daily (n = 27) or placebo (n = 24) for 3 months. Main Outcomes and Measures: The primary end point was peak oxygen consumption during upright bicycle ergometry. Secondary end points were 6-minute walk distance, quality of life (Minnesota Living with Heart Failure questionnaire), frequency of ventricular ectopic beats, diastolic function, serum N-terminal pro-brain natriuretic peptide level, and troponin T level. Results: Of 49 participants who received trimetazidine (n = 26) or placebo (n = 23) and completed the study, 34 (70%) were male; the mean (SD) age was 50 (13) years. Trimetazidine therapy did not improve exercise capacity, with patients in the trimetazidine group walking 38.4 m (95% CI, 5.13 to 71.70 m) less than patients in the placebo group at 3 months after adjustment for their baseline walking distance measurements. After adjustment for baseline values, peak oxygen consumption was 1.35 mL/kg per minute lower (95% CI, -2.58 to -0.11 mL/kg per minute; P = .03) in the intervention group after 3 months. Conclusions and Relevance: In symptomatic patients with nonobstructive hypertrophic cardiomyopathy, trimetazidine therapy does not improve exercise capacity. Pharmacologic therapy for this disease remains limited. Trial Registration: ClinicalTrials.gov identifier: NCT01696370

Prediction of thrombo-embolic risk in patients with hypertrophic cardiomyopathy (HCM Risk-CVA)

Aims Atrial fibrillation (AF) and thrombo-embolism (TE) are associated with reduced survival in hypertrophic cardiomyopathy (HCM), but the absolute risk of TE in patients with and without AF is unclear. The primary aim of this study was to derive and validate a model for estimating the risk of TE in HCM. Exploratory analyses were performed to determine predictors of TE, the performance of the CHA2DS2-VASc score, and outcome with vitamin K antagonists (VKAs). Methods and results A retrospective, longitudinal cohort of seven institutions was used to develop multivariable Cox regression models fitted with pre-selected predictors. Bootstrapping was used for validation. Of 4821 HCM patients recruited between 1986 and 2008, 172 (3.6%) reached the primary endpoint of cerebrovascular accident (CVA), transient ischaemic attack (TIA), or systemic peripheral embolus within 10 years. A total of 27.5% of patients had a CHA2DS2-VASc score of 0, of whom 9.8% developed TE during follow-up. Cox regression revealed an association between TE and age, AF, the interaction between age and AF, TE prior to first evaluation, NYHA class, left atrial (LA) diameter, vascular disease, and maximal LV wall thickness. There was a curvilinear relationship between LA size and TE risk. The model predicted TE with a C-index of 0.75 [95% confidence interval (CI) 0.70-0.80] and the D-statistic was 1.30 (95% CI 1.05-1.56). VKA treatment was associated with a 54.8% (95% CI 31-97%, P = 0.037) relative risk reduction in HCM patients with AF. Conclusions The study shows that the risk of TE in HCM patients can be identified using a small number of simple clinical features. LA size, in particular, should be monitored closely, and the assessment and treatment of conventional vascular risk factors should be routine practice in older patients. Exploratory analyses show for the first time evidence for a reduction of TE with VKA treatment. The CHA2DS2-VASc score does not appear to correlate well with the clinical outcome in patients with HCM and should not be used to assess TE risk in this population