Pharmaceutical Statistics最新文献

{"title":"Finding the Optimal Number of Splits and Repetitions in Double Cross-Fitting Targeted Maximum Likelihood Estimators.","authors":"Mohammad Ehsanul Karim, Momenul Haque Mondol","doi":"10.1002/pst.70022","DOIUrl":"10.1002/pst.70022","url":null,"abstract":"<p><p>Flexible machine learning algorithms are increasingly utilized in real-world data analyses. When integrated within double robust methods, such as the Targeted Maximum Likelihood Estimator (TMLE), complex estimators can result in significant undercoverage-an issue that is even more pronounced in singly robust methods. The Double Cross-Fitting (DCF) procedure complements these methods by enabling the use of diverse machine learning estimators, yet optimal guidelines for the number of data splits and repetitions remain unclear. This study aims to explore the effects of varying the number of splits and repetitions in DCF on TMLE estimators through statistical simulations and a data analysis. We discuss two generalizations of DCF beyond the conventional three splits and apply a range of splits to fit the TMLE estimator, incorporating a super learner without transforming covariates. The statistical properties of these configurations are compared across two sample sizes (3000 and 5000) and two DCF generalizations (equal splits and full data use). Additionally, we conduct a real-world analysis using data from the National Health and Nutrition Examination Survey (NHANES) 2017-18 cycle to illustrate the practical implications of varying DCF splits, focusing on the association between obesity and the risk of developing diabetes. Our simulation study reveals that five splits in DCF yield satisfactory bias, variance, and coverage across scenarios. In the real-world application, the DCF TMLE method showed consistent risk difference estimates over a range of splits, though standard errors increased with more splits in one generalization, suggesting potential drawbacks to excessive splitting. This research underscores the importance of judicious selection of the number of splits and repetitions in DCF TMLE methods to achieve a balance between computational efficiency and accurate statistical inference. Optimal performance seems attainable with three to five splits. Among the generalizations considered, using full data for nuisance estimation offered more consistent variance estimation and is preferable for applied use. Additionally, increasing the repetitions beyond 25 did not enhance performance, providing crucial guidance for researchers employing complex machine learning algorithms in causal studies and advocating for cautious split management in DCF procedures.</p>","PeriodicalId":19934,"journal":{"name":"Pharmaceutical Statistics","volume":"24 5","pages":"e70022"},"PeriodicalIF":1.4,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12425639/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145041041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Estimand Framework and Causal Inference: Complementary Not Competing Paradigms.","authors":"Thomas Drury, Jonathan W Bartlett, David Wright, Oliver N Keene","doi":"10.1002/pst.70035","DOIUrl":"10.1002/pst.70035","url":null,"abstract":"<p><p>The creation of the ICH E9 (R1) estimands framework has led to more precise specification of the treatment effects of interest in the design and statistical analysis of clinical trials. However, it is unclear how the new framework relates to causal inference, as both approaches appear to define what is being estimated and have a quantity labeled an estimand. Using illustrative examples, we show that both approaches can be used to define a population-based summary of an effect on an outcome for a specified population and highlight the similarities and differences between these approaches. We demonstrate that the ICH E9 (R1) estimand framework offers a descriptive, structured approach that is more accessible to non-mathematicians, facilitating clearer communication of trial objectives and results. We then contrast this with the causal inference framework, which provides a mathematically precise definition of an estimand and allows the explicit articulation of assumptions through tools such as causal graphs. Despite these differences, the two paradigms should be viewed as complementary rather than competing. The combined use of both approaches enhances the ability to communicate what is being estimated. We encourage those familiar with one framework to appreciate the concepts of the other to strengthen the robustness and clarity of clinical trial design, analysis, and interpretation.</p>","PeriodicalId":19934,"journal":{"name":"Pharmaceutical Statistics","volume":"24 5","pages":"e70035"},"PeriodicalIF":1.4,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144964825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Correction to \"Sample Size Estimation for Correlated Count Data With Changes in Dispersion\".","authors":"","doi":"10.1002/pst.70034","DOIUrl":"10.1002/pst.70034","url":null,"abstract":"","PeriodicalId":19934,"journal":{"name":"Pharmaceutical Statistics","volume":"24 5","pages":"e70034"},"PeriodicalIF":1.4,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145023976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Tutorial on Improving RCT Power Using Prognostic Score Adjustment for Linear Models.","authors":"Emilie Højbjerre-Frandsen, Mathias Lerbech Jeppesen, Rasmus Kuhr Jensen, Claus Dethlefsen, Rasmus Waagepetersen","doi":"10.1002/pst.70028","DOIUrl":"10.1002/pst.70028","url":null,"abstract":"<p><p>The use of historical data to increase power in clinical trials has been a topic of interest for many years. A recent approach adjusts linearly for a prognostic score. This is supported by asymptotic optimality results using influence functions for asymptotically linear estimators as well as finite sample optimality results. We review plug-in and linear estimators of average treatment effect in randomized clinical trials, sample size determination, and linear adjustment for a prognostic score. Guidelines and recommendations for the implementation of linear adjustment for a prognostic score are given including curation of historical data and construction of a prognostic score based on the historical data. A simulation study is conducted to investigate the performance in finite samples, comparing it to standard procedures such as propensity score matching for RCTs (PSM-RCT) and ANCOVA using simple baseline adjustment. Unlike PSM-RCT, linear adjustment for a prognostic score avoids biased treatment effect estimates and maintains control of type I error probability. The simulation study shows that the method is robust against deviations from method assumptions and poor performance of the prognostic model. A case study demonstrates an increase in prospective power using linear adjustment with a prognostic score in a phase IIIb clinical trial for type 2 diabetes. A final discussion considers limitations of the method for example in regard to subgroup analysis and the existence of already known prognostic baseline covariates.</p>","PeriodicalId":19934,"journal":{"name":"Pharmaceutical Statistics","volume":"24 5","pages":"e70028"},"PeriodicalIF":1.4,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144754021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Comment on \"Average Hazard as Harmonic Mean\" by Chiba (2025).","authors":"Hajime Uno, Lu Tian, Miki Horiguchi, Satoshi Hattori","doi":"10.1002/pst.70032","DOIUrl":"10.1002/pst.70032","url":null,"abstract":"","PeriodicalId":19934,"journal":{"name":"Pharmaceutical Statistics","volume":"24 5","pages":"e70032"},"PeriodicalIF":1.4,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12806506/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144799848","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mediation Analysis of Path-Specific Effects in Randomised Clinical Trials With Repeatedly Measured Mediators and Outcomes.","authors":"Martin Linder, Jesper Madsen, Stijn Vansteelandt","doi":"10.1002/pst.70030","DOIUrl":"10.1002/pst.70030","url":null,"abstract":"<p><p>Questions about the mode of action (MoA) of a drug have interest to scientific communities as well as regulatory authorities. In the absence of an already established MoA such questions may be enlightened by causal mediation analysis in clinical trials. In this paper, we present a general framework that facilitates causal mediation analysis in a setting of a clinical trial where both the outcome of interest, one or more mediators and additional potential post-baseline confounders are measured repeatedly at planned visits. The targeted estimands are path-specific effects implicitly defined from a causal diagram that includes all the longitudinally measured variables. The framework including estimation method is developed with inspiration from a similar approach for time-to-event outcomes. The novelty of our approach compared to many currently used methods is that it directly establishes MoA, takes the full amount of longitudinal data into account, and properly adjusts for sources of confounding. We motivate and illustrate the approach with examples from the STEP 2 clinical trial. Modular SAS code is provided that can be used in a general setting.</p>","PeriodicalId":19934,"journal":{"name":"Pharmaceutical Statistics","volume":"24 5","pages":"e70030"},"PeriodicalIF":1.4,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144732705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Prediction Intervals for Overdispersed Binomial Endpoints and Their Application to Toxicological Historical Control Data.","authors":"Max Menssen, Jonathan Rathjens","doi":"10.1002/pst.70033","DOIUrl":"10.1002/pst.70033","url":null,"abstract":"<p><p>For toxicology studies, the validation of the concurrent control group by historical control data (HCD) has become requirements. This validation is usually done by historical control limits (HCL), which should cover the observations of the concurrent control with a predefined level of confidence. In many applications, HCL are applied to dichotomous data, for example, the number of rats with a tumor versus the number of rats without a tumor (carcinogenicity studies) or the number of cells with a micronucleus out of a total number of cells. Dichotomous HCD may be overdispersed and can be heavily right- (or left-) skewed, which is usually not taken into account in the practical applications of HCL. To overcome this problem, four different prediction intervals (two frequentist, two Bayesian), that can be applied to such data, are proposed. Based on comprehensive Monte-Carlo simulations, the coverage probabilities of the proposed prediction intervals were compared to heuristical HCL typically used in daily toxicological routine (historical range, limits of the np-chart, mean <math> <semantics><mrow><mo>±</mo></mrow> <annotation>$$ pm $$</annotation></semantics> </math> 2 SD). Our simulations reveal, that frequentist bootstrap calibrated prediction intervals control the type-1-error best, but, also prediction intervals calculated based on Bayesian generalized linear mixed models appear to be practically applicable. Contrary, all heuristics fail to control the type-1-error. The application of HCL is demonstrated based on a real life data set containing historical controls from long-term carcinogenicity studies run on behalf of the U.S. National Toxicology Program. The proposed frequentist prediction intervals are publicly available from the R package predint, whereas R code for the computation of the two Bayesian prediction intervals is provided via GitHub.</p>","PeriodicalId":19934,"journal":{"name":"Pharmaceutical Statistics","volume":"24 5","pages":"e70033"},"PeriodicalIF":1.4,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12433933/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145065356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Design Considerations for a Phase II Platform Trial in Major Depressive Disorder.","authors":"Michaela Maria Freitag, Dario Zocholl, Elias Laurin Meyer, Stefan M Gold, Marta Bofill Roig, Heidi De Smedt, Martin Posch, Franz König","doi":"10.1002/pst.70025","DOIUrl":"10.1002/pst.70025","url":null,"abstract":"<p><p>Major depressive disorder (MDD) is one of the leading causes of disability globally. Despite its prevalence, approximately one-third of patients do not benefit sufficiently from available treatments, and few new drugs have been developed recently. Consequently, more efficient methods are needed to evaluate a broader range of treatment options quickly. Platform trials offer a promising solution, as they allow for the assessment of multiple investigational treatments simultaneously by sharing control groups and by reducing both trial activation and patient recruitment times. The objective of this simulation study was to support the design and optimisation of a phase II superiority platform trial for MDD, considering the disease-specific characteristics. In particular, we assessed the efficiency of platform trials compared to traditional two-arm trials by investigating key design elements, including allocation and randomisation strategies, as well as per-treatment arm sample sizes and interim futility analyses. Through extensive simulations, we refined these design components and evaluated their impact on trial performance. The results demonstrated that platform trials not only enhance efficiency but also achieve higher statistical power in evaluating individual treatments compared to conventional trials. The efficiency of platform trials is particularly prominent when interim futility analyses are performed to eliminate treatments that have either no or a negligible treatment effect early. Overall, this work provides valuable insights into the design of platform trials in the superiority setting and underscores their potential to accelerate therapy development in MDD and other therapeutic areas, providing a flexible and powerful alternative to traditional trial designs.</p>","PeriodicalId":19934,"journal":{"name":"Pharmaceutical Statistics","volume":"24 5","pages":"e70025"},"PeriodicalIF":1.5,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12384050/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144964785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sample Size for Enriched Biomarker Designs With Measurement Error for Time-to-Event Outcomes.","authors":"Siyuan Guo, Susan Halabi, Aiyi Liu","doi":"10.1002/pst.70027","DOIUrl":"10.1002/pst.70027","url":null,"abstract":"<p><p>A major emphasis in personalized medicine is to optimally treat subgroups of patients who may benefit from certain therapeutic agents. One relevant study design is the targeted design, in which patients have consented for their specimens to be obtained at baseline and the specimens are sent to a laboratory for assessing the biomarker status prior to randomization. Here, only biomarker-positive patients will be randomized to either an experimental or the standard of care arms. Many biomarkers, however, are derived from patient tissue specimens, which are heterogeneous leading to variability in the biomarker levels and status. This heterogeneity would have an adverse impact on the power of an enriched biomarker clinical trial. In this article, we show the adverse effect of using the uncorrected sample size and overcome this challenge by presenting an approach to adjust for misclassification for the targeted design. Specifically, we propose a sample size formula that adjusts for misclassification and apply it in the design of two phase III clinical trials in renal and prostate cancer.</p>","PeriodicalId":19934,"journal":{"name":"Pharmaceutical Statistics","volume":"24 5","pages":"e70027"},"PeriodicalIF":1.4,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12683776/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144708386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Flexible Seamless Phase 2/3 Design With Biomarker-Driven Subgroup Enrichment and Sample Size Re-Estimation.","authors":"Zizhong Tian, Liwen Wu, Rachael Liu, Jianchang Lin","doi":"10.1002/pst.70026","DOIUrl":"10.1002/pst.70026","url":null,"abstract":"<p><p>To support the expedited drug development addressing unmet medical needs, the seamless phase 2/3 design that makes the phase switching decision based on early surrogate endpoints is gaining popularity in practice. For also catering to potentially more beneficial patient subgroups based on predictive biomarkers, it is appealing to incorporate the subgroup enrichment feature into the seamless phase 2/3 design. However, the sample size planning for such a complex adaptive design is challenging, as it must strike a balance among shortening development timeline, mitigating development risks, and accounting for uncertainty related to subgroup effects. To fill this gap, we propose a flexible seamless phase 2/3 design framework with population selection and sample size re-estimation using surrogate endpoints. We elucidate the patterns of the overall type I error for the proposed adaptive design and propose an easy-to-implement approach to control the overall type I error. Extensive simulation studies are conducted to demonstrate the advantages of our proposal design compared to the fixed-sample design in terms of efficiency, power, and timeline saving. We also illustrate our proposed design in a case study for relapsed/refractory multiple myeloma.</p>","PeriodicalId":19934,"journal":{"name":"Pharmaceutical Statistics","volume":"24 5","pages":"e70026"},"PeriodicalIF":1.4,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144760677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}