arXiv subjects

František Bartoš

Publications and source records attributed to František Bartoš.

At least 19 recordsLinked to original sources

arXiv2026

Living Synthetic Benchmarks: A Neutral and Cumulative Framework for Simulation Studies

Simulation studies are widely used to evaluate statistical methods. However, new methods are often introduced and evaluated using data-generating mechanisms (DGMs) devised by the same authors. This coupling creates misaligned incentives, e.g., the need to demonstrate the superiority of new methods, potentially compromising the neutrality of simulation studies. Furthermore, results of simulation studies are often difficult to compare due to differences in DGMs, competing methods, and performance measures. This fragmentation can lead to conflicting conclusions, hinder methodological progress, and delay the adoption of effective methods. To address these challenges, we introduce the concept of living synthetic benchmarks. The key idea is to disentangle method and simulation study development and continuously update the benchmark whenever a new DGM, method, or performance measure becomes available. This separation benefits the neutrality of method evaluation, emphasizes the development of both methods and DGMs, and enables systematic comparisons. In this paper, we outline a blueprint for building and maintaining such benchmarks, discuss the technical and organizational challenges of implementation, and demonstrate feasibility with a prototype benchmark for publication bias adjustment methods. We conclude that living synthetic benchmarks have the potential to foster neutral, reproducible, and cumulative evaluation of methods, benefiting both method developers and users.

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arXiv2026

Why the unrestricted weighted least squares should be routinely reported in medical meta-analyses

The unrestricted weighted least squares (UWLS) meta-analysis estimator of mean effect is an alternative to the conventional random-effects model (RE). It is a weighted least squares regression estimator that can be represented as a multiplicative random-effects model. UWLS has been shown to fit medical research better than RE as measured by AIC/BIC widely across Cochrane Database of Systematic Reviews (CDSR). The independence of UWLS's mean and heterogeneity estimators provide small-sample advantages that RE does not possess. Large small-sample biases and uncertainty in RE's heterogeneity variance estimates explain most of RE's relatively poor fit along with RE's boundary problem, where RE's heterogeneity variance is estimated to be zero. We prove that UWLS almost always has superior fit at RE's boundary with uncommon exceptions. UWLS has also been found to have generally superior statistical properties: bias, MSE, and coverage relative to RE across 1,665 simulation designs compiled from four published studies authored by different teams of researchers. A recent study in this journal replicated UWLS's superior goodness of fit widely across both the CDSR and a new set of simulations. Due to reporting and interpretation errors, this recent study calls for the continued use of RE as the default meta-analysis estimator with limited applications of UWLS. We address this recent study's concerns and show why UWLS should be routinely reported in medical meta-analyses.

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arXiv2026

Z-Curve Plot: A Visual Diagnostic for Publication Bias in Meta-Analysis

Publication bias undermines meta-analytic inference, yet visual diagnostics for detecting and understanding model misfit due to publication bias are lacking. We propose the z-plot, a visual publication bias-focused absolute model fit diagnostic. The z-plot overlays the model-implied distribution of z-statistics on the observed distribution of z-statistics. Models that approximate the data well show minimal discrepancy between the observed and predicted distributions of z-statistics, whereas models that approximate the data poorly show systematic discrepancies. Discontinuities in the observed distribution of z-statistics at significance thresholds or at zero provide visual evidence of publication bias; models that account for this bias track these discontinuities. In addition, the z-plot facilitates visual model fit comparison of competing meta-analytic models within a single figure. We demonstrate the visualization and its interpretation with a Bayesian random-effects meta-analysis, a Bayesian PET model, a Bayesian three-parameter selection model, and RoBMA on simulated datasets and a real meta-analysis. The method is implemented in the RoBMA R package.

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arXiv2026

Meta-Analysis with JASP, Part I: Classical Approaches

Meta-analyses play a crucial part in empirical science, enabling researchers to synthesize evidence across studies and draw more precise and generalizable conclusions. Despite their importance, access to advanced meta-analytic methodology is often limited to scientists and students with considerable expertise in computer programming. To lower the barrier for adoption, we have developed the Meta-Analysis module in JASP (https://jasp-stats.org/), a free and open-source software for statistical analyses. The module offers standard and advanced meta-analytic techniques through an easy-to-use graphical user interface (GUI), allowing researchers with diverse technical backgrounds to conduct state-of-the-art analyses. This manuscript presents an overview of the meta-analytic tools implemented in the module and showcases how JASP supports a meta-analytic practice that is rigorous, relevant, and reproducible. Tutorial videos accompany the examples presented in this manuscript.

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arXiv2026

Comparing Variable Selection and Model Averaging Methods for Logistic Regression

Model uncertainty is a central challenge in statistical models for binary outcomes such as logistic regression, arising when it is unclear which predictors should be included in the model. Many methods have been proposed to address this issue for logistic regression, but their relative performance under realistic conditions remains poorly understood. We therefore conducted a preregistered, simulation-based comparison of 28 established methods for variable selection and inference under model uncertainty, using 11 empirical datasets spanning a range of sample sizes and number of predictors, in cases both with and without separation. We found that Bayesian model averaging (BMA) methods based on g-priors, particularly g = max(n, p^2), show the strongest overall performance when separation is absent. When separation occurs, penalized likelihood approaches, especially the LASSO, provide the most stable results, while BMA with the local empirical Bayes (EB-local) prior is competitive in both situations. These findings offer practical guidance for applied researchers on how to effectively address model uncertainty in logistic regression in modern empirical and machine learning research.

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arXiv2026

Efficient Bayes Factor Sensitivity Analysis via Posterior Density Ratios

Bayes factor sensitivity analysis examines how the evidence for one hypothesis over another depends on the prior distribution. In complex models, the standard approach refits the model at each hyper-parameter value, and the total computational cost scales linearly in the grid size. We propose a method that recovers the entire sensitivity curve from a single additional model fit. The key identity decomposes the Bayes factor at any hyper-parameter value $γ_x$ into an ``anchor'' Bayes factor at a fixed reference $γ_0$ and a Savage--Dickey density ratio in an extended model that places a hyper-prior on $γ$. Once this extended model is fit, the Bayes factor at any $γ_x$ follows from the anchor value and a ratio of two posterior density ordinates. To approximate this ratio, we employ the importance-weighted marginal density estimator (IWMDE). Because the sensitivity parameter enters the model only through the prior distribution on the model parameters, the data likelihood cancels in the IWMDE, reducing it to a simple ratio of prior density evaluations on the MCMC draws, without any additional likelihood computation. The resulting estimator is fast, remains accurate even with small MCMC samples, and substantially outperforms kernel density estimation across the full sensitivity range. The method extends naturally to simultaneous sensitivity over multiple hyper-parameters and to Bayesian model averaging. We illustrate it on a univariate Bayesian $t$-test with exact Bayes factors for validation, a bivariate informed $t$-test, and a Bayesian model-averaged meta-analysis, obtaining accurate sensitivity curves at a fraction of the brute-force cost.

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arXiv2025

Single-Dataset Meta-Analysis For Many-Analysts And Multiverse Studies

Empirical claims often rely on one population, design, and analysis. Many-analysts, multiverse, and robustness studies expose how results can vary across plausible analytic choices. Synthesizing these results, however, is nontrivial as all results are computed from the same dataset. We introduce single-dataset meta-analysis, a weighted-likelihood approach that incorporates the information in the dataset at most once. It prevents overconfident inferences that would arise if a standard meta-analysis was applied to the data. Single-dataset meta-analysis yields meta-analytic point and interval estimates of the average effect across analytic approaches and of between-analyst heterogeneity, and can be supplied by classical and Bayesian hypothesis tests. Both the common-effect and random-effects versions of the model can be estimated by standard meta-analytic software with small input adjustments. We demonstrate the method via application to the many-analysts study on racial bias in soccer, the many-analysts study of marital status and cardiovascular disease, and the multiverse study on technology use and well-being. The results show how single-dataset meta-analysis complements the qualitative evaluation of many-analysts and multiverse studies.

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arXiv2025

Meta-Analysis with JASP, Part II: Bayesian Approaches

Bayesian inference is on the rise, partly because it allows researchers to quantify parameter uncertainty, evaluate evidence for competing hypotheses, incorporate model ambiguity, and seamlessly update knowledge as information accumulates. All of these advantages apply to the meta-analytic settings; however, advanced Bayesian meta-analytic methodology is often restricted to researchers with programming experience. In order to make these tools available to a wider audience, we implemented state-of-the-art Bayesian meta-analysis methods in the Meta-Analysis module of JASP, a free and open-source statistical software package (https://jasp-stats.org/). The module allows researchers to conduct Bayesian estimation, hypothesis testing, and model averaging with models such as meta-regression, multilevel meta-analysis, and publication bias adjusted meta-analysis. Results can be interpreted using forest plots, bubble plots, and estimated marginal means. This manuscript provides an overview of the Bayesian meta-analysis tools available in JASP and demonstrates how the software enables researchers of all technical backgrounds to perform advanced Bayesian meta-analysis.

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arXiv2025

Handling Missingness, Failures, and Non-Convergence in Simulation Studies: A Review of Current Practices and Recommendations

Simulation studies are commonly used in methodological research for the empirical evaluation of data analysis methods. They generate artificial data sets under specified mechanisms and compare the performance of methods across conditions. However, simulation repetitions do not always produce valid outputs, e.g., due to non-convergence or other algorithmic failures. This phenomenon complicates the interpretation of results, especially when its occurrence differs between methods and conditions. Despite the potentially serious consequences of such "missingness", quantitative data on its prevalence and specific guidance on how to deal with it are currently limited. To this end, we reviewed 482 simulation studies published in various methodological journals and systematically assessed the prevalence and handling of missingness. We found that only 23% (111/482) of the reviewed simulation studies mention missingness, with even fewer reporting frequency (92/482 = 19%) or how it was handled (67/482 = 14%). We propose a classification of missingness and possible solutions. We give various recommendations, most notably to always quantify and report missingness, even if none was observed, to align missingness handling with study goals, and to share code and data for reproduction and reanalysis. Using a case study on publication bias adjustment methods, we illustrate common pitfalls and solutions.

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arXiv2025

Fair coins tend to land on the same side they started: Evidence from 350,757 flips

Many people have flipped coins but few have stopped to ponder the statistical and physical intricacies of the process. We collected $350{,}757$ coin flips to test the counterintuitive prediction from a physics model of human coin tossing developed by Diaconis, Holmes, and Montgomery (DHM; 2007). The model asserts that when people flip an ordinary coin, it tends to land on the same side it started -- DHM estimated the probability of a same-side outcome to be about 51\%. Our data lend strong support to this precise prediction: the coins landed on the same side more often than not, $\text{Pr}(\text{same side}) = 0.508$, 95\% credible interval (CI) [$0.506$, $0.509$], $\text{BF}_{\text{same-side bias}} = 2359$. Furthermore, the data revealed considerable between-people variation in the degree of this same-side bias. Our data also confirmed the generic prediction that when people flip an ordinary coin -- with the initial side-up randomly determined -- it is equally likely to land heads or tails: $\text{Pr}(\text{heads}) = 0.500$, 95\% CI [$0.498$, $0.502$], $\text{BF}_{\text{heads-tails bias}} = 0.182$. Furthermore, this lack of heads-tails bias does not appear to vary across coins. Additional analyses revealed that the within-people same-side bias decreased as more coins were flipped, an effect that is consistent with the possibility that practice makes people flip coins in a less wobbly fashion. Our data therefore provide strong evidence that when some (but not all) people flip a fair coin, it tends to land on the same side it started.

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arXiv2024

Assessing quality of selection procedures: Lower bound of false positive rate as a function of inter-rater reliability

Inter-rater reliability (IRR) is one of the commonly used tools for assessing the quality of ratings from multiple raters. However, applicant selection procedures based on ratings from multiple raters usually result in a binary outcome; the applicant is either selected or not. This final outcome is not considered in IRR, which instead focuses on the ratings of the individual subjects or objects. We outline the connection between the ratings' measurement model (used for IRR) and a binary classification framework. We develop a simple way of approximating the probability of correctly selecting the best applicants which allows us to compute error probabilities of the selection procedure (i.e., false positive and false negative rate) or their lower bounds. We draw connections between the inter-rater reliability and the binary classification metrics, showing that binary classification metrics depend solely on the IRR coefficient and proportion of selected applicants. We assess the performance of the approximation in a simulation study and apply it in an example comparing the reliability of multiple grant peer review selection procedures. We also discuss possible other uses of the explored connections in other contexts, such as educational testing, psychological assessment, and health-related measurement and implement the computations in IRR2FPR R package.

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arXiv2023

Footprint of publication selection bias on meta-analyses in medicine, environmental sciences, psychology, and economics

Publication selection bias undermines the systematic accumulation of evidence. To assess the extent of this problem, we survey over 68,000 meta-analyses containing over 700,000 effect size estimates from medicine (67,386/597,699), environmental sciences (199/12,707), psychology (605/23,563), and economics (327/91,421). Our results indicate that meta-analyses in economics are the most severely contaminated by publication selection bias, closely followed by meta-analyses in environmental sciences and psychology, whereas meta-analyses in medicine are contaminated the least. After adjusting for publication selection bias, the median probability of the presence of an effect decreased from 99.9% to 29.7% in economics, from 98.9% to 55.7% in psychology, from 99.8% to 70.7% in environmental sciences, and from 38.0% to 29.7% in medicine. The median absolute effect sizes (in terms of standardized mean differences) decreased from d = 0.20 to d = 0.07 in economics, from d = 0.37 to d = 0.26 in psychology, from d = 0.62 to d = 0.43 in environmental sciences, and from d = 0.24 to d = 0.13 in medicine.

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arXiv2023

Contextual aggregation and rapid updating of trial outcomes within a user-friendly open-source environment

The delayed and incomplete availability of historical findings and the lack of integrative and user-friendly software hampers the reliable interpretation of new clinical data. We developed a free, open, and user-friendly clinical trial aggregation program combining a large and representative sample of existing trial data with the latest classical and Bayesian meta-analytical models, including clear output visualizations. Our software is of particular interest for (post-graduate) educational programs (e.g., medicine, epidemiology) and global health initiatives. We demonstrate the database, interface, and plot functionality with a recent randomized controlled trial on effective epileptic seizure reduction in children treated for a parasitic brain infection. The single trial data is placed into context and we show how to interpret new results against existing knowledge instantaneously. Our program is of particular interest to those working on the contextualizing of medical findings. It may facilitate the advancement of global clinical progress as efficiently and openly as possible and simulate further bridging clinical data with the latest biostatistical models.

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arXiv2023

Empirical prior distributions for Bayesian meta-analyses of binary and time to event outcomes

Bayesian model-averaged meta-analysis allows quantification of evidence for both treatment effectiveness $μ$ and across-study heterogeneity $τ$. We use the Cochrane Database of Systematic Reviews to develop discipline-wide empirical prior distributions for $μ$ and $τ$ for meta-analyses of binary and time-to-event clinical trial outcomes. First, we use 50% of the database to estimate parameters of different required parametric families. Second, we use the remaining 50% of the database to select the best-performing parametric families and explore essential assumptions about the presence or absence of the treatment effectiveness and across-study heterogeneity in real data. We find that most meta-analyses of binary outcomes are more consistent with the absence of the meta-analytic effect or heterogeneity while meta-analyses of time-to-event outcomes are more consistent with the presence of the meta-analytic effect or heterogeneity. Finally, we use the complete database - with close to half a million trial outcomes - to propose specific empirical prior distributions, both for the field in general and for specific medical subdisciplines. An example from acute respiratory infections demonstrates how the proposed prior distributions can be used to conduct a Bayesian model-averaged meta-analysis in the open-source software R and JASP.

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arXiv2023

A general approximation to nested Bayes factors with informed priors

A staple of Bayesian model comparison and hypothesis testing, Bayes factors are often used to quantify the relative predictive performance of two rival hypotheses. The computation of Bayes factors can be challenging, however, and this has contributed to the popularity of convenient approximations such as the BIC. Unfortunately, these approximations can fail in the case of informed prior distributions. Here we address this problem by outlining an approximation to informed Bayes factors for a focal parameter $θ$. The approximation is computationally simple and requires only the maximum likelihood estimate $\hatθ$ and its standard error. The approximation uses an estimated likelihood of $θ$ and assumes that the posterior distribution for $θ$ is unaffected by the choice of prior distribution for the nuisance parameters. The resulting Bayes factor for the null hypothesis $\mathcal{H}_0: θ= θ_0$ versus the alternative hypothesis $\mathcal{H}_1: θ\sim g(θ)$ is then easily obtained using the Savage--Dickey density ratio. Three real-data examples highlight the speed and closeness of the approximation compared to bridge sampling and Laplace's method. The proposed approximation facilitates Bayesian reanalyses of standard frequentist results, encourages application of Bayesian tests with informed priors, and alleviates the computational challenges that often frustrate both Bayesian sensitivity analyses and Bayes factor design analyses. The approximation is shown to suffer under small sample sizes and when the posterior distribution of the focal parameter is substantially influenced by the prior distributions on the nuisance parameters. The proposed methodology may also be used to approximate the posterior distribution for $θ$ under $\mathcal{H}_1$.

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arXiv2023

Assessing inter-rater reliability with heterogeneous variance components models: Flexible approach accounting for contextual variables

Inter-rater reliability (IRR), which is a prerequisite of high-quality ratings and assessments, may be affected by contextual variables such as the rater's or ratee's gender, major, or experience. Identification of such heterogeneity sources in IRR is important for implementation of policies with the potential to decrease measurement error and to increase IRR by focusing on the most relevant subgroups. In this study, we propose a flexible approach for assessing IRR in cases of heterogeneity due to covariates by directly modeling differences in variance components. We use Bayes factors to select the best performing model, and we suggest using Bayesian model-averaging as an alternative approach for obtaining IRR and variance component estimates, allowing us to account for model uncertainty. We use inclusion Bayes factors considering the whole model space to provide evidence for or against differences in variance components due to covariates. The proposed method is compared with other Bayesian and frequentist approaches in a simulation study, and we demonstrate its superiority in some situations. Finally, we provide real data examples from grant proposal peer-review, demonstrating the usefulness of this method and its flexibility in the generalization of more complex designs.

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arXiv2023

Estimating the false discovery risk of (randomized) clinical trials in medical journals based on published p-values

The influential claim that most published results are false raised concerns about the trustworthiness and integrity of science. Since then, there have been numerous attempts to examine the rate of false-positive results that have failed to settle this question empirically. Here we propose a new way to estimate the false positive risk and apply the method to the results of (randomized) clinical trials in top medical journals. Contrary to claims that most published results are false, we find that the traditional significance criterion of $α= .05$ produces a false positive risk of 13%. Adjusting $α$ to .01 lowers the false positive risk to less than 5%. However, our method does provide clear evidence of publication bias that leads to inflated effect size estimates. These results provide a solid empirical foundation for evaluations of the trustworthiness of medical research.

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arXiv2022

Informed Bayesian survival analysis

We overview Bayesian estimation, hypothesis testing, and model-averaging and illustrate how they benefit parametric survival analysis. We contrast the Bayesian framework to the currently dominant frequentist approach and highlight advantages, such as seamless incorporation of historical data, continuous monitoring of evidence, and incorporating uncertainty about the true data generating process. We illustrate the application of the Bayesian approaches on an example data set from a colon cancer trial. We compare the Bayesian parametric survival analysis and frequentist models with AIC/BIC model selection in fixed-n and sequential designs with a simulation study. In the example data set, the Bayesian framework provided evidence for the absence of a positive treatment effect on disease-free survival in patients with resected colon cancer. Furthermore, the Bayesian sequential analysis would have terminated the trial 10.3 months earlier than the standard frequentist analysis. In a simulation study with sequential designs, the Bayesian framework on average reached a decision in almost half the time required by the frequentist counterparts, while maintaining the same power, and an appropriate false-positive rate. Under model misspecification, the Bayesian framework resulted in higher false-negative rate compared to the frequentist counterparts, which resulted in a higher proportion of undecided trials. In fixed-n designs, the Bayesian framework showed slightly higher power, slightly elevated error rates, and lower bias and RMSE when estimating treatment effects in small samples. We have made the analytic approach readily available in RoBSA R package. The outlined Bayesian framework provides several benefits when applied to parametric survival analyses. It uses data more efficiently, is capable of greatly shortening the length of clinical trials, and provides a richer set of inferences.

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