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The design of neural networks typically involves trial-and-error, a time-consuming process for obtaining an optimal architecture, even for experienced researchers. Additionally, it is widely accepted that loss functions of deep neural networks are generally non-convex with respect to the parameters to be optimised. We propose the Layer-wise Convex Theorem to ensure that the loss is convex with respect to the parameters of a given layer, achieved by constraining each layer to be an overdetermined system of non-linear equations. Based on this theorem, we developed an end-to-end algorithm (the AutoNet) to automatically generate layer-wise convex networks (LCNs) for any given training set. We then demonstrate the performance of the AutoNet-generated LCNs (AutoNet-LCNs) compared to state-of-the-art models on three electrocardiogram (ECG) classification benchmark datasets, with further validation on two non-ECG benchmark datasets for more general tasks. The AutoNet-LCN was able to find networks customised for each dataset without manual fine-tuning under 2 GPU-hours, and the resulting networks outperformed the state-of-the-art models with fewer than 5% parameters on all the above five benchmark datasets. The efficiency and robustness of the AutoNet-LCN markedly reduce model discovery costs and enable efficient training of deep learning models in resource-constrained settings.

ObjectiveTo externally evaluate the performance of QRISK3 for predicting 10 year risk of cardiovascular disease (CVD) in the UK Biobank cohort.MethodsWe used data from the UK Biobank, a large-scale prospective cohort study of 403 370 participants aged 40–69 years recruited between 2006 and 2010 in the UK. We included participants with no previous history of CVD or statin treatment and defined the outcome to be the first occurrence of coronary heart disease, ischaemic stroke or transient ischaemic attack, derived from linked hospital inpatient records and death registrations.ResultsOur study population included 233 233 women and 170 137 men, with 9295 and 13 028 incident CVD events, respectively. Overall, QRISK3 had moderate discrimination for UK Biobank participants (Harrell’s C-statistic 0.722 in women and 0.697 in men) and discrimination declined by age (<0.62 in all participants aged 65 years or older). QRISK3 systematically overpredicted CVD risk in UK Biobank, particularly in older participants, by as much as 20%.ConclusionsQRISK3 had moderate overall discrimination in UK Biobank, which was best in younger participants. The observed CVD risk for UK Biobank participants was lower than that predicted by QRISK3, particularly for older participants. It may be necessary to recalibrate QRISK3 or use an alternate model in studies that require accurate CVD risk prediction in UK Biobank.

Sleep disturbance occurs in most patients with delusions or hallucinations and should be treated as a clinical problem in its own right. However, cognitive behavioural therapy (CBT)—the best evidence-based treatment for insomnia—has not been tested in this patient population. We aimed to pilot procedures for a randomised trial testing CBT for sleep problems in patients with current psychotic experiences, and to provide a preliminary assessment of potential benefit.

We illustrate the approach of randomising treatments and compare it with the traditional approach of randomising patients, using a case study drawn from the authors’ experience in clinical trials. The setting is a double-blind parallel two-arm randomised controlled trial (RCT), but the method in this paper can be extended to single-blind, cross-over, or multi-arm RCTs.

We discuss different methods of sample size calculation for two independent means, aiming to provide insight into the calculation of sample size at the design stage of a parallel two-arm randomised controlled trial (RCT). We compare different methods for sample size calculation, using published results from a previous RCT. We use variances and correlation coefficients to compare sample sizes using different methods, including