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Background Risk prediction models are routinely used to assist in clinical decision making. A small sample size for model development can compromise model performance when the model is applied to new patients. For binary outcomes, the calibration slope (CS) and the mean absolute prediction error (MAPE) are two key measures on which sample size calculations for the development of risk models have been based. CS quantifies the degree of model overfitting while MAPE assesses the accuracy of individual predictions. Methods Recently, two formulae were proposed to calculate the sample size required, given anticipated features of the development data such as the outcome prevalence and c-statistic, to ensure that the expectation of the CS and MAPE (over repeated samples) in models fitted using MLE will meet prespecified target values. In this article, we use a simulation study to evaluate the performance of these formulae. Results We found that both formulae work reasonably well when the anticipated model strength is not too high (c-statistic < 0.8), regardless of the outcome prevalence. However, for higher model strengths the CS formula underestimates the sample size substantially. For example, for c-statistic = 0.85 and 0.9, the sample size needed to be increased by at least 50% and 100%, respectively, to meet the target expected CS. On the other hand, the MAPE formula tends to overestimate the sample size for high model strengths. These conclusions were more pronounced for higher prevalence than for lower prevalence. Similar results were drawn when the outcome was time to event with censoring. Given these findings, we propose a simulation-based approach, implemented in the new R package ‘samplesizedev’, to correctly estimate the sample size even for high model strengths. The software can also calculate the variability in CS and MAPE, thus allowing for assessment of model stability. Conclusions The calibration and MAPE formulae suggest sample sizes that are generally appropriate for use when the model strength is not too high. However, they tend to be biased for higher model strengths, which are not uncommon in clinical risk prediction studies. On those occasions, our proposed adjustments to the sample size calculations will be relevant.

Multiparametric MRI of the prostate followed by targeted biopsy is recommended for patients at risk of prostate cancer. However, multiparametric ultrasound is more readily available than multiparametric MRI. Data from paired-cohort validation studies and randomised, controlled trials support the use of multiparametric MRI, whereas the evidence for individual ultrasound methods and multiparametric ultrasound is only derived from case series. We aimed to establish the overall agreement between multiparametric ultrasound and multiparametric MRI to diagnose clinically significant prostate cancer. We conducted a prospective, multicentre, paired-cohort, confirmatory study in seven hospitals in the UK. Patients at risk of prostate cancer, aged 18 years or older, with an elevated prostate-specific antigen concentration or abnormal findings on digital rectal examination underwent both multiparametric ultrasound and multiparametric MRI. Multiparametric ultrasound consisted of B-mode, colour Doppler, real-time elastography, and contrast-enhanced ultrasound. Multiparametric MRI included high-resolution T2-weighted images, diffusion-weighted imaging (dedicated high B 1400 s/mm2 or 2000 s/mm2 and apparent diffusion coefficient map), and dynamic contrast-enhanced axial T1-weighted images. Patients with positive findings on multiparametric ultrasound or multiparametric MRI underwent targeted biopsies but were masked to their test results. If both tests yielded positive findings, the order of targeting at biopsy was randomly assigned (1:1) using stratified (according to centre only) block randomisation with randomly varying block sizes. The co-primary endpoints were the proportion of positive lesions on, and agreement between, multiparametric MRI and multiparametric ultrasound in identifying suspicious lesions (Likert score of ≥3), and detection of clinically significant cancer (defined as a Gleason score of ≥4 + 3 in any area or a maximum cancer core length of ≥6 mm of any grade [PROMIS definition 1]) in those patients who underwent a biopsy. Adverse events were defined according to Good Clinical Practice and trial regulatory guidelines. The trial is registered on ISRCTN, 38541912, and ClinicalTrials.gov, NCT02712684, with recruitment and follow-up completed. Between March 15, 2016, and Nov 7, 2019, 370 eligible patients were enrolled; 306 patients completed both multiparametric ultrasound and multiparametric MRI and 257 underwent a prostate biopsy. Multiparametric ultrasound was positive in 272 (89% [95% CI 85–92]) of 306 patients and multiparametric MRI was positive in 238 patients (78% [73–82]; difference 11·1% [95% CI 5·1–17·1]). Positive test agreement was 73·2% (95% CI 67·9–78·1; κ=0·06 [95% CI –0·56 to 0·17]). Any cancer was detected in 133 (52% [95% CI 45·5–58]) of 257 patients, with 83 (32% [26–38]) of 257 being clinically significant by PROMIS definition 1. Each test alone would result in multiparametric ultrasound detecting PROMIS definition 1 cancer in 66 (26% [95% CI 21–32]) of 257 patients who had biopsies and multiparametric MRI detecting it in 77 (30% [24–36]; difference –4·3% [95% CI –8·3% to –0·3]). Combining both tests detected 83 (32% [95% CI 27–38]) of 257 clinically significant cancers as per PROMIS definition 1; of these 83 cancers, six (7% [95% CI 3–15]) were detected exclusively with multiparametric ultrasound, and 17 (20% [12–31]) were exclusively detected by multiparametric MRI (agreement 91·1% [95% CI 86·9–94·2]; κ=0·78 [95% CI 0·69–0·86]). No serious adverse events were related to trial activity. Multiparametric ultrasound detected 4·3% fewer clinically significant prostate cancers than multiparametric MRI, but it would lead to 11·1% more patients being referred for a biopsy. Multiparametric ultrasound could be an alternative to multiparametric MRI as a first test for patients at risk of prostate cancer, particularly if multiparametric MRI cannot be carried out. Both imaging tests missed clinically significant cancers detected by the other, so the use of both would increase the detection of clinically significant prostate cancers compared with using each test alone. The Jon Moulton Charity Trust, Prostate Cancer UK, and UCLH Charity and Barts Charity.

Background Clustered data arise in research when patients are clustered within larger units. Generalised Estimating Equations (GEE) and Generalised Linear Models (GLMM) can be used to provide marginal and cluster-specific inference and predictions, respectively. Methods Confounding by Cluster (CBC) and Informative cluster size (ICS) are two complications that may arise when modelling clustered data. CBC can arise when the distribution of a predictor variable (termed ‘exposure’), varies between clusters causing confounding of the exposure-outcome relationship. ICS means that the cluster size conditional on covariates is not independent of the outcome. In both situations, standard GEE and GLMM may provide biased or misleading inference, and modifications have been proposed. However, both CBC and ICS are routinely overlooked in the context of risk prediction, and their impact on the predictive ability of the models has been little explored. We study the effect of CBC and ICS on the predictive ability of risk models for binary outcomes when GEE and GLMM are used. We examine whether two simple approaches to handle CBC and ICS, which involve adjusting for the cluster mean of the exposure and the cluster size, respectively, can improve the accuracy of predictions. Results Both CBC and ICS can be viewed as violations of the assumptions in the standard GLMM; the random effects are correlated with exposure for CBC and cluster size for ICS. Based on these principles, we simulated data subject to CBC/ICS. The simulation studies suggested that the predictive ability of models derived from using standard GLMM and GEE ignoring CBC/ICS was affected. Marginal predictions were found to be mis-calibrated. Adjusting for the cluster-mean of the exposure or the cluster size improved calibration, discrimination and the overall predictive accuracy of marginal predictions, by explaining part of the between cluster variability. The presence of CBC/ICS did not affect the accuracy of conditional predictions. We illustrate these concepts using real data from a multicentre study with potential CBC. Conclusion Ignoring CBC and ICS when developing prediction models for clustered data can affect the accuracy of marginal predictions. Adjusting for the cluster mean of the exposure or the cluster size can improve the predictive accuracy of marginal predictions.

ObjectivesAtrial fibrillation (AF) is associated with increased morbidity and mortality in patients with hypertrophic cardiomyopathy (HCM). The primary aim of this study (HCM Risk-AF) was to determine the predictors of AF in a large multicentre cohort of patients with HCM. Exploratory analyses were performed to investigate the association between AF and survival and the efficacy of antiarrhythmic therapy in maintaining sinus rhythm (SR).MethodsA retrospective, longitudinal cohort of patients recruited between 1986 and 2008 in seven centres was used to develop multivariable Cox regression models fitted with preselected predictors. HCM was defined as unexplained hypertrophy (maximum left ventricular wall thickness of ≥15 mm or in accordance with published criteria for the diagnosis of familial disease). 28% of patients (n=1171) had coexistent hypertension. The primary end point was paroxysmal, permanent or persistent AF detected on ECG, Holter monitoring or implantable device interrogation.ResultsOf the 4248 patients with HCM without pre-existing AF, 740 (17.4%) reached the primary end point. Multivariable Cox regression revealed an association between AF and female sex, age, left atrial diameter, New York Heart Association (NYHA) class, hypertension and vascular disease. The proportion of patients with cardiovascular death at 10 years was 4.9% in the SR group and 10.9% in the AF group (difference in proportions=5.9%; 95% CI (4.1% to 7.8%)). The proportion of patients with non-cardiovascular death at 10 years was 3.2% in the SR group and 5.9% in the AF group (difference in proportions=2.8%; 95% CI (0.1% to 4.2%)). An intention-to-treat propensity score analysis demonstrated that β-blockers, calcium channel antagonists and disopyramide initially maintained SR during follow-up, but their protective effect diminished with time. Amiodarone therapy did not prevent AF during follow-up.ConclusionThis study shows that patients with HCM who are at risk of AF development can be identified using readily available clinical parameters. The development of AF is associated with a poor prognosis but there was no evidence that antiarrhythmic therapy prevents AF in the long term.

Background Institutions or clinicians (units) are often compared according to a performance indicator such as in-hospital mortality. Several approaches have been proposed for the detection of outlying units, whose performance deviates from the overall performance. Methods We provide an overview of three approaches commonly used to monitor institutional performances for outlier detection. These are the common-mean model, the ‘Normal-Poisson’ random effects model and the ‘Logistic’ random effects model. For the latter we also propose a visualisation technique. The common-mean model assumes that the underlying true performance of all units is equal and that any observed variation between units is due to chance. Even after applying case-mix adjustment, this assumption is often violated due to overdispersion and a post-hoc correction may need to be applied. The random effects models relax this assumption and explicitly allow the true performance to differ between units, thus offering a more flexible approach. We discuss the strengths and weaknesses of each approach and illustrate their application using audit data from England and Wales on Adult Cardiac Surgery (ACS) and Percutaneous Coronary Intervention (PCI). Results In general, the overdispersion-corrected common-mean model and the random effects approaches produced similar p -values for the detection of outliers. For the ACS dataset (41 hospitals) three outliers were identified in total but only one was identified by all methods above. For the PCI dataset (88 hospitals), seven outliers were identified in total but only two were identified by all methods. The common-mean model uncorrected for overdispersion produced several more outliers. The reason for observing similar p -values for all three approaches could be attributed to the fact that the between-hospital variance was relatively small in both datasets, resulting only in a mild violation of the common-mean assumption; in this situation, the overdispersion correction worked well. Conclusion If the common-mean assumption is likely to hold, all three methods are appropriate to use for outlier detection and their results should be similar. Random effect methods may be the preferred approach when the common-mean assumption is likely to be violated.

The increasing prevalence of patients with aortic stenosis worldwide highlights a clinical need for improved and accurate prediction of clinical outcomes following surgery. We investigated patient demographic and cardiovascular magnetic resonance (CMR) characteristics to formulate a dedicated risk score estimating long-term survival following surgery. We recruited consecutive patients undergoing CMR with gadolinium administration prior to surgical aortic valve replacement from 2003 to 2016 in two UK centres. The outcome was overall mortality. A total of 250 patients were included (68 ± 12 years, male 185 (60%), with pre-operative mean aortic valve area 0.93 ± 0.32cm 2 , LVEF 62 ± 17%) and followed for 6.0 ± 3.3 years. Sixty-one deaths occurred, with 10-year mortality of 23.6%. Multivariable analysis showed that increasing age (HR 1.04, P  = 0.005), use of antiplatelet therapy (HR 0.54, P  = 0.027), presence of infarction or midwall late gadolinium enhancement (HR 1.52 and HR 2.14 respectively, combined P  = 0.12), higher indexed left ventricular stroke volume (HR 0.98, P  = 0.043) and higher left atrial ejection fraction (HR 0.98, P  = 0.083) associated with mortality and developed a risk score with good discrimination. This is the first dedicated risk prediction score for patients with aortic stenosis undergoing surgical aortic valve replacement providing an individualised estimate for overall mortality. This model can help clinicians individualising medical and surgical care. Trial Registration ClinicalTrials.gov Identifier: NCT00930735 and ClinicalTrials.gov Identifier: NCT01755936.

Children with Auditory Processing Disorder (APD) often have poor auditory processing skills in the presence of normal peripheral hearing. These children have worse listening-in-noise skills compared to typically developing peers, while other commonly reported symptoms include poor attention and distractibility. One of the management strategies for children with APD is the use of Remote Microphone Hearing Aids (RMHAs), which can help improve the signal-to-noise ratio in the child's ears. The aim of this randomised controlled trial was to examine whether RMHAs improved classroom listening in children with APD, and to further test their effects on children's listening-in-noise and attention skills following a 6-month intervention. Twenty-six children diagnosed with APD, aged 7-12, in primary mainstream education, were randomised into the intervention ( = 13) and control group ( = 13). The primary outcome measure was the Listening Inventory for Education - Revised questionnaire, completed by children to assess their listening using RMHAs under several acoustically challenging situations in the classroom. Secondary outcome measures included the Listening in Spatialised Noise - Sentences test, assessing speech-in-noise perception and spatial listening, and the Test of Everyday Attention for Children, assessing different types of attention skills. Tests were conducted in unaided conditions. Mixed analysis of variance was used to analyse the data. The clinical trial was registered at clinicaltrials.gov (unique identifier: NCT02353091). The questionnaire scores of self-reported listening skills in the classroom significantly improved in the intervention group after 3, = 7.31, = 2.113, = 0.014, and after 6 months, = 5.00, = 1.468, = 0.016. The behavioural measures of listening-in-noise and attention did not significantly change. Use of RMHAs improves classroom listening, evidenced by the results of the questionnaire analysis, while a 6-month use did not have adverse effects on unaided spatial listening or attention skills.

Empyema is an increasingly frequent clinical problem worldwide, and has substantial morbidity and mortality. Our objectives were to identify the clinical, surgical and microbiological features, and management outcomes, of empyema. A retrospective observational study over 12 years (1999-2010) was carried out at The Heart Hospital, London, United Kingdom. Patients with empyema were identified by screening the hospital electronic 'Clinical Data Repository'. Demographics, clinical and microbiological characteristics, underlying risk factors, peri-operative blood tests, treatment and outcomes were identified. Univariable and multivariable statistical analyses were performed. Patients (n = 406) were predominantly male (74.1%); median age = 53 years (IQR = 37-69). Most empyema were community-acquired (87.4%) and right-sided (57.4%). Microbiological diagnosis was obtained in 229 (56.4%) patients, and included streptococci (16.3%), staphylococci (15.5%), gram-negative organisms (8.9%), anaerobes (5.7%), pseudomonads (4.4%) and mycobacteria (9.1%); 8.4% were polymicrobial. Most (68%) cases were managed by open thoracotomy and decortication. Video-assisted thoracoscopic surgery (VATS) reduced hospitalisation from 10 to seven days (P = 0.0005). All-cause complication rate was 25.1%, and 28 day mortality 5.7%. Predictors of early mortality included: older age (P = 0.006), major co-morbidity (P = 0.01), malnutrition (P = 0.001), elevated red cell distribution width (RDW, P<0.001) and serum alkaline phosphatase (P = 0.004), and reduced serum albumin (P = 0.01) and haemoglobin (P = 0.04). Empyema remains an important cause of morbidity and hospital admissions. Microbiological diagnosis was only achieved in just over 50% of cases, and tuberculosis is a notable causative organism. Treatment of empyema with VATS may reduce duration of hospital stay. Raised RDW appears to associate with early mortality.

Sexual health problems such as unwanted pregnancy and sexually transmitted infection are important public health concerns and there is huge potential for health promotion using digital interventions. Evaluations of digital interventions are increasingly conducted online. Trial administration and data collection online offers many advantages, but concerns remain over fraudulent registration to obtain compensation, the quality of self-reported data, and high attrition. This study addresses the feasibility of several dimensions of online trial design-recruitment, online consent, participant identity verification, randomization and concealment of allocation, online data collection, data quality, and retention at 3-month follow-up. Young people aged 16 to 20 years and resident in the United Kingdom were recruited to the \"Sexunzipped\" online trial between November 2010 and March 2011 (n=2036). Participants filled in baseline demographic and sexual health questionnaires online and were randomized to the Sexunzipped interactive intervention website or to an information-only control website. Participants were also randomly allocated to a postal request (or no request) for a urine sample for genital chlamydia testing and receipt of a lower (£10/US$16) or higher (£20/US$32) value shopping voucher compensation for 3-month outcome data. The majority of the 2006 valid participants (90.98%, 1825/2006) were aged between 18 and 20 years at enrolment, from all four countries in the United Kingdom. Most were white (89.98%, 1805/2006), most were in school or training (77.48%, 1545/1994), and 62.81% (1260/2006) of the sample were female. In total, 3.88% (79/2036) of registrations appeared to be invalid and another 4.00% (81/2006) of participants gave inconsistent responses within the questionnaire. The higher value compensation (£20/US$32) increased response rates by 6-10%, boosting retention at 3 months to 77.2% (166/215) for submission of online self-reported sexual health outcomes and 47.4% (118/249) for return of chlamydia urine samples by post. It was quick and efficient to recruit young people to this online trial. Our procedures for obtaining online consent, verifying participant identity, automated randomization, and concealment of allocation worked well. The optimal response rate for the online sexual health outcome measurement was comparable to face-to-face trials. Multiple methods of participant contact, requesting online data only, and higher value compensation increased trial retention at 3-month follow-up. International Standard Randomized Controlled Trial Number (ISRCTN): 55651027; http://www.controlled-trials.com/ISRCTN55651027 (Archived by WebCite at http://www.webcitation.org/6LbkxdPKf).