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The COVID-19 pandemic has caused severe public health consequences in the United States. In this study, we use a hierarchical Bayesian model to estimate the age-specific COVID-19 attributable deaths over time in the United States. The model is specified by a novel non-parametric spatial approach over time and age, a low-rank Gaussian Process (GP) projected by regularised Bsplines. We show that this projection defines a GP with attractive smoothness and computational efficiency properties, derive its kernel function, and discuss the penalty terms induced by the projected GP. Simulation analyses and benchmark results show that the B-splines projected GP may perform better than standard B-splines and Bayesian P-splines, and equivalently well as a standard GP at considerably lower runtimes. We apply the model to weekly, age-stratified COVID-19 attributable deaths reported by the US Centers for Disease Control, which are subject to censoring and reporting biases. Using the B-splines projected GP, we can estimate longitudinal trends in COVID-19 associated deaths across the US by 1-year age bands. These estimates are instrumental to calculate age-specific mortality rates, describe variation in age-specific deaths across the US, and for fitting epidemic models. Here, we couple the model with age-specific vaccination rates to show that vaccination rates were significantly associated with the magnitude of resurgences in COVID-19 deaths during the summer 2021. With counterfactual analyses, we quantify the avoided COVID-19 deaths under lower vaccination rates and avoidable COVID-19 deaths under higher vaccination rates. The Bsplines projected GP priors that we develop are likely an appealing addition to the arsenal of Bayesian regularising priors. [ABSTRACT FROM AUTHOR]

After surgery for a broken ankle, patients are usually instructed to avoid walking for 6 weeks (delayed weight-bearing). Walking 2 weeks after surgery (early weight-bearing) might be a safe and preferable rehabilitation strategy. This study aimed to determine the clinical and cost effectiveness of an early weight-bearing strategy compared with a delayed weight-bearing strategy. This was a pragmatic, multicentre, randomised, non-inferiority trial including 561 participants (aged ≥18 years) who received acute surgery for an unstable ankle fracture in 23 UK National Health Service (NHS) hospitals who were assigned to either a delayed weight-bearing (n=280) or an early weight-bearing rehabilitation strategy (n=281). Patients treated with a hindfoot nail, those who did not have protective ankle sensation (eg, peripheral neuropathy), did not have the capacity to consent, or did not have the ability to adhere to trial procedures were excluded. Neither participants nor clinicians were masked to the treatment. The primary outcome was ankle function measured using the Olerud and Molander Ankle Score (OMAS) at 4 months after randomisation, in the per-protocol population. The pre-specified non-inferiority OMAS margin was –6 points and superiority testing was included in the intention-to-treat population in the event of non-inferiority. The trial was prospectively registered with ISRCTN Registry, ISRCTN12883981, and the trial is closed to new participants. Primary outcome data were collected from 480 (86%) of 561 participants. Recruitment was conducted between Jan 13, 2020, and Oct 29, 2021. At 4 months after randomisation, the mean OMAS score was 65·9 in the early weight-bearing and 61·2 in the delayed weight-bearing group and adjusted mean difference was 4·47 (95% CI 0·58 to 8·37, p=0·024; superiority testing adjusted difference 4·42, 95% CI 0·53 to 8·32, p=0·026) in favour of early weight-bearing. 46 (16%) participants in the early weight-bearing group and 39 (14%) in the delayed weight-bearing group had one or more complications (adjusted odds ratio 1·18, 95% CI 0·80 to 1·75, p=0·40). The mean costs from the perspective of the NHS and personal social services in the early and delayed weight-bearing groups were £725 and £785, respectively (mean difference –£60 [95% CI –342 to 232]). The probability that early weight-bearing is cost-effective exceeded 80%. An early weight-bearing strategy was found to be clinically non-inferior and highly likely to be cost-effective compared with the current standard of care (delayed weight-bearing). National Institute for Health and Care Research (NIHR), NIHR Barts Biomedical Research Centre, and NIHR Applied Research Collaboration Oxford and Thames Valley. [ABSTRACT FROM AUTHOR]