statistical association analysis

Statistical methods face persistent conceptual disagreements, interpretive ambiguities, and practical controversies across disciplines, exacerbated by textbook and journal guidelines that propagate a monolithic paradigm while obscuring foundational uncertainties. Human cognitive limitations and fragmented domain knowledge further impede rigorous statistical reasoning. Method: We propose a critical statistical thinking framework that rejects dogmatic interpretations of *p*-values and confidence intervals. Instead, it advocates descriptive modeling as an initial step, explicit documentation of assumption dependencies, systematic cross-disciplinary literature comparison, and integration of epistemological reflection with empirical constraint assessment. Contribution/Results: This reframes statistical inference as plausible reasoning grounded in inherently unverifiable premises—not definitive conclusions. The framework enhances transparency, reproducibility, and interdisciplinary communicability of statistical practice, fostering a more reflective, evidence-informed, and consensual methodological discourse.

In matched case-control studies, conventional statistical analyses of secondary outcomes can yield biased estimates by ignoring the unequal sampling probabilities induced by the matching design. This work proposes a novel likelihood-based approach that systematically incorporates the sampling structure inherent to matched designs, introducing sampling weights to produce unbiased estimation and valid inference for secondary outcomes. The method is theoretically guaranteed to deliver consistent estimators and confidence intervals with accurate coverage. Extensive simulations and an application to real-world diabetes data demonstrate its substantial superiority over existing methods. An R implementation of the proposed approach is publicly available.

This study addresses the lack of a unified computational, management, and visualization framework for characterizing diverse pairwise associations—such as linear correlation, nonlinear dependence, and Simpson’s paradox—between numeric and categorical variables. Methodologically, we propose an end-to-end analytical framework: (1) a unified R interface integrating 12 heterogeneous association measures; (2) a standardized tidy data structure enabling consistent storage, retrieval, and cross-type comparison of results; and (3) an enhanced multidimensional heatmap (implemented in the *bullseye* package, built upon *ggplot2*) supporting grouped comparisons, metric overlay, and automated paradox detection. Our key contribution is the first standardized,全流程 implementation of association analysis in R, significantly improving exploratory efficiency, reproducibility, and interpretability. The framework uniquely enhances detection of nonlinear relationships, mixed-variable dependencies, and structural biases—filling a critical gap in the R ecosystem for out-of-the-box, principled association analysis.

In large-scale observational studies, complete observation and control of confounders is often infeasible, leading conventional regression models (e.g., linear, logistic, Cox) to yield spurious associations. To address this, we propose a latent-variable-driven confounding structure model. Using both real-world and synthetic data simulations, we quantify how residual spurious association decays as the number of controlled confounders increases, and derive its closed-form mathematical expression. Our results demonstrate that even after adjusting for over 20 confounders, highly implausible causal hypotheses may still appear statistically “confirmed”; residual bias arising from unobserved latent confounders proves systematic and persistent. This work exposes a fundamental limitation of standard regression in causal inference and provides a computationally tractable theoretical framework—along with empirical benchmarks—for quantifying confounding bias. It thereby advances rigor, transparency, and caution in causal interpretation within survey-based research.

This study addresses the limitation of traditional canonical correlation analysis (CCA) in capturing spatially varying local associations between sets of variables. To overcome this, the authors propose, for the first time, a geographically weighted canonical correlation analysis (GWCCA), which localizes classical CCA by incorporating a spatial distance–based weighting scheme. This approach enables the estimation of location-specific canonical correlation coefficients, thereby revealing fine-grained, multivariate heterogeneous association structures between two variable sets across geographic space. The method’s effectiveness is demonstrated through synthetic data and an empirical application to county-level health outcomes and social determinants in the United States, where GWCCA successfully recovers known spatial patterns. These results underscore its potential utility in public health, urban planning, and other domains requiring spatially explicit multivariate analysis.

Traditional genome-wide association studies (GWAS) typically perform separate single-nucleotide polymorphism (SNP) association tests and Hardy–Weinberg equilibrium (HWE) tests, relying on arbitrary thresholds to filter loci—a practice that can introduce false positives or discard valuable information. This work proposes a unified conditional testing framework that integrates HWE information directly into the association analysis by conditioning the Pearson χ² statistic from the 3×2 case–control contingency table on the HWE χ² statistic computed from controls alone. By leveraging asymptotic distribution theory, this approach eliminates the need for a standalone HWE filtering step and yields more accurate p-values. Both simulations and real-data analyses on alopecia demonstrate that the method substantially improves statistical power and SNP ranking accuracy compared to existing retrospective approaches, thereby reducing replication costs and enhancing fine-mapping resolution.

This study addresses the common misuse of Pearson correlation for mixed variable types—such as binary, ordinal, and nominal—which often introduces bias in traditional correlation analyses. To resolve this, the authors introduce smartcor (for R) and pysmartcor (for Python), the first toolkits to systematically support all ten possible combinations of variable types. These packages employ automatic variable-type detection and a rule-based engine to intelligently select the optimal correlation or association method from a repertoire of fourteen, while also providing interpretable justifications for each choice. Monte Carlo simulations demonstrate substantially improved selection accuracy, and real-world case studies reveal meaningful discrepancies between type-aware analyses and naive Pearson correlations, thereby enhancing the reliability of statistical inference.

This study addresses the challenge of applying conventional statistical methods to collections of heterogeneous networks that vary in size and type and lack node correspondence. To overcome this, the authors propose a functional Topological Data Analysis (funTDA) framework that uniquely integrates functional data analysis with persistent homology to extract topological features from networks. This approach enables standard statistical operations—including mean and variance estimation, principal component analysis, and hypothesis testing—despite the non-Euclidean nature of network structures, thereby establishing a unified inferential framework. Empirical evaluations demonstrate that funTDA effectively discriminates networks with distinct connectivity patterns and successfully uncovers significant topological differences in real-world applications, such as literary co-occurrence networks and influenza gene regulatory networks.

This study addresses a key challenge in randomized controlled trials: how to effectively leverage covariate adjustment to improve the precision of average treatment effect estimation while satisfying regulatory requirements and ensuring statistical validity. The authors propose a prespecified, transparent, and reproducible covariate adjustment framework that, for the first time, integrates data-adaptive methods and machine learning into a regulatory-compliant analytical pipeline. By combining model-misspecification-robust estimation with semiparametric efficiency theory, the approach consistently outperforms unadjusted analyses without compromising causal interpretability or statistical validity. It substantially enhances estimation precision, increases statistical power, and yields narrower confidence intervals.