{"title":"Beyond weighting: Propensity score modeling for causal inference.","authors":"Rong J B Zhu","doi":"10.1177/09622802261436960","DOIUrl":"https://doi.org/10.1177/09622802261436960","url":null,"abstract":"<p><p>Propensity score weighting is a common method in causal inference methods. However, this approach faces two well-known challenges: (i) high variance due to small probability values in the denominator, and (ii) sensitivity to model specification errors when estimating propensity scores in observational studies. In this article, we establish that the expected potential outcomes, conditional on the propensity score, can be identified as a function of the propensity score. Based on this identification result, we utilize spline regression to estimate the function. Treatment effect estimation and inference are derived from the asymptotic normality of the spline regression. Our approach preserves the low bias of inverse probability weighting (IPW), benefiting from the flexibility of nonparametric models, while achieving significantly lower variance due to its model-based stability. Furthermore, we extend this method to regression-based adjustment for improved efficiency in causal inference. Extensive simulations show that our approach achieves lower variance than IPW-based methods while maintaining low bias and robustness to propensity score misspecification. A real-data application further demonstrates its reliability in inference.</p>","PeriodicalId":22038,"journal":{"name":"Statistical Methods in Medical Research","volume":" ","pages":"9622802261436960"},"PeriodicalIF":1.9,"publicationDate":"2026-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147634260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Bayesian likely responder approach for the analysis of randomized controlled trials.","authors":"Annan Deng, Carole Siegel, Hyung G Park","doi":"10.1177/09622802261427026","DOIUrl":"https://doi.org/10.1177/09622802261427026","url":null,"abstract":"<p><p>An important goal of precision medicine is to personalize medical treatment by identifying individuals who are most likely to benefit from a specific treatment. The likely responder (LR) framework, which identifies a subpopulation where treatment response is expected to exceed a certain clinical threshold, plays a role in this effort. However, the LR framework, and more generally, data-driven subgroup analyses, often fail to account for uncertainty in the estimation of model-based data-driven subgrouping. We propose a simple two-stage approach that integrates subgroup identification with subsequent subgroup-specific inference on treatment effects. We incorporate model estimation uncertainty from the first stage into subgroup-specific treatment effect estimation in the second stage, by utilizing Bayesian posterior distributions from the first stage. We evaluate our method through simulations, demonstrating that the proposed Bayesian two-stage model produces better calibrated confidence intervals than naïve approaches. We apply our method to an international COVID-19 treatment trial, which shows substantial variation in treatment effects across data-driven subgroups.</p>","PeriodicalId":22038,"journal":{"name":"Statistical Methods in Medical Research","volume":" ","pages":"9622802261427026"},"PeriodicalIF":1.9,"publicationDate":"2026-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147634151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ying Cui, Jeong Hoon Jang, Robert G Mannino, Amita K Manatunga
{"title":"Model-based clustering of multiple images incorporating covariates.","authors":"Ying Cui, Jeong Hoon Jang, Robert G Mannino, Amita K Manatunga","doi":"10.1177/09622802251393631","DOIUrl":"https://doi.org/10.1177/09622802251393631","url":null,"abstract":"<p><p>In this paper, we develop a novel method for clustering multiple images while adjusting for the effect of available covariates on cluster membership. The key strategy is to represent each image as two-dimensional functional data and formulate a functional latent class mixed model, which fully leverages the structural information of images while effectively addressing their high dimensionality and accounting for covariate effects. We apply the proposed method to color intensity matrices extracted from patient-sourced smartphone fingernail photos to identify distinct subgroups, while adjusting for the effect of image metadata, which may act as an effect modifier on cluster membership. Information on these subgroups can assist public health officials in low-resource settings by enabling rapid and non-invasive identification of high-risk subpopulations for anemia, thereby facilitating the timely delivery of targeted interventions. The results suggest that the three clusters identified by the proposed method correspond to varying levels of anemia risk, with 0%, 79%, and 86% of subjects in each cluster classified as anemic. These findings demonstrate the utility of the proposed method and highlight the potential of a smartphone application leveraging fingernail images for non-invasive and cost-effective anemia screening.</p>","PeriodicalId":22038,"journal":{"name":"Statistical Methods in Medical Research","volume":" ","pages":"9622802251393631"},"PeriodicalIF":1.9,"publicationDate":"2026-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147634231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sima Sharghi, Kevin E Stoll, Sally W Thurston, Emily Barrett, Brent Johnson
{"title":"Implementing empirical likelihood within the causal inference framework to study causal effects of air pollution on reproductive development.","authors":"Sima Sharghi, Kevin E Stoll, Sally W Thurston, Emily Barrett, Brent Johnson","doi":"10.1177/09622802261435966","DOIUrl":"https://doi.org/10.1177/09622802261435966","url":null,"abstract":"<p><p>To study whether air pollution is detrimental to reproductive development is imperative. In the absence of randomized trials to study the effects of air pollution on human health, data from observational studies have been utilized in which the researchers attempted to capture the causal associations between air pollution and the health outcomes. Many of these studies rely on parametric assumptions which may be limiting. In this tutorial, we explain and implement the nonparametric empirical likelihood (EL) Algorithm within the causal inference framework of a classic methodology and a newer technique based on machine learning tools. We show the competitive results of the assumption free EL in simulations. We also apply the developed methods to study the causal association between PM2.5 and NO2 exposure and anogenital distance at birth, a marker of androgen activity.</p>","PeriodicalId":22038,"journal":{"name":"Statistical Methods in Medical Research","volume":" ","pages":"9622802261435966"},"PeriodicalIF":1.9,"publicationDate":"2026-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147634213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Sensitivity bounds for bias in hazard ratios: A causal hazard perspective.","authors":"Yan-Lin Chen, Hsiang-Hsi Hung, Sheng-Hsuan Lin","doi":"10.1177/09622802261436811","DOIUrl":"https://doi.org/10.1177/09622802261436811","url":null,"abstract":"<p><p>The Cox proportional hazards model has popularized the conventional hazard ratio as a standard measure for assessing the effect of exposure on time-to-event outcomes. However, as noted in Hernán's influential critique, interpreting the hazard ratio as a causal effect can introduce substantial selection bias. While Hernán's work discusses this issue qualitatively, it lacks a method to quantify the extent of bias or the strength an unmeasured confounder would need to account for it. Our study fills this gap by proposing a nonparametric sensitivity analysis framework, inspired by Ding and VanderWeele, which quantifies \"how hazardous the hazard ratio is.\" Using the causal hazard ratio proposed by Aalen as the \"true hazard ratio,\" we derive an upper bound for the bias in the conventional hazard ratio (termed HR bias) in both discrete and continuous time settings, demonstrating that this bias accumulates over time. Additionally, we derive the <i>E</i>-value for HR bias, allowing researchers to evaluate whether unmeasured confounding alone could fully explain the conventional hazard ratio under a certain level of the causal hazard ratio. This approach provides researchers with a robust sensitivity analysis framework, reducing reliance on restrictive assumptions and enhancing the reliability of causal interpretations in survival analysis.</p>","PeriodicalId":22038,"journal":{"name":"Statistical Methods in Medical Research","volume":" ","pages":"9622802261436811"},"PeriodicalIF":1.9,"publicationDate":"2026-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147610052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Linearized maximum rank correlation estimation of doubly truncated data.","authors":"Peijie Wang, Qihao Wang, Jianguo Sun","doi":"10.1177/09622802261432834","DOIUrl":"https://doi.org/10.1177/09622802261432834","url":null,"abstract":"<p><p>Truncated data frequently arise in many areas such as economics, astronomical studies, and survival analysis, and the existence of truncation makes statistical inference more difficult due to the incomplete information. In this paper, we propose a linearized maximum rank correlation estimation of doubly truncated data under a single-index model. Unlike the existing methods, the proposed estimation has a closed-form expression and does not need knowledge of the unknown link function or the error distribution, which makes it more appealing in theory and computation. The proposed estimators are shown to be consistent and asymptotically normal, and an extensive simulation study is conducted and indicates that the proposed method works well in various situations. The method is further demonstrated by applying it to an AIDS study.</p>","PeriodicalId":22038,"journal":{"name":"Statistical Methods in Medical Research","volume":" ","pages":"9622802261432834"},"PeriodicalIF":1.9,"publicationDate":"2026-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147594651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Vaccine efficacy estimands and power considerations.","authors":"Andrea Callegaro, Nathan W Bean","doi":"10.1177/09622802251412833","DOIUrl":"https://doi.org/10.1177/09622802251412833","url":null,"abstract":"<p><p>The ICH E9(R1) addendum stresses the importance of clearly pre-specifying clinically interpretable treatment effect measures (estimands) and proposes different strategies to deal with intercurrent events. In this paper, we consider different estimands of the vaccine efficacy that are interpretable even when the proportional hazard assumption is not met, including estimands based on the average hazard ratio, the cumulative incidence ratio, and the restricted mean time lost ratio. Under the assumption that different estimands target relevant clinical questions, power becomes a crucial factor in choosing the preferred estimand. We focus on the power of these different estimands in vaccine efficacy trials, and we illustrate them in a human papillomavirus phase III vaccine trial. In classical settings of prophylactic vaccine efficacy trials, our results show that the average hazard ratio and cumulative incidence ratio give similar results, while the restricted mean time lost ratio is expected to be less powerful.</p>","PeriodicalId":22038,"journal":{"name":"Statistical Methods in Medical Research","volume":" ","pages":"9622802251412833"},"PeriodicalIF":1.9,"publicationDate":"2026-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147610112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Christine Bang, Janine Witte, Ronja Foraita, Vanessa Didelez
{"title":"Improving finite sample performance of causal discovery by exploiting temporal structure.","authors":"Christine Bang, Janine Witte, Ronja Foraita, Vanessa Didelez","doi":"10.1177/09622802261422162","DOIUrl":"https://doi.org/10.1177/09622802261422162","url":null,"abstract":"<p><p>Methods of causal discovery aim to identify causal structures in a data-driven way. Existing algorithms are known to be unstable and sensitive to statistical errors, and are therefore rarely used with biomedical or epidemiological data. We investigate an algorithm that efficiently exploits temporal structure, so-called <i>tiered background knowledge</i>, for estimating causal structures. Tiered background knowledge is readily available from, for example, cohort or registry data. When used efficiently it renders the algorithm more robust to statistical errors and ultimately increases accuracy in finite samples. We describe the algorithm and illustrate how it proceeds. Moreover, we offer formal proofs as well as examples of desirable properties of the algorithm, which we demonstrate empirically in an extensive simulation study. To illustrate its usefulness in practice, we apply the algorithm to data from a children's cohort study investigating the interplay of diet, physical activity and other lifestyle factors for health outcomes.</p>","PeriodicalId":22038,"journal":{"name":"Statistical Methods in Medical Research","volume":" ","pages":"9622802261422162"},"PeriodicalIF":1.9,"publicationDate":"2026-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147594648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Eliminating residual confounding in the stratified estimator via smoothing along with the propensity score.","authors":"Naoto Tsujimoto, Satoshi Hattori","doi":"10.1177/09622802261432998","DOIUrl":"https://doi.org/10.1177/09622802261432998","url":null,"abstract":"<p><p>The stratified estimator by the propensity score is one of the most popular estimator for the average causal effect in the presence of confounding. Despite of its advantages of robustness and simplicity, it has a serious shortcoming of residual confounding even with the correctly specified propensity score. On the other hand, the inverse probability weighting estimator by the propensity score is free from residual confounding and many corresponding variants have been proposed. Wang et al. (2021, <i>Robust estimation of propensity score weights via subclassification</i>) pointed it out that the stratified estimator can be regarded as a special case of the inverse probability weighting estimator with piecewise constant propensity score and proposed a method eliminating residual confounding in the stratified estimator. In this paper, we provide an alternative interpretation of the stratified estimator as the outcome regression with a piecewise constant function over the propensity score. By considering kernel smoothing, an estimator free from residual confounding is proposed based on the stratified estimator, which preserves the robustness of the stratified estimator. We also propose a doubly robust estimator, which does not rely on the inverse probability weighting.</p>","PeriodicalId":22038,"journal":{"name":"Statistical Methods in Medical Research","volume":" ","pages":"9622802261432998"},"PeriodicalIF":1.9,"publicationDate":"2026-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147582389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Penalized estimation of linear transformation models for interval-censored data with time-dependent covariates.","authors":"Minggen Lu, Yahui Zhang, Chin-Shang Li, Guogen Shan","doi":"10.1177/09622802261433000","DOIUrl":"10.1177/09622802261433000","url":null,"abstract":"<p><p>We investigate efficient estimation strategies for partially linear transformation models with time-dependent covariates under interval censoring. The unknown monotone function is approximated using a monotone <math><mi>B</mi></math>-spline basis to enable flexible semiparametric modeling, and we develop a computationally efficient nested hybrid EM algorithm that integrates Newton's method with isotonic regression. To support large-sample inference, we propose a straightforward variance-covariance estimation procedure for the regression parameters and introduce a score test to assess the adequacy of the proportional hazards (PH) specification within the broader class of transformation models. The numerical performance of the penalized estimators is examined extensively and compared with both the time-invariant covariate model by Lu et al. and the semiparametric transformation model by Zeng et al. Finally, the proposed methodology is applied to data from the National Alzheimer's Coordinating Center (NACC) to demonstrate its practical utility in a real-world clinical setting.</p>","PeriodicalId":22038,"journal":{"name":"Statistical Methods in Medical Research","volume":" ","pages":"9622802261433000"},"PeriodicalIF":1.9,"publicationDate":"2026-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147594714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}