OBJECTIVE To review and critically appraise published and preprint reports of prediction models for diagnosing coronavirus disease 2019 (covid-19) in patients with suspected infection, for prognosis of patients with covid-19, and for detecting people in the general population at increased risk of becoming infected with covid-19 or being admitted to hospital with the disease. DESIGNLiving systematic review and critical appraisal. DATA SOURCESPubMed and Embase through Ovid, Arxiv, medRxiv, and bioRxiv up to 7 April 2020.Cite this as: BMJ 2020;369:m1328 http://dx.

Calculating the sample size required for developing a clinical prediction model Clinical prediction models aim to predict outcomes in individuals, to inform diagnosis or prognosis in healthcare. Hundreds of prediction models are published in the medical literature each year, yet many are developed using a dataset that is too small for the total number of participants or outcome events. This leads to inaccurate predictions and consequently incorrect healthcare decisions for some individuals. In this article, the authors provide guidance on how to calculate the sample size required to develop a clinical prediction model.

Objectives When developing a clinical prediction model, penalization techniques are recommended to address overfitting, as they shrink predictor effect estimates toward the null and reduce mean-square prediction error in new individuals. However, shrinkage and penalty terms (‘tuning parameters’) are estimated with uncertainty from the development data set. We examined the magnitude of this uncertainty and the subsequent impact on prediction model performance. Study Design and Setting This study comprises applied examples and a simulation study of the following methods: uniform shrinkage (estimated via a closed-form solution or bootstrapping), ridge regression, the lasso, and elastic net. Results In a particular model development data set, penalization methods can be unreliable because tuning parameters are estimated with large uncertainty. This is of most concern when development data sets have a small effective sample size and the model's Cox-Snell is low. The problem can lead to considerable miscalibration of model predictions in new individuals. Conclusion Penalization methods are not a ‘carte blanche’; they do not guarantee a reliable prediction model is developed. They are more unreliable when needed most (i.e., when overfitting may be large). We recommend they are best applied with large effective sample sizes, as identified from recent sample size calculations that aim to minimize the potential for model overfitting and precisely estimate key parameters.

BackgroundClinical prediction models (CPMs) are increasingly deployed to support healthcare decisions but they are derived inconsistently, in part due to limited data. An emerging alternative is to aggregate existing CPMs developed for similar settings and outcomes. This simulation study aimed to investigate the impact of between-population-heterogeneity and sample size on aggregating existing CPMs in a defined population, compared with developing a model de novo.MethodsSimulations were designed to mimic a scenario in which multiple CPMs for a binary outcome had been derived in distinct, heterogeneous populations, with potentially different predictors available in each. We then generated a new ‘local’ population and compared the performance of CPMs developed for this population by aggregation, using stacked regression, principal component analysis or partial least squares, with redevelopment from scratch using backwards selection and penalised regression.ResultsWhile redevelopment approaches resulted in models that were miscalibrated for local datasets of less than 500 observations, model aggregation methods were well calibrated across all simulation scenarios. When the size of local data was less than 1000 observations and between-population-heterogeneity was small, aggregating existing CPMs gave better discrimination and had the lowest mean square error in the predicted risks compared with deriving a new model. Conversely, given greater than 1000 observations and significant between-population-heterogeneity, then redevelopment outperformed the aggregation approaches. In all other scenarios, both aggregation and de novo derivation resulted in similar predictive performance.ConclusionThis study demonstrates a pragmatic approach to contextualising CPMs to defined populations. When aiming to develop models in defined populations, modellers should consider existing CPMs, with aggregation approaches being a suitable modelling strategy particularly with sparse data on the local population.Electronic supplementary materialThe online version of this article (doi:10.1186/s12874-016-0277-1) contains supplementary material, which is available to authorized users.

Background Disease populations, clinical practice, and healthcare systems are constantly evolving. This can result in clinical prediction models quickly becoming outdated and less accurate over time. A potential solution is to develop ‘dynamic’ prediction models capable of retaining accuracy by evolving over time in response to observed changes. Our aim was to review the literature in this area to understand the current state-of-the-art in dynamic prediction modelling and identify unresolved methodological challenges. Methods MEDLINE, Embase and Web of Science were searched for papers which used or developed dynamic clinical prediction models. Information was extracted on methods for model updating, choice of update windows and decay factors and validation of models. We also extracted reported limitations of methods and recommendations for future research. Results We identified eleven papers that discussed seven dynamic clinical prediction modelling methods which split into three categories. The first category uses frequentist methods to update models in discrete steps, the second uses Bayesian methods for continuous updating and the third, based on varying coefficients, explicitly describes the relationship between predictors and outcome variable as a function of calendar time. These methods have been applied to a limited number of healthcare problems, and few empirical comparisons between them have been made. Conclusion Dynamic prediction models are not well established but they overcome one of the major issues with static clinical prediction models, calibration drift. However, there are challenges in choosing decay factors and in dealing with sudden changes. The validation of dynamic prediction models is still largely unexplored terrain.

Clinical prediction models (CPMs) can inform decision making about treatment initiation, which requires predicted risks assuming no treatment is given. However, this is challenging since CPMs are usually derived using data sets where patients received treatment, often initiated postbaseline as “treatment drop‐ins.” This study proposes the use of marginal structural models (MSMs) to adjust for treatment drop‐in. We illustrate the use of MSMs in the CPM framework through simulation studies that represent randomized controlled trials and real‐world observational data and the example of statin initiation for cardiovascular disease prevention. The simulations include a binary treatment and a covariate, each recorded at two timepoints and having a prognostic effect on a binary outcome. The bias in predicted risk was examined in a model ignoring treatment, a model fitted on treatment‐naïve patients (at baseline), a model including baseline treatment, and the MSM. In all simulation scenarios, all models except the MSM underestimated the risk of outcome given absence of treatment. These results were supported in the statin initiation example, which showed that ignoring statin initiation postbaseline resulted in models that significantly underestimated the risk of a cardiovascular disease event occurring within 10 years. Consequently, CPMs that do not acknowledge treatment drop‐in can lead to underallocation of treatment. In conclusion, when developing CPMs to predict treatment‐naïve risk, researchers should consider using MSMs to adjust for treatment drop‐in, and also seek to exploit the ability of MSMs to allow estimation of individual treatment effects.

BackgroundThe performance of emerging transcatheter aortic valve implantation (TAVI) clinical prediction models (CPMs) in national TAVI cohorts distinct from those where they have been derived is unknown. This study aimed to investigate the performance of the German Aortic Valve, FRANCE-2, OBSERVANT and American College of Cardiology (ACC) TAVI CPMs compared with the performance of historic cardiac CPMs such as the EuroSCORE and STS-PROM, in a large national TAVI registry.MethodsThe calibration and discrimination of each CPM were analyzed in 6676 patients from the UK TAVI registry, as a whole cohort and across several subgroups. Strata included gender, diabetes status, access route, and valve type. Furthermore, the amount of agreement in risk classification between each of the considered CPMs was analyzed at an individual patient level.ResultsThe observed 30-day mortality rate was 5.4%. In the whole cohort, the majority of CPMs over-estimated the risk of 30-day mortality, although the mean ACC score (5.2%) approximately matched the observed mortality rate. The areas under ROC curve were between 0.57 for OBSERVANT and 0.64 for ACC. Risk classification agreement was low across all models, with Fleiss's kappa values between 0.17 and 0.50.ConclusionsAlthough the FRANCE-2 and ACC models outperformed all other CPMs, the performance of current TAVI-CPMs was low when applied to an independent cohort of TAVI patients. Hence, TAVI specific CPMs need to be derived outside populations previously used for model derivation, either by adapting existing CPMs or developing new risk scores in large national registries.

No abstract