The main objective of most clinical trials is to estimate the effect of some treatment compared to a control condition. We define the signal-to-noise ratio (SNR) as the ratio of the true treatment... Show moreThe main objective of most clinical trials is to estimate the effect of some treatment compared to a control condition. We define the signal-to-noise ratio (SNR) as the ratio of the true treatment effect to the SE of its estimate. In a previous publication in this journal, we estimated the distribution of the SNR among the clinical trials in the Cochrane Database of Systematic Reviews (CDSR). We found that the SNR is often low, which implies that the power against the true effect is also low in many trials. Here we use the fact that the CDSR is a collection of meta-analyses to quantitatively assess the consequences. Among trials that have reached statistical significance we find considerable overoptimism of the usual unbiased estimator and under-coverage of the associated confidence interval. Previously, we have proposed a novel shrinkage estimator to address this "winner's curse." We compare the performance of our shrinkage estimator to the usual unbiased estimator in terms of the root mean squared error, the coverage and the bias of the magnitude. We find superior performance of the shrinkage estimator both conditionally and unconditionally on statistical significance. Show less
The "significance filter" refers to focusing exclusively on statistically significant results. Since frequentist properties such as unbiasedness and coverage are valid only before the data have... Show moreThe "significance filter" refers to focusing exclusively on statistically significant results. Since frequentist properties such as unbiasedness and coverage are valid only before the data have been observed, there are no guarantees if we condition on significance. In fact, the significance filter leads to overestimation of the magnitude of the parameter, which has been called the "winner's curse." It can also lead to undercoverage of the confidence interval. Moreover, these problems become more severe if the power is low. These issues clearly deserve our attention. They have been studied mostly through empirical observation and simulation, while there are relatively few mathematical results. Here we study them both from the frequentist and the Bayesian perspective. We prove that the relative bias of the magnitude is a decreasing function of the power and that the usual confidence interval undercovers when the power is less than 50%. We conclude that it is important to apply the appropriate amount of shrinkage to counter the winner's curse. Show less
Calster, B. van; Smeden, M. van; Cock, B. de; Steyerberg, E.W. 2020
When developing risk prediction models on datasets with limited sample size, shrinkage methods are recommended. Earlier studies showed that shrinkage results in better predictive performance on... Show moreWhen developing risk prediction models on datasets with limited sample size, shrinkage methods are recommended. Earlier studies showed that shrinkage results in better predictive performance on average. This simulation study aimed to investigate the variability of regression shrinkage on predictive performance for a binary outcome. We compared standard maximum likelihood with the following shrinkage methods: uniform shrinkage (likelihood-based and bootstrap-based), penalized maximum likelihood (ridge) methods, LASSO logistic regression, adaptive LASSO, and Firth's correction. In the simulation study, we varied the number of predictors and their strength, the correlation between predictors, the event rate of the outcome, and the events per variable. In terms of results, we focused on the calibration slope. The slope indicates whether risk predictions are too extreme (slope < 1) or not extreme enough (slope > 1). The results can be summarized into three main findings. First, shrinkage improved calibration slopes on average. Second, the between-sample variability of calibration slopes was often increased relative to maximum likelihood. In contrast to other shrinkage approaches, Firth's correction had a small shrinkage effect but showed low variability. Third, the correlation between the estimated shrinkage and the optimal shrinkage to remove overfitting was typically negative, with Firth's correction as the exception. We conclude that, despite improved performance on average, shrinkage often worked poorly in individual datasets, in particular when it was most needed. The results imply that shrinkage methods do not solve problems associated with small sample size or low number of events per variable. Show less
Jong, V.M.T. de; Eijkemans, M.J.C.; Calster, B. van; Timmerman, D.; Moons, K.G.M.; Steyerberg, E.W.; Smeden, M. van 2019
