Stats

Survival analysis plays a central role in medical research. Although the Cox proportional hazards (CoxPH) model remains the standard approach, machine learning and deep learning methods have been increasingly adopted. However, many published comparisons have relied on a single train–test split, which may produce unreliable performance estimates, particularly for unstable modelling approaches. This study compared CoxPH (LASSO-selected), Random Survival Forest (RSF), and Long Short-Term Memory (LSTM) networks using four survival datasets: breast cancer ($n=4024$), heart failure ($n=299$), recidivism ($n=4618$), and the Mayo Clinic Primary Biliary Cholangitis Sequential Dataset (PBC2; $n=312$) containing time-varying covariates. Model performance was evaluated using a two-stage protocol comprising a conventional 80–20 stratified train–test split followed by 100 repeated stratified 80–20 train–test splits. Performance was assessed using the concordance index (C-index), integrated Brier score (IBS), and time-dependent area under the receiver operating characteristic curve (AUC), with statistical significance determined through distributional assumption testing, adaptive omnibus tests, and Bonferroni-adjusted pairwise comparisons. For the three static datasets, single train–test splits suggested moderate LSTM performance (C-index: 0.65–0.70); however, repeated evaluation showed that this finding was not robust. Across 100 iterations, CoxPH and RSF consistently outperformed LSTM (all $p<0.001$), achieving mean C-index values ranging from 0.66 to 0.73 compared with 0.31 to 0.42 for LSTM, with very large effect sizes (Cohen’s d: 6–30). In contrast, on the longitudinal PBC2 dataset, the LSTM-based model achieved the highest repeated C-index ($0.806\pm 0.040$), compared with $0.777\pm 0.042$ for CoxPH and $0.779\pm 0.040$ for RSF, with only 1.2% performance degradation under repeated evaluation. These findings indicate that reliance on a single train–test split can produce unstable and potentially unrepresentative estimates of model performance. Traditional survival models were more accurate and stable for datasets containing only static baseline covariates, whereas the LSTM-based model showed higher discrimination on longitudinal survival data with genuine temporal structure, though this advantage is confounded with greater access to patient history and cannot be attributed to architecture alone. Overall, the results underscored the importance of repeated evaluation as a more reliable framework for comparing survival models, and are consistent with, though do not conclusively establish, the importance of matching model architecture to data characteristics. Full article

Supervised learning in fields such as genomics and medical imaging is often hindered by the high cost of expert data annotation. Active learning addresses this bottleneck by iteratively selecting the most informative unlabeled samples for labeling. However, in high-dimensional environments, traditional diversity-based query strategies lose their effectiveness due to the degradation of global distance metrics. To address these challenges, this paper proposes a novel framework, Active Learning via Subspace Ensembles and Similarity (ALSES). Instead of relying on global distances, ALSES constructs a similarity matrix by sampling an ensemble of random feature subspaces. The subspaces are filtered based on their discriminative power, and pairwise sample similarities are aggregated using cluster co-occurrence. This structural representation is integrated into a hybrid batch selection strategy that balances model uncertainty and data representativeness. Extensive evaluations on simulated datasets and real-world high-dimensional cancer cohorts demonstrate that ALSES consistently outperforms standard active learning baselines. The framework effectively isolates informative variables and achieves superior classification accuracy with significantly fewer labeled instances, demonstrating its robustness in complex, noisy applications. Full article

Background. Human populations are exposed to complex chemical mixtures, making interaction detection a central challenge in environmental epidemiology. We benchmarked methods for prediction and recovery of interaction structure. Methods. Eight approaches—main-effects Lasso (glmnet_main), interaction Lasso (glmnet_int), hierNet, Random Forests, Bayesian Kernel Machine Regression (BKMR), quantile g-computation (qgcomp), weighted quantile sum regression (gWQS) and SuperLearner—were evaluated across eight linear/nonlinear, additive/interaction, continuous/binary data-generating processes (500 replicates each). Every method completed in all 500 replicates of all eight scenarios. Prediction was assessed on held-out test data using observed-outcome and oracle-referenced metrics; interaction detection was assessed against three known pairwise interactions among 45 candidate pairs, using both hard selection and a threshold-free ranking criterion. BKMR was evaluated at 2000 versus 25,000 MCMC iterations with multi-chain convergence diagnostics. Sensitivity analyses varied sample size, exposure correlation, signal strength, and interaction form. BKMR was also applied illustratively to six metals and prevalent diabetes in NHANES. Results. In additive settings, observed-outcome prediction was similar across methods, but oracle-referenced continuous-outcome error differed by up to six-fold. With interactions, interaction-aware methods clearly outperformed additive-only approaches on the continuous oracle-referenced metrics: in LMI, the oracle MSE was 1.57 for hierNet and 1.87 for glmnet_int against 3.80 for glmnet_main and 4.94 for qgcomp. glmnet_int and hierNet showed comparable sensitivity; hierNet had a modestly lower mean per-replicate false discovery proportion in paired comparisons, while pooled false discovery favored hierNet in the continuous scenarios and glmnet_int in the binary ones; pooled false discovery rates were 0.79 to 0.82 in every interaction scenario, so roughly four in five selected pairs were false. In the scenarios without true interactions, the pooled false discovery rate was exactly 1. Under threshold-free ranking, BKMR was competitive with the penalized methods (pair-ranking AUC: 0.758 to 0.781 across the four interaction scenarios). BKMR’s apparent instability at 2000 iterations reflected inadequate sampling: 93% of monitored parameters had a Gelman–Rubin statistic above 1.1 and the minimum effective sample size was 7.5, whereas at 25,000 iterations the median statistic was 1.02 and the oracle MSE in LMI fell from 6.38 to 2.08. In NHANES, lead, manganese, and iron had the highest posterior inclusion probabilities, with predominantly nonlinear exposure–response functions. Conclusions. Method choice matters most when interactions are present. Interaction-aware methods are preferable when joint effects are relevant, selected interactions require replication given the high false discovery burden, and BKMR comparisons should report sampling budgets and convergence diagnostics rather than treating a short chain as characteristic of the method. Full article

Non-inferiority (NI) clinical trials have gained immense popularity within the last decades, especially in cancer and cardiovascular studies. These trials are designed to establish the non-inferiority of a new experimental treatment as compared to the existing active control. In other words, NI trials are required to demonstrate that the efficacy of an experimental treatment is not unacceptably worse than that of an active control by more than a pre-specified small margin. We consider three-arm NI trials that have been widely acknowledged as the Gold Standard. Three-arm NI trials aim to simultaneously establish both NI and the assay sensitivity (AS). Hence, the analysis of three-arm NI trials involves multiple hypothesis testing. The existing literature on the Bayesian modeling of three-arm NI trials suggests implementing a test procedure based on the joint posterior probability of the NI and AS hypotheses. This joint testing of NI with AS resembles the framework of intersection-union (IU) testing, which may result in a very conservative test. In this article we propose a novel Bayesian testing based on an isotonic transformation in conjunction with Bayes factors. Bayes factors for assessing NI with AS are computed based on Gibbs Sampling. The performance of the proposed testing is evaluated through simulated data sets under varying scenarios. Empirical results show that the proposed Bayesian method gives better control in terms of Type-I error rates, and more powers than existing Bayesian tests. The usefulness of our test is illustrated by synthetic data from the Mildly Asthmatic Study. Full article

Subjective wellbeing is multidimensional, and satisfaction with financial circumstances, personal relationships, and time use may be interrelated while displaying different temporal, sociodemographic, and contextual patterns. Comparative evidence examining these domains jointly, including their interactions and country-level clustering, remains limited. This study examined variation in financial-situation, personal-relationship, and time-use satisfaction across survey years, education levels, age groups, sexes, and European national contexts. A repeated cross-sectional comparative analysis was conducted using 864 aggregated country–year–education–age–sex cells from Denmark, Estonia, Finland, Norway, Slovakia, Slovenia, Sweden, and Türkiye in 2013, 2018, and 2022. The data comprised three education levels, six age groups, and female and male categories. Pairwise comparisons between survey years were assessed using independent-samples tests, with Cohen’s d and 95% confidence intervals used to summarize standardized temporal differences. Three weighted partial linear mixed-effects models were estimated, with financial-situation, personal-relationship, and time-use satisfaction serving separately as outcomes. The models included the other two satisfaction domains, education, age, sex, two-way interactions, selected three-way interactions, and random intercepts for country and country–year combinations. Type III tests with Satterthwaite’s approximation assessed overall fixed-effect contributions. Financial-situation satisfaction declined from 2013 to 2018 and gained to approximately its 2013 level from 2018 to 2022, while the 2013 and 2022 levels were not clearly different. Personal-relationship satisfaction was higher in 2018 and 2022 than in 2013, whereas no clear difference was found between 2018 and 2022. Time-use satisfaction showed no statistically clear temporal variation. Temporal effect sizes were generally small. Personal-relationship satisfaction was positively associated with financial-situation satisfaction and was strongly associated with time-use satisfaction. Education, age, and sex made domain-specific contributions, and several domain associations varied across sociodemographic groups, particularly through education-by-age interactions. Marginal (R²) values ranged from 0.628 to 0.807, while conditional (R²) values ranged from 0.953 to 0.965. Financial, relational, and time-use satisfaction were connected but not interchangeable, and their associations varied across demographic and national contexts. Wellbeing monitoring may therefore benefit from considering material, relational, and temporal domains jointly. Because the analysis used aggregated observational data from selected eight countries, causal, individual-level, and Europe-wide conclusions cannot be drawn. Full article

This study proposes a flexible three-parameter distribution to capture complex patterns in continuous positive data. By combining the generalized log-logistic odd generator with an error function distribution, our model successfully accommodates various density shapes, including strong skewness and bimodality. Using Monte Carlo simulations and maximum likelihood estimation, we validate our regression model’s estimators and confirm that larger sample sizes yield high precision, consistency, and inferential stability. Using data from hospitalized depression patients, we demonstrate the model’s practical application. This new distribution fits the data better than competing models, supported by lower statistical metrics and likelihood ratio tests. Furthermore, the variables’ “simplicity” and “fatalism” significantly influence observed depression levels. Full article

Sparse count data, such as patent document–keyword matrices, often contain excessive zeros and overdispersion, making conventional distance-based clustering methods less suitable. This study proposes a zero-inflated likelihood-based graph neural clustering method with a zero-inflated negative binomial likelihood, denoted as ZIL-GNC-ZINB. The proposed method combines graph-smoothed node representations with cluster-specific zero-inflation probabilities and count-intensity parameters. By incorporating graph-neighborhood information into the cluster membership update, ZIL-GNC-ZINB jointly accounts for structural zeros, overdispersion, and local graph relationships among observations. The proposed method was applied to a quantum-computing patent document–term matrix consisting of 9416 patent documents and 82 reduced keywords. Compared with K-means, K-means clustering based on principal component analysis (PCA+K-means), and K-means clustering based on graph convolutional networks (GCN+K-means), ZIL-GNC-ZINB achieved the best performance in terms of negative log-likelihood (NLL), zero area underneath the receiver operating characteristic (ROC) curve (AUC), and zero Brier score. The resulting clusters revealed interpretable quantum-computing sub-technologies, including photonic qubit control, hybrid quantum–classical computing, superconducting qubit hardware, and quantum security networks. Simulation experiments under zero proportions of 0.5, 0.7, and 0.9 further showed that the proposed method becomes increasingly effective as zero inflation becomes more severe. In the extreme zero-inflation setting, ZIL-GNC-ZINB achieved the best performance in NLL, Zero AUC, adjusted rand index (ARI), normalized mutual information (NMI), and clustering accuracy (ACC). These results demonstrate that zero-inflated likelihood modeling combined with graph-based clustering provides an effective and interpretable framework for sparse high-dimensional count data. Full article

Background: The proliferation of fitness apps and wearable technology provides researchers interested in health and fitness with vast opportunities to test hypotheses involving a continuous stream of data collected on individual research participants in real-world settings. Although there are a variety of methods available to analyze such repeated measures data, one method that may benefit researchers in these endeavors is Area Under the Curve (AUC). To our knowledge, AUC has yet to be assessed for efficacy with many repeated measures collected from fitness apps. As such, the purpose of this study was to assess the efficacy of AUC with larger numbers of repeated measures typical of a fitness app using simulated data. Methods: We generated two samples of 21 hypothetical cyclists with 30 and 100 repeated measures of performance data (speed, time, and power) based on a Strava app segment, and calculated AUC using the trapezoidal rule and definite integrals with the best-fitting line. We then assessed the relations between time, speed, and power with all three calculations using bivariate correlations, multiple regression analysis, and a mediation analysis whereby power was hypothesized to predict a reduction in time indirectly through speed. We repeated these analyses with data assuming a normal and a lognormal distribution, and with equal versus unequal timepoints between consecutive repeated measures in the normal distribution. Results: There was little difference in relative performance comparing the two AUC calculation methods in the two samples (30 versus 100 repeated measures). However, there was a difference in the proportion mediated in the mediation results when comparing the two samples based on the number of repeated measures and spacing between consecutive repeated measures. Conclusions: The results of this study suggest that Area Under the Curve may be a viable method for assessing cumulative level of a behavior when dealing with datasets including many repeated measures such as those acquired from wearable technology and fitness apps. However, there may be differences in results when dealing with different numbers of repeated measures and variability in time between events. As such, future studies should assess AUC with larger numbers of repeated measures using non-simulated data in diverse performance scenarios. Full article

Sample sizes might be small in a variety of applications. Many classical and often-applied statistical methods rely on asymptotic approximations and, therefore, should not be used in the case of small sample sizes. Approaches that can be applied to small data sets often involve computer-intensive methods such as permutation tests and bootstrapping. As an alternative, a modified Chebyshev inequality was proposed by Beasley et al. (Applied Statistics 2004; 53, 95–108) and suggested for nonparametric testing. Here, it is shown that this modified Chebyshev inequality does not hold in general and, therefore, it should not be used to construct a statistical test. Available nonparametric tests that can be recommended for small sample sizes are discussed. Full article

Rule-defined rankings often transform continuous marks, discrete judgments, trimming rules, caps, truncation, and tie-breaking variables into a single official order. When ranking margins are small, a formally valid outcome may nevertheless be sensitive to marginal changes in the recorded decision state. This article presents Score Cloud Analysis as a rule-aware statistical sensitivity-reporting method for such systems. The method represents the official score as a deterministic function of recorded inputs and recomputes scores and ranks under finite perturbations, rather than relying on local linear approximations. It defines deterministic diagnostics, including directional Group A/Group C (A/C) decision exposures and their aggregate contested-point exposure, total sensitivity exposure, fragility-to-margin ratios, Score Cloud overlap, and single-call rank sensitivity, and separates these from scenario-conditional Monte Carlo Rank Cloud frequencies. The method is illustrated using a synthetic Wushu Taolu case study because that setting contains majority decisions, trimmed rater marks, discrete difficulty values, Head Judge adjustments, and tie-break rules. The synthetic experiment is an internal-consistency stress test, not an empirical validation and not an estimate of judging-error rates. A small sensitivity study varies perturbation scale and intra-athlete dependence to show which conclusions are scenario-specific. The method separates procedural validity from local rank robustness and is transferable to other reconstructable, rule-based, rater-mediated ranking systems. Full article

Distinguishingstructured nonlinear temporal behaviour from stochastic variability remains a fundamental challenge in the analysis of noisy and nonstationary time series, particularly when conventional nonlinear methods are sensitive to noise and finite observational records. This study presents a simulation-based modified Singular Spectrum Analysis (SSA) framework for investigating finite-time nonlinear temporal structures through signal extraction, component-wise simulation, and eigenvalue distribution analysis. The proposed framework decomposes time series into interpretable components and systematically compares empirical behaviour with white-noise processes and canonical nonlinear benchmark systems. Using a noisy chaotic benchmark with a known three-dimensional state-space structure, a direct comparison with standard SSA criteria was conducted to examine component identification under the same benchmark setting, with the proposed framework identifying three components compared with two indicated by the conventional criteria. The methodology is demonstrated using COVID-19 case time series from the United Kingdom (UK) and the Kingdom of Saudi Arabia (KSA), together with monthly sunspot numbers as an independent application, as representative real-world time series. The modified SSA identified distinct temporal structures within these datasets, with eigenvalue distributions differing from those expected under pure white-noise processes while exhibiting similarities to canonical nonlinear benchmark systems. Reconstructed phase spaces displayed bounded attractor-like geometries consistent with structured nonlinear temporal behaviour over finite observational intervals. The proposed framework provides a complementary nonparametric statistical methodology for investigating structured nonlinear temporal behaviour in noisy observational time series through signal extraction and simulation-based benchmarking. Full article

Increasing the accuracy of age-at-death estimation using two skeletal-characteristic stages can enhance confidence in biological identification using forensic science. Transition analysis and the inverse prediction method with a Bayesian approach was proposed in this study to estimate age from skeletal characteristics measured as binary variables. The Bayesian approach with adaptive rejection sampling was employed to derive the posterior distributions of the transition model parameters and the age classification threshold in order to reverse the age-at-death estimation from a binary predictor. The posterior odds ratio was proposed to assess the value of observed evidence for the age estimation. Subsequently, the efficiency of our proposed method, measured by the percentage of correct classification, was evaluated by Monte Carlo simulation and compared with the Maximum Likelihood Estimation with the inverse prediction method. The simulation results supported the advantages of our proposed method, especially when using small sample sizes. In an application involving chest X-ray images with two chest plate ossification stages, the results showed that our method could identify suitable features of the chest plate, providing good age-prediction performance with a high percentage of accuracy. Full article

Generative probabilistic models differ in a fundamental way that is rarely measured directly: some permit exact inference, while others are more expressive but require their likelihood to be estimated. This study compares three model families on binarized Fashion-MNIST and MNIST under identical preprocessing, identical data splits, and matched parameter counts, evaluating every model by test log-likelihood on a common scale. Sum-product networks and mixtures of Bernoullis return exact likelihoods; the likelihood of a restricted Boltzmann machine is obtained by annealed importance sampling and reported with the effective sample size of the importance weights and a convergence study. Three results follow. First, the structure of a sum-product network matters more than its size: changing only which pixels are assigned to which leaf region, at a fixed parameter count of 706,800, is worth 38.7 nats on Fashion-MNIST and 41.2 nats on MNIST, whereas multiplying the capacity of a flat mixture eightfold yields approximately 13 nats. A network whose regions are misaligned with the data performs worse than a model with no hierarchy at all. Second, once the regions are aligned, the benefit of hierarchy depends on the data: the network exceeds the best flat mixture by 17.2 nats on Fashion-MNIST but falls 2.0 nats short on MNIST, where whole-image prototypes already suffice. Third, the restricted Boltzmann machine outperforms every tractable model tested at matched capacity, leading the best of them by 11.4 nats on Fashion-MNIST and 46.1 nats on MNIST, which quantifies the cost of guaranteeing exact inference. Exact inference nonetheless carries a practical benefit: for image completion, the sum-product network computes conditional marginals exactly and improves on max-product in every configuration tested. Training a fully connected Boltzmann machine to convergence proved infeasible on the available hardware, and the computational limitations are reported quantitatively. Full article

Feature selection is critical for resolving cell-type heterogeneity in single-cell RNA sequencing (scRNA-seq). DUBStepR (Determining the Underlying Basis using Stepwise Regression) is a widely used gene selection method for scRNA-seq designed to identify feature genes that maximize cell-type separation. DUBStepR has been reported to perform effectively in this domain; however, its reliance on linear Pearson correlation and rigid thresholding limits its effectiveness on complex, high-dimensional datasets. Three enhancements are presented in this study: RFCell-DUBStepR, which uses random forests to capture expression-level importance; Copula-DUBStepR, which models non-linear correlations via Gaussian Copulas; and Zqt-DUBStepR, which utilizes quantile-based selection for improved gene retention. Using both simulated and real-world datasets (scRNA-seq), these modifications are shown to resolve the biases of the original algorithm. The modified methods consistently select a more representative gene set and yield higher clustering accuracy across varying levels of biological complexity. These findings establish the modified DUBStepR frameworks as more reliable tools for high-fidelity subpopulation identification in downstream single-cell analysis. Full article

In this paper, we introduce the type II exponentiated half logistic-odd log-logistic-G power series class of distributions for modeling symmetric, skewed and heavy-tailed data with diverse hazard rate shapes. The proposed class of distributions is obtained by compounding the generalized family of distributions involving the type II exponentiated half logistic-G and odd log-logistic-G families with a discrete power series distribution. Various statistical properties of the proposed class of distributions, including moments, survival and hazard rate functions, order statistics, probability weighted moments, and Rényi entropy are derived. The model parameters are estimated using different estimation methods, and their performance is evaluated through Monte Carlo simulation studies. Finally, the flexibility and applicability of the proposed class of distributions are illustrated using real data sets. The results demonstrate that the proposed model provides a better fit than several existing competing models. Full article

Continuous healthcare data often deviate from normality, which can substantially increase the risk of making invalid inferences, given that many inferential statistical procedures rely on normality assumption. To obviate this issue, we propose a new family of non-normal distributions based on a linear combination of the quantile functions of standard logistic and uniform (0, 1) distributions. This new family of non-normal distributions is studied within three different methods: L-moments, conventional moments, and percentiles. Its performance is compared among the three methods in the context of parameter estimation and data modeling. The results of Monte Carlo simulation and bootstrapping techniques indicate that the L-moment-based estimates of parameters of L-skewness and L-kurtosis are substantially less biased than their percentile-based estimates of left–right tail-weight ratio (a measure of skewness) and tail-weight factor (a measure of kurtosis), which in turn are superior to their moment-based counterparts of skewness and kurtosis, especially for small sample sizes and higher-order moments. On the other hand, the data modeling results indicate that the percentile-based fits of the proposed distributions provide slightly better approximations to real-world healthcare data than their L-moment-based counterparts, whereas both percentile- and L-moment-based methods are superior to their conventional moment-based counterparts. Full article

In the present work, we study combined m-consecutive-$k$-out-of-n and consecutive $k_c$-out-of-n reliability systems under imperfect cold standby redundancy. The proposed framework extends the ordinary perfect standby assumption by allowing the activation of the spare system to be successful with a given coverage probability. The system-level redundancy policy is considered, while the classical perfect cold standby model is obtained as a special case. Exact reliability representations for the resulting structures are discussed through signature-based arguments. In particular, expressions for the reliability function, the Mean Time to Failure and the Mean Residual Lifetime are provided. Special emphasis is also placed on statistical inference under right-censored lifetime data. A numerical study is carried out to illustrate the effect of imperfect coverage, censoring, and design parameters on the performance of the proposed reliability schemes. Full article