The DerSimonian and Laird (DL) method, commonly used in meta-analysis, often underestimates the between-study variance. The underestimation causes the confidence intervals to have less than the expected 95% coverage, resulting in inconclusive research findings. The present study introduces the use of the jackknife technique to improve the DL between-study variance estimator for meta-analyses of proportions from single-arm studies, as well as suggests certain transformations in combination with the jackknife technique. The proposed methodology is intended for settings in which the parameter of interest is an event probability or proportion, particularly for small numbers of studies with large variation. Simulation studies for binomial observations are conducted to compare the relative biases and coverage probabilities of the mean ( mu$$ \mu $$ ) obtained by the DL, Paule and Mandel (PM), Restricted Maximum Likelihood (REML), and Hartung-Knapp-Sidik-Jonkman (HKSJ) methods with our proposed DerSimonian and Laird jackknife (DLJ) and transformed DerSimonian and Laird jackknife (TDLJs) methods. The simulation results show that our proposed DLJ and TDLJ estimators better quantify the between-study variance in meta-analysis of binary events, especially for small numbers of studies with larger variation and high probability of mu$$ \mu $$ respectively. Three real life examples are presented to determine the performance of our new proposed between-study variance estimators.
Epidemic waves are often shaped by uncertain external drivers, such as environmental variability or behavioral and policy changes, that can randomly amplify or dampen transmission. Capturing this randomness requires models whose dynamics evolve under time-varying, stochastic influences. In this paper, we introduce a stochastic Susceptible-Asymptomatic-Symptomatic-Removed (SuASR) framework that embeds random external factors directly into the epidemic mechanism through an extended continuous-time Markov chain (CTMC). The proposed framework is flexible enough to represent epidemic dynamics both with reinfection and with infection-induced immunity, depending on the epidemiological setting under study. Unlike standard Markovian epidemic models, our formulation explicitly tracks two concurrent infectious sources (asymptomatic and symptomatic), yielding coupled infection pathways and substantially richer transient behavior. A key contribution is analytical tractability, where we derive computable expressions for the joint distribution of asymptomatic and symptomatic infection-event counts and develop tools tailored to extreme-outbreak risk, including the distribution of the maximum infectious burden. These results enable probabilistic quantification of epidemic severity beyond mean trajectories, providing direct estimates of the likelihood of rare but consequential surges. We validate the model through extensive sensitivity analysis and an application to the H1N1 influenza epidemic, illustrating how stochastic external influences reshape outbreak profiles, total infections from both sources, and the probability of extreme epidemic scenarios
ABSTRACT Machine learning (ML) models are increasingly used in precision medicine to predict outcomes, prioritize candidate biomarkers, and support treatment decision‐making. Despite their growing adoption, clinical interpretability remains challenging because different optimization objectives correspond to distinct statistical estimands, while post hoc explanation methods often produce complex outputs that are difficult for nontechnical users to interpret. Therefore, frameworks are needed to clarify what model outputs represent and translate technical explanations into clinically meaningful language. To demonstrate how clinical practitioners can select appropriate models, loss functions, and interpretability techniques, we present a tutorial designed to enhance the interpretability of supervised ML models in clinical settings. Our framework integrates feature attribution methods with large language models (LLMs). We first clarify how commonly used loss functions define distinct clinical objectives, ranging from prognostic outcome prediction to individualized treatment rule (ITR) estimation. We then introduce SHapley Additive exPlanations (SHAP) and local interpretable model‐agnostic explanations (LIME) as complementary approaches for global and local interpretation, illustrating how their visualizations summarize model‐based feature contributions. To reduce the programming burden of implementing end‐to‐end ML workflows, we develop an interactive Shiny application that guides users through data input, model training, feature attribution, and LLM‐assisted interpretation. Once installed and configured, users can perform these analyses through a graphical interface without writing analysis code. LLMs serve as an interpretation layer that translates model objectives, predictions, and SHAP/LIME results into concise, clinically meaningful explanations. We also evaluate the reproducibility, faithfulness, and sensitivity of these LLM‐assisted explanations.
ABSTRACT Competing‐risks prediction requires validation methods that assess predictive support for both event time and event type. This is difficult for cause‐specific hazard models because out‐of‐sample log‐scores require positive, well‐defined hazards over the validation horizon, and rare event causes can lead to unstable cause‐specific estimates. We develop the Bayesian hierarchical piecewise‐exponential cause‐specific hazards model (), a competing‐risks model designed for posterior predictive validation using cross‐validated log‐scores. The model specifies positive piecewise‐exponential baseline hazards for each cause and places hierarchical priors on cause‐specific regression coefficients, allowing covariate effects to borrow information across causes while retaining cause‐specific interpretation. Predictive performance is evaluated using cross‐validated posterior predictive log‐scores under the cause‐specific hazards representation. Simulation studies show that the Bayesian piecewise‐exponential framework improves out‐of‐sample predictive support and model‐selection performance across settings with varying signal strength, sample size, censoring, cause imbalance, and cross‐cause heterogeneity. Hierarchical pooling provides the largest benefit when cross‐cause heterogeneity is low to moderate, event causes are imbalanced, or information for rare causes is limited. When true cause‐specific effects are highly heterogeneous, the advantage of partial pooling diminishes, reflecting the expected bias–variance trade‐off. A Surveillance, Epidemiology, and End Results (SEER) colorectal cancer application further demonstrates the practical utility of the method: the treatment‐extended specification evaluated with achieves the best predictive performance, and hierarchical pooling narrows posterior credible intervals for selected rare‐cause coefficients. These findings support as a stable Bayesian posterior predictive framework for imbalanced multi‐cause competing‐risks prediction.
ABSTRACT Mendelian randomization (MR) using genome‐wide association study (GWAS) summary statistics is widely used for causal inference. However, conventional MR methods relying on population‐based GWAS are vulnerable to biases arising from family‐level confounders. While family‐based GWAS (FGWAS) designs offer a solution to address these effects, existing MR methodologies are not optimized for the unique structure of FGWAS data, often resulting in reduced statistical power. Therefore, in this paper, we propose the MRcML‐Family (MR based on constrained maximum likelihood for families), a novel method specifically tailored for FGWAS summary statistics. The core innovation of MRcML‐Family lies in its unified framework which simultaneously integrates genetic information from offspring (direct effects) and parents (indirect effects) as instrumental variables. By applying different constraints, the method effectively identifies and corrects for horizontal pleiotropy. Comprehensive simulation studies demonstrate that MRcML‐Family yields nearly unbiased causal estimates and maintains robust Type I error rate control whether or not the instrument strength independent of direct effect assumption holds, even in challenging scenarios with a limited number of SNPs and small FGWAS sample sizes. Furthermore, real‐world data analyses using UK Biobank data show that MRcML‐Family provides causal estimates highly consistent with existing literature and recovers the established “gold standard” relationship between height and body mass index. Additionally, it showed higher statistical power than the compared methods in the evaluated scenarios, mitigating the efficiency loss typically associated with family‐based designs.
