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On Anticipation Effect in Stepped Wedge Cluster Randomized Trials. 阶梯形聚类随机试验的预期效应。
IF 1.8 4区 医学 Q3 MATHEMATICAL & COMPUTATIONAL BIOLOGY Pub Date : 2026-02-01 DOI: 10.1002/sim.70380
Hao Wang, Xinyuan Chen, Katherine R Courtright, Scott D Halpern, Michael O Harhay, Monica Taljaard, Fan Li

In stepped wedge cluster randomized trials (SW-CRTs), the intervention is rolled out to clusters over multiple periods. A standard approach for analyzing SW-CRTs utilizes the linear mixed model, where the treatment effect is only present after the treatment adoption, under the assumption of no anticipation. This assumption, however, may not always hold in practice because stakeholders, providers, or individuals who are aware of the treatment adoption timing (especially when blinding is challenging or infeasible) can inadvertently change their behaviors in anticipation of the forthcoming intervention. We provide an analytical framework to address the anticipation effect in SW-CRTs and study its impact. We derive expectations of the estimators based on a collection of linear mixed models and demonstrate that when the anticipation effect is ignored, these estimators give biased estimates of the treatment effect. We also provide updated sample size formulas that explicitly account for anticipation effects, exposure-time heterogeneity, or both in SW-CRTs and illustrate their impact on study power. Through simulation studies and empirical analyses, we compare the treatment effect estimators with and without adjusting for anticipation, and provide some practical considerations.

在阶梯楔形随机试验(sw - crt)中,干预措施在多个时期内进行。分析sw - crt的标准方法是使用线性混合模型,在没有预期的假设下,治疗效果只有在采用治疗后才会出现。然而,这一假设在实践中可能并不总是成立,因为意识到治疗采用时机的利益相关者、提供者或个人(特别是当盲法具有挑战性或不可行时)可能会在预期即将到来的干预时无意中改变他们的行为。我们提供了一个分析框架来解决sw - crt中的预期效应并研究其影响。我们基于一组线性混合模型推导了估计器的期望,并证明当忽略预期效应时,这些估计器给出了治疗效果的有偏估计。我们还提供了更新的样本量公式,明确说明了sw - crt中的预期效应、暴露时间异质性或两者兼而有之,并说明了它们对研究能力的影响。通过模拟研究和实证分析,比较了考虑预期和不考虑预期的治疗效果估计量,并提出了一些实际考虑。
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引用次数: 0
A Concave Pairwise Fusion Approach to Heterogeneous Q-Learning for Dynamic Treatment Regimes. 基于凹对融合的动态治疗方案异构q -学习。
IF 1.8 4区 医学 Q3 MATHEMATICAL & COMPUTATIONAL BIOLOGY Pub Date : 2026-02-01 DOI: 10.1002/sim.70415
Jubo Sun, Wensheng Zhu, Guozhe Sun

A dynamic treatment regime is a sequence of decision rules that map available history information to a treatment option at each decision point. The optimal dynamic treatment regime seeks to make these decisions to maximize the expected outcome of interest. Most existing methods assume population homogeneity. In many complex applications, ignoring latent heterogeneous structures may compromise estimation, highlighting the necessity of exploring heterogeneous structures during the estimation of optimal treatment regimes. We propose heterogeneous Q-learning that facilitates the estimation of optimal dynamic treatment regimes using a concave pairwise fusion penalized approach. The proposed method employs an alternating direction method of multipliers algorithm to solve the concave pairwise fusion penalized least squares problem in each stage. Simulation studies demonstrate that our proposed method outperforms the standard Q-learning method, and it is further illustrated through a real data analysis from the China Rural Hypertension Control Project (CRHCP) study group.

动态治疗方案是一系列决策规则,将可用的历史信息映射到每个决策点的治疗方案。最佳动态治疗方案寻求做出这些决定,以最大限度地提高预期结果的兴趣。大多数现有的方法都假定人口同质性。在许多复杂的应用中,忽略潜在的异质结构可能会损害估计,强调在估计最佳处理方案时探索异质结构的必要性。我们提出了异构q -学习,它有助于使用凹成对融合惩罚方法估计最优动态处理方案。该方法采用交替方向乘法器算法求解凹对融合惩罚最小二乘问题。仿真研究表明,我们提出的方法优于标准的q -学习方法,并通过中国农村高血压控制项目(CRHCP)研究组的真实数据分析进一步证明了这一点。
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引用次数: 0
Patient Retreat in Dose Escalation for Phase I Clinical Trials With Rare Diseases. 罕见病I期临床试验中剂量递增的患者撤退
IF 1.8 4区 医学 Q3 MATHEMATICAL & COMPUTATIONAL BIOLOGY Pub Date : 2026-02-01 DOI: 10.1002/sim.70409
Jialu Fang, Guosheng Yin

Phase I clinical trials aim to identify the maximum tolerated dose (MTD), a task that becomes challenging in rare disease due to limited patient recruitment. Traditional dose-finding designs, which assign one dose per patient, require a sufficient sample size that may be infeasible for rare disease trials. To address these limitations, we propose the patient retreat in dose escalation (PRIDE) scheme, which integrates intra-patient dose escalation and considers intra-patient correlations by incorporating random effects into a Bayesian hierarchical framework. We further introduce PRIDE-FA (flexible allocation), an extension of PRIDE with a flexible allocation strategy. By allowing retreated patients to be assigned to any dose level based on trial needs, PRIDE-FA improves resource efficiency, leading to greater reductions in required sample size and trial duration. This paper incorporates random effects into established dose-finding designs, including the calibration-free odds (CFO) design, the Bayesian optimal interval (BOIN) design, and the continual reassessment method (CRM) to account for intra-patient correlations when each patient may receive multiple doses. Simulation studies demonstrate that PRIDE and PRIDE-FA significantly improve the accuracy of MTD selection, reduce required sample size, and shorten trial duration compared to existing dose-finding methods. Together, PRIDE and PRIDE-FA provide a robust and efficient framework for phase I clinical trials with rare diseases.

I期临床试验旨在确定最大耐受剂量(MTD),由于患者招募有限,这一任务在罕见疾病中变得具有挑战性。传统的剂量发现设计,即为每个病人分配一个剂量,需要足够的样本量,这对于罕见病试验可能是不可行的。为了解决这些局限性,我们提出了患者剂量递增撤退(PRIDE)方案,该方案整合了患者内部剂量递增,并通过将随机效应纳入贝叶斯分层框架来考虑患者内部相关性。我们进一步介绍了PRIDE- fa(灵活分配),它是PRIDE的扩展,具有灵活的分配策略。PRIDE-FA允许根据试验需要将患者分配到任何剂量水平,从而提高了资源效率,从而大大减少了所需的样本量和试验时间。本文将随机效应纳入已建立的剂量发现设计,包括无校准几率(CFO)设计、贝叶斯最优区间(BOIN)设计和持续重新评估方法(CRM),以解释每个患者可能接受多个剂量时的患者内部相关性。仿真研究表明,与现有的剂量寻找方法相比,PRIDE和PRIDE- fa显著提高了MTD选择的准确性,减少了所需的样本量,缩短了试验时间。PRIDE和PRIDE- fa共同为罕见病的I期临床试验提供了一个强大而有效的框架。
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引用次数: 0
Nothing to See Here? A Non-Inferiority Approach to Parallel Trends. 这里没什么可看的?平行趋势的非劣效性方法。
IF 1.8 4区 医学 Q3 MATHEMATICAL & COMPUTATIONAL BIOLOGY Pub Date : 2026-02-01 DOI: 10.1002/sim.70296
Alyssa Bilinski, Laura A Hatfield

Difference-in-differences is a popular method for observational health policy evaluation. It relies on a causal assumption that in the absence of intervention, treatment groups' outcomes would have evolved in parallel to those of comparison groups. Researchers frequently look for parallel trends in the pre-intervention period to bolster confidence in this assumption. The popular "parallel trends test" evaluates a null hypothesis of parallel trends and, failing to find evidence against the null, concludes that the assumption holds. This tightly controls the probability of falsely concluding that trends are not parallel, but may have low power to detect non-parallel trends. When used as a screening step, it can also introduce bias in treatment effect estimates. We propose a non-inferiority/equivalence approach that tightly controls the probability of missing large violations of parallel trends, measured on the scale of the treatment effect. Our framework nests several common use cases, including linear trend tests and event studies. We show that our approach may induce no or minimal bias when used as a screening step under commonly assumed error structures and, absent violations, can offer a higher-power alternative to testing treatment effects in more flexible models. We illustrate our ideas by reconsidering a study of the impact of the Affordable Care Act's dependent coverage provision.

差异中的差异是一种流行的观察性卫生政策评估方法。它依赖于一个因果假设,即在没有干预的情况下,治疗组的结果将与对照组的结果平行发展。研究人员经常在干预前时期寻找类似的趋势,以增强对这一假设的信心。流行的“平行趋势检验”评估平行趋势的零假设,由于没有找到反对零假设的证据,因此得出结论认为该假设成立。这严格控制了错误地得出趋势不平行的结论的概率,但可能在检测非平行趋势方面能力较低。当用作筛选步骤时,它也可能在治疗效果估计中引入偏差。我们提出了一种非劣效性/等效性方法,该方法严格控制了在治疗效果的尺度上测量的平行趋势的重大违规缺失的概率。我们的框架嵌套了几个常见的用例,包括线性趋势测试和事件研究。我们表明,我们的方法在通常假设的错误结构下作为筛选步骤时可能不会产生偏差或偏差很小,并且在没有违规的情况下,可以在更灵活的模型中提供更高功率的替代方案来测试治疗效果。我们通过重新考虑对《平价医疗法案》的依赖保险条款的影响进行研究来说明我们的观点。
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引用次数: 0
Preference-Informed Cluster Randomized Design for Pragmatic Clinical Trials. 实用临床试验的偏好知情聚类随机设计。
IF 1.8 4区 医学 Q3 MATHEMATICAL & COMPUTATIONAL BIOLOGY Pub Date : 2026-02-01 DOI: 10.1002/sim.70426
Yuwei Cheng, Adriana Tremoulet, Sonia Jain

Cluster randomized trials (CRTs), in which entire clusters of subjects are randomized to treatment arms, are widely used in pragmatic trials to evaluate interventions under real-world conditions. However, CRTs are particularly vulnerable to treatment non-adherence, especially when cluster-level preferences lead subjects in clusters to deviate from their assigned treatment. Such deviations can reduce power, introduce bias, and compromise generalizability if not properly addressed. This research is directly motivated by a planned multi-center trial in Kawasaki Disease patients with high risk for coronary artery abnormalities, in which institutional treatment preferences influence both willingness to participate and adhere. To address this issue, we propose a Bayesian hierarchical model under a Preference-Informed Cluster Randomized Design (PICRD). This model explicitly incorporates cluster-level treatment switching into the analysis rather than excluding non-willing or non-adherent clusters. We conduct a simulation study to evaluate the performance of the PICRD model across a range of treatment effect sizes and switching proportions. Results demonstrate that the PICRD model consistently outperforms per-protocol analyses by maintaining higher power for the main treatment effect, producing narrower 95% credible intervals, and yielding more stable bias and root mean square error in the presence of substantial non-adherence. By explicitly modeling preference within a Bayesian hierarchical framework, the PICRD approach provides a flexible and robust solution for CRTs conducted in pragmatic settings when willingness to accept randomization assignment or adherence to randomization is often unrealistic.

聚类随机试验(CRTs)在实际试验中被广泛使用,以评估现实世界条件下的干预措施,其中整组受试者被随机分配到治疗组。然而,crt特别容易受到治疗依从性的影响,特别是当集群水平的偏好导致集群中的受试者偏离其指定的治疗时。如果处理不当,这种偏差会降低功率,引入偏差,并损害通用性。本研究的直接动机是一项计划在冠状动脉异常高危川崎病患者中进行的多中心试验,其中机构治疗偏好影响参与和坚持的意愿。为了解决这一问题,我们提出了一个偏好知情聚类随机设计(PICRD)下的贝叶斯分层模型。该模型明确地将集群水平的治疗转换纳入分析,而不是排除不愿意或不依附的集群。我们进行了一项模拟研究,以评估PICRD模型在一系列治疗效果大小和切换比例中的性能。结果表明,PICRD模型通过保持较高的主要治疗效果的功率,产生更窄的95%可信区间,并且在存在大量不依从性的情况下产生更稳定的偏差和均方根误差,始终优于每个方案分析。通过在贝叶斯层次框架内明确建模偏好,PICRD方法为在实际环境中进行的crt提供了灵活而稳健的解决方案,当愿意接受随机分配或坚持随机化通常是不现实的。
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引用次数: 0
An Empirical Assessment of the Cost of Dichotomization of the Outcome of Clinical Trials. 临床试验结果二分类成本的实证评估。
IF 1.8 4区 医学 Q3 MATHEMATICAL & COMPUTATIONAL BIOLOGY Pub Date : 2026-02-01 DOI: 10.1002/sim.70402
Erik W van Zwet, Frank E Harrell, Stephen J Senn

We have studied 21 435 unique randomized controlled trials (RCTs) from the Cochrane Database of Systematic Reviews (CDSR). Of these trials, 7224 (34%) have a continuous (numerical) outcome and 14 211 (66%) have a binary outcome. We find that trials with a binary outcome have larger sample sizes on average, but also larger standard errors and fewer statistically significant results. We conclude that researchers tend to increase the sample size to compensate for the low information content of binary outcomes, but not sufficiently. In many cases, the binary outcome is the result of dichotomization of a continuous outcome, which is sometimes referred to as "responder analysis". In those cases, the loss of information is avoidable. Burdening more participants than necessary is wasteful, costly, and unethical. We provide a method to convert a sample size calculation for the comparison of two proportions into one for the comparison of the means of the underlying continuous outcomes. This demonstrates how much the sample size may be reduced if the outcome were not dichotomized. We also provide a method to calculate the loss of information after a dichotomization. We apply this method to all the trials from the CDSR with a binary outcome, and estimate that on average, only about 60% of the information is retained after dichotomization. We provide R code and a shiny app at: https://vanzwet.shinyapps.io/info_loss/ to do these calculations. We hope that quantifying the loss of information will discourage researchers from dichotomizing continuous outcomes. Instead, we recommend they "model continuously but interpret dichotomously". For example, they might present "percentage achieving clinically meaningful improvement" derived from a continuous analysis rather than by dichotomizing raw data.

我们研究了来自Cochrane系统评价数据库(CDSR)的21435个独特的随机对照试验(rct)。在这些试验中,7224项(34%)具有连续(数字)结果,14211项(66%)具有二元结果。我们发现,具有二元结果的试验平均样本量较大,但也有较大的标准误差和较少的统计显著性结果。我们的结论是,研究人员倾向于增加样本量来弥补二元结果的低信息含量,但不够。在许多情况下,二元结果是连续结果的二分类结果,这有时被称为“应答者分析”。在这些情况下,信息的丢失是可以避免的。让更多的参与者承担不必要的负担是浪费、昂贵和不道德的。我们提供了一种方法,将两个比例比较的样本大小计算转换为一个用于比较潜在连续结果的平均值。这表明如果结果不进行二分类,样本量可能会减少多少。我们还提供了一种计算二分类后信息损失的方法。我们将该方法应用于所有具有二值结果的CDSR试验,并估计平均而言,二值化后仅保留约60%的信息。我们提供了R代码和一个闪亮的应用程序:https://vanzwet.shinyapps.io/info_loss/来做这些计算。我们希望量化信息损失将阻止研究人员对连续结果进行二分类。相反,我们建议他们“连续建模,但进行二分解释”。例如,他们可能会提出“实现临床有意义改善的百分比”,这是由连续分析得出的,而不是通过对原始数据进行二分法。
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引用次数: 0
Missing Value Imputation With Adversarial Random Forests-MissARF. 基于对抗随机森林的缺失值输入。
IF 1.8 4区 医学 Q3 MATHEMATICAL & COMPUTATIONAL BIOLOGY Pub Date : 2026-02-01 DOI: 10.1002/sim.70379
Pegah Golchian, Jan Kapar, David S Watson, Marvin N Wright

Handling missing values is a common challenge in biostatistical analyses, typically addressed by imputation methods. We propose a novel, fast, and easy-to-use imputation method called missing value imputation with adversarial random forests (MissARF), based on generative machine learning, that provides both single and multiple imputation. MissARF employs adversarial random forest (ARF) for density estimation and data synthesis. To impute a missing value of an observation, we condition on the non-missing values and sample from the estimated conditional distribution generated by ARF. Our experiments demonstrate that MissARF performs comparably to state-of-the-art single and multiple imputation methods in terms of imputation quality and fast runtime with no additional costs for multiple imputation.

处理缺失值是生物统计分析中常见的挑战,通常通过imputation方法来解决。我们提出了一种新颖,快速,易于使用的imputation方法,称为基于生成机器学习的对抗随机森林缺失值imputation (MissARF),它提供单次和多次imputation。MissARF采用对抗随机森林(ARF)进行密度估计和数据合成。为了估算观测值的缺失值,我们将ARF生成的估计条件分布中的非缺失值和样本作为条件。我们的实验表明,MissARF在输入质量和快速运行时间方面可以与最先进的单次和多次输入方法相媲美,而无需额外的多次输入成本。
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引用次数: 0
Causal Inference With Survey Data: A Robust Framework for Propensity Score Weighting in Probability and Non-Probability Samples. 调查数据的因果推理:概率和非概率样本中倾向得分加权的稳健框架。
IF 1.8 4区 医学 Q3 MATHEMATICAL & COMPUTATIONAL BIOLOGY Pub Date : 2026-02-01 DOI: 10.1002/sim.70420
Wei Liang, Changbao Wu

Confounding bias and selection bias are two major challenges in causal inference with observational data. While numerous methods have been developed to mitigate confounding bias, they often assume that the data are representative of the study population and ignore the potential selection bias introduced during data collection. In this paper, we propose a unified weighting framework-survey-weighted propensity score weighting-to simultaneously address both confounding and selection biases when the observational dataset is a probability survey sample from a finite population, which is itself viewed as a random sample from the target superpopulation. The proposed method yields a doubly robust inferential procedure for a class of population weighted average treatment effects. We further extend our results to non-probability observational data when the sampling mechanism is unknown but auxiliary information of the confounding variables is available from an external probability sample. We focus on practically important scenarios where the confounders are only partially observed in the external data. Our analysis reveals that the key variables in the external data are those related to both treatment effect heterogeneity and the selection mechanism. We also discuss how to combine auxiliary information from multiple reference probability samples. Monte Carlo simulations and an application to a real-world non-probability observational dataset demonstrate the superiority of our proposed methods over standard propensity score weighting approaches.

混淆偏差和选择偏差是观测数据因果推理中的两个主要挑战。虽然已经开发了许多方法来减轻混杂偏差,但它们通常假设数据代表研究人群,而忽略了数据收集过程中引入的潜在选择偏差。在本文中,我们提出了一个统一的加权框架-调查加权倾向得分加权-以同时解决混淆和选择偏差,当观测数据集是来自有限总体的概率调查样本时,该样本本身被视为来自目标超总体的随机样本。所提出的方法对一类总体加权平均处理效果产生了双重鲁棒推理过程。当抽样机制未知,但从外部概率样本中可以获得混杂变量的辅助信息时,我们进一步将结果扩展到非概率观测数据。我们关注的是在外部数据中只能部分观察到混杂因素的实际重要场景。我们的分析表明,外部数据中的关键变量是与治疗效果异质性和选择机制有关的变量。我们还讨论了如何结合多个参考概率样本的辅助信息。蒙特卡罗模拟和对现实世界非概率观测数据集的应用表明,我们提出的方法优于标准倾向得分加权方法。
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引用次数: 0
A Path-Specific Effect Approach to Mediation Analysis With Time-Varying Mediators and Time-to-Event Outcomes Accounting for Competing Risks. 具有时变中介和时间-事件结果的竞争风险的中介分析的路径特定效应方法。
IF 1.8 4区 医学 Q3 MATHEMATICAL & COMPUTATIONAL BIOLOGY Pub Date : 2026-02-01 DOI: 10.1002/sim.70425
Arce Domingo-Relloso, Yuchen Zhang, Ziqing Wang, Astrid M Suchy-Dicey, Dedra S Buchwald, Ana Navas-Acien, Joel Schwartz, Kiros Berhane, Brent A Coull, Linda Valeri

Not accounting for competing events in survival analysis can lead to biased estimates, as individuals who die from other causes do not have the opportunity to develop the event of interest. Formal definitions and considerations for causal effects in the presence of competing risks have been published, but not for the mediation analysis setting when the exposure is not separable and both the outcome and the mediator are nonterminal events. We propose, for the first time, an approach based on the path-specific effects framework to account for competing risks in longitudinal mediation analysis with time-to-event outcomes. We do so by considering the pathway through the competing event as another mediator, which is nested within our longitudinal mediator of interest. We provide a theoretical formulation and related definitions of the effects of interest based on the mediational g-formula, as well as a detailed description of the algorithm. We also present a simulation study and an application of our algorithm to data from the Strong Heart Study, a prospective cohort of American Indian adults. In this application, we evaluated the mediating role of the blood pressure trajectory (measured in three visits) on the association of arsenic and cadmium with time to cardiovascular disease, accounting for competing risks by death. Identifying the effects through different paths enables us to evaluate the impact of metals on the outcome of interest, as well as through competing risks, more transparently.

在生存分析中不考虑竞争事件可能导致有偏见的估计,因为死于其他原因的个体没有机会发展感兴趣的事件。在存在竞争风险的情况下,对因果效应的正式定义和考虑已经发表,但当暴露不可分离且结果和中介都是非终止事件时,没有针对中介分析设置。我们首次提出了一种基于路径特定效应框架的方法,以考虑纵向中介分析中与事件时间相关的结果的竞争风险。我们通过考虑通过竞争事件的路径作为另一个中介来做到这一点,该中介嵌套在我们感兴趣的纵向中介中。我们提供了基于中介g公式的兴趣效应的理论公式和相关定义,以及算法的详细描述。我们还提出了一项模拟研究,并将我们的算法应用于来自强心脏研究的数据,这是一项美国印第安成年人的前瞻性队列研究。在本应用中,我们评估了血压轨迹(在三次就诊中测量)对砷和镉随时间与心血管疾病的关联的中介作用,并考虑了死亡的竞争风险。通过不同途径确定影响,使我们能够更透明地评估金属对感兴趣的结果的影响,以及通过竞争风险。
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引用次数: 0
Integrating Omics and Pathological Imaging Data for Cancer Prognosis via a Deep Neural Network-Based Cox Model. 基于深度神经网络的Cox模型整合组学和病理成像数据用于癌症预后。
IF 1.8 4区 医学 Q3 MATHEMATICAL & COMPUTATIONAL BIOLOGY Pub Date : 2026-02-01 DOI: 10.1002/sim.70435
Jingmao Li, Shuangge Ma

Modeling prognosis has unique significance in cancer research. For this purpose, omics data have been routinely used. In a series of recent studies, pathological imaging data derived from biopsy have also been shown as informative. Motivated by the complementary information contained in omics and pathological imaging data, we examine integrating them under a Cox modeling framework. The two types of data have distinct properties: for omics variables, which are more actionable and demand stronger interpretability, we model their effects in a parametric way; whereas for pathological imaging features, which are not actionable and do not have lucid interpretations, we model their effects in a nonparametric way for better flexibility and prediction performance. Specifically, we adopt deep neural networks (DNNs) for nonparametric estimation, considering their advantages over regression models in accommodating nonlinearity and providing better prediction. As both omics and pathological imaging data are high-dimensional and are expected to contain noises, we propose applying penalization for selecting relevant variables and regulating estimation. Different from some existing studies, we pay unique attention to overlapping information contained in the two types of data. Numerical investigations are carefully carried out. In the analysis of TCGA data, sensible selection and superior prediction performance are observed, which demonstrates the practical utility of the proposed analysis.

预后建模在肿瘤研究中具有独特的意义。为此目的,组学数据已被常规使用。在最近的一系列研究中,来自活检的病理成像数据也被证明是有用的。由于组学和病理成像数据中包含的互补信息,我们研究了在Cox建模框架下整合它们。这两种类型的数据具有不同的属性:对于组学变量,它们更具可操作性,需要更强的可解释性,我们以参数化的方式建模它们的影响;然而,对于不可操作且没有清晰解释的病理成像特征,我们以非参数方式对其影响进行建模,以获得更好的灵活性和预测性能。具体来说,我们采用深度神经网络(dnn)进行非参数估计,考虑到它们在适应非线性和提供更好的预测方面优于回归模型。由于组学和病理成像数据都是高维的,并且预计会包含噪声,我们建议使用惩罚来选择相关变量和调节估计。与现有的一些研究不同,我们特别关注两类数据中包含的重叠信息。数值研究是认真进行的。在对TCGA数据的分析中,发现了合理的选择和良好的预测性能,证明了该分析方法的实用性。
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引用次数: 0
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Statistics in Medicine
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