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Propensity Score Estimation Using Classification and Regression Trees in the Presence of Missing Covariate Data 在协变量数据缺失的情况下使用分类和回归树进行倾向评分估计
Q3 Mathematics Pub Date : 2018-07-25 DOI: 10.1515/em-2017-0020
Bas B L Penning de Vries, M. van Smeden, R. Groenwold
Abstract Data mining and machine learning techniques such as classification and regression trees (CART) represent a promising alternative to conventional logistic regression for propensity score estimation. Whereas incomplete data preclude the fitting of a logistic regression on all subjects, CART is appealing in part because some implementations allow for incomplete records to be incorporated in the tree fitting and provide propensity score estimates for all subjects. Based on theoretical considerations, we argue that the automatic handling of missing data by CART may however not be appropriate. Using a series of simulation experiments, we examined the performance of different approaches to handling missing covariate data; (i) applying the CART algorithm directly to the (partially) incomplete data, (ii) complete case analysis, and (iii) multiple imputation. Performance was assessed in terms of bias in estimating exposure-outcome effects among the exposed, standard error, mean squared error and coverage. Applying the CART algorithm directly to incomplete data resulted in bias, even in scenarios where data were missing completely at random. Overall, multiple imputation followed by CART resulted in the best performance. Our study showed that automatic handling of missing data in CART can cause serious bias and does not outperform multiple imputation as a means to account for missing data.
数据挖掘和机器学习技术,如分类和回归树(CART)代表了传统逻辑回归对倾向评分估计的一个有希望的替代方案。虽然不完整的数据排除了对所有受试者进行逻辑回归的拟合,但CART之所以吸引人,部分原因是一些实现允许将不完整的记录纳入树拟合中,并为所有受试者提供倾向得分估计。基于理论上的考虑,我们认为CART对丢失数据的自动处理可能并不合适。通过一系列模拟实验,我们检验了处理缺失协变量数据的不同方法的性能;(i)将CART算法直接应用于(部分)不完整的数据,(ii)完整的案例分析,以及(iii)多次插值。评估的标准是评估暴露者的暴露-结果效应偏差、标准误差、均方误差和覆盖率。将CART算法直接应用于不完整的数据会导致偏差,即使在数据完全随机丢失的情况下也是如此。总体而言,多次插补后进行CART的效果最好。我们的研究表明,自动处理CART中缺失的数据可能会导致严重的偏差,并且作为一种解释缺失数据的手段,多重输入的效果并不好。
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引用次数: 8
Mediation Analysis with Attributable Fractions 可归因分数的中介分析
Q3 Mathematics Pub Date : 2018-04-13 DOI: 10.1515/EM-2017-0010
A. Sjölander
Abstract The attributable fraction is a common measure in epidemiological research, which quantifies the public health impact of a particular exposure on a particular outcome. Often, the exposure effect may be mediated through a third variable, which lies on the causal pathway between the exposure and the outcome. To assess the role of such mediators we propose a decomposition of the attributable fraction into a direct component and a mediated component. We show how these components can be estimated in cross-sectional, cohort and case-control studies, using either maximum likelihood or doubly robust estimation methods. We illustrate the proposed methods by an application to a study of physical activity, overweight and CVD. In an Appendix we provide R-code, which implements the proposed methods.
归因分数是流行病学研究中常用的测量方法,它量化了特定暴露对特定结果的公共卫生影响。通常,暴露效应可以通过第三个变量来调节,这是暴露与结果之间的因果关系。为了评估这些中介的作用,我们建议将归因分数分解为直接成分和中介成分。我们展示了如何在横断面、队列和病例对照研究中使用最大似然或双稳健估计方法来估计这些成分。我们通过一个应用于体力活动、超重和心血管疾病的研究来说明所提出的方法。在附录中,我们提供了r代码,它实现了所提出的方法。
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引用次数: 6
Identification of Spikes in Time Series 时间序列中峰值的识别
Q3 Mathematics Pub Date : 2018-01-24 DOI: 10.1515/em-2018-0005
D. Goin, J. Ahern
Abstract Researchers interested in the effects of exposure spikes on an outcome need tools to identify unexpectedly high values in a time series. However, the best method to identify spikes in time series is not known. This paper aims to fill this gap by testing the performance of several spike detection methods in a simulation setting. We created simulations parameterized by monthly violence rates in nine California cities that represented different series features, and randomly inserted spikes into the series. We then compared the ability to detect spikes of the following methods: ARIMA modeling, Kalman filtering and smoothing, wavelet modeling with soft thresholding, and an iterative outlier detection method. We varied the magnitude of spikes from 10 to 50 % of the mean rate over the study period and varied the number of spikes inserted from 1 to 10. We assessed performance of each method using sensitivity and specificity. The Kalman filtering and smoothing procedure had the best overall performance. We applied each method to the monthly violence rates in nine California cities and identified spikes in the rate over the 2005–2012 period.
对暴露峰值对结果的影响感兴趣的研究人员需要工具来识别时间序列中意外的高值。然而,识别时间序列中尖峰的最佳方法尚不清楚。本文旨在通过在仿真环境中测试几种尖峰检测方法的性能来填补这一空白。我们创建了模拟,以加利福尼亚九个城市的月暴力率为参数,代表不同的系列特征,并随机插入峰值到系列中。然后,我们比较了以下方法检测峰值的能力:ARIMA建模、卡尔曼滤波和平滑、软阈值小波建模和迭代离群值检测方法。在研究期间,我们将峰值的幅度从平均速率的10%到50%不等,并将插入的峰值数量从1到10不等。我们使用敏感性和特异性来评估每种方法的性能。卡尔曼滤波平滑方法综合性能最好。我们将每种方法应用于加利福尼亚九个城市的月度暴力率,并确定了2005-2012年期间暴力率的峰值。
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引用次数: 11
Robust and Flexible Estimation of Stochastic Mediation Effects: A Proposed Method and Example in a Randomized Trial Setting. 随机中介效应的稳健和灵活估计:一种在随机试验环境下提出的方法和实例。
Q3 Mathematics Pub Date : 2018-01-01 Epub Date: 2017-12-13 DOI: 10.1515/em-2017-0007
Kara E Rudolph, Oleg Sofrygin, Wenjing Zheng, Mark J van der Laan

Background: Causal mediation analysis can improve understanding of the mechanism s underlying epidemiologic associations. However, the utility of natural direct and indirect effect estimation has been limited by the assumption of no confounder of the mediator-outcome relationship that is affected by prior exposure (which we call an intermediate confounder)--an assumption frequently violated in practice.

Methods: We build on recent work that identified alternative estimands that do not require this assumption and propose a flexible and double robust targeted minimum loss-based estimator for stochastic direct and indirect effects. The proposed method intervenes stochastically on the mediator using a distribution which conditions on baseline covariates and marginalizes over the intermediate confounder.

Results: We demonstrate the estimator's finite sample and robustness properties in a simple simulation study. We apply the method to an example from the Moving to Opportunity experiment. In this application, randomization to receive a housing voucher is the treatment/instrument that influenced moving with the voucher out of public housing, which is the intermediate confounder. We estimate the stochastic direct effect of randomization to the voucher group on adolescent marijuana use not mediated by change in school district and the stochastic indirect effect mediated by change in school district. We find no evidence of mediation.

Conclusions: Our estimator is easy to implement in standard statistical software, and we provide annotated R code to further lower implementation barriers.

背景:因果中介分析可以提高对潜在流行病学关联机制的理解。然而,自然直接和间接效应估计的效用受到受先前暴露影响的中介-结果关系没有混杂因素的假设(我们称之为中间混杂因素)的限制,这是一个在实践中经常违反的假设。方法:我们以最近的工作为基础,确定了不需要这种假设的替代估计,并提出了一个灵活的、双鲁棒的、基于随机直接和间接影响的目标最小损失估计器。所提出的方法使用一个以基线协变量为条件的分布对中介进行随机干预,并在中间混杂因素上边缘化。结果:我们在一个简单的仿真研究中证明了估计器的有限样本和鲁棒性。我们将该方法应用于“抓住机遇”实验中的一个例子。在本应用程序中,随机接收住房券是影响带着住房券离开公共住房的治疗/工具,这是中间混杂因素。我们估计了券组随机化对青少年大麻使用的随机直接效应,不受学区变化的介导,以及学区变化介导的随机间接效应。我们没有发现调解的证据。结论:我们的估计器易于在标准统计软件中实现,并且我们提供了注释的R代码,以进一步降低实现障碍。
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引用次数: 28
Compartmental Model Diagrams as Causal Representations in Relation to DAGs. 作为与 DAG 相关的因果关系表示的隔室模型图。
Q3 Mathematics Pub Date : 2017-12-01 Epub Date: 2017-05-05 DOI: 10.1515/em-2016-0007
S F Ackley, E R Mayeda, L Worden, W T A Enanoria, M M Glymour, T C Porco

Compartmental model diagrams have been used for nearly a century to depict causal relationships in infectious disease epidemiology. Causal directed acyclic graphs (DAGs) have been used more broadly in epidemiology since the 1990s to guide analyses of a variety of public health problems. Using an example from chronic disease epidemiology, the effect of type 2 diabetes on dementia incidence, we illustrate how compartmental model diagrams can represent the same concepts as causal DAGs, including causation, mediation, confounding, and collider bias. We show how to use compartmental model diagrams to explicitly depict interaction and feedback cycles. While DAGs imply a set of conditional independencies, they do not define conditional distributions parametrically. Compartmental model diagrams parametrically (or semiparametrically) describe state changes based on known biological processes or mechanisms. Compartmental model diagrams are part of a long-term tradition of causal thinking in epidemiology and can parametrically express the same concepts as DAGs, as well as explicitly depict feedback cycles and interactions. As causal inference efforts in epidemiology increasingly draw on simulations and quantitative sensitivity analyses, compartmental model diagrams may be of use to a wider audience. Recognizing simple links between these two common approaches to representing causal processes may facilitate communication between researchers from different traditions.

近一个世纪以来,分区模型图一直被用于描述传染病流行病学中的因果关系。自 20 世纪 90 年代以来,有向无环图(DAG)被更广泛地用于流行病学,以指导对各种公共卫生问题的分析。我们以慢性病流行病学中 2 型糖尿病对痴呆症发病率的影响为例,说明了分区模型图如何表示与因果有向无环图相同的概念,包括因果关系、中介关系、混杂关系和碰撞偏差。我们展示了如何使用分区模型图来明确描述相互作用和反馈循环。虽然 DAG 意味着一组条件独立性,但它们并没有参数化地定义条件分布。区室模型图可以参数化(或半参数化)描述基于已知生物过程或机制的状态变化。分区模型图是流行病学因果思维长期传统的一部分,可以参数化表达与 DAG 相同的概念,并明确描述反馈循环和相互作用。随着流行病学中的因果推断越来越多地使用模拟和定量敏感性分析,分区模型图可能会被更多人使用。认识到这两种表示因果过程的常用方法之间的简单联系,可能会促进来自不同传统的研究人员之间的交流。
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引用次数: 0
A General Framework for and New Normalization of Attributable Proportion 归属比例的一般框架与新归一化
Q3 Mathematics Pub Date : 2017-11-27 DOI: 10.1515/em-2015-0028
O. Hössjer, I. Kockum, L. Alfredsson, A. Hedström, T. Olsson, M. Lekman
Abstract A unified theory is developed for attributable proportion (AP) and population attributable fraction (PAF) of joint effects, marginal effects or interaction among factors. We use a novel normalization with a range between –1 and 1 that gives the traditional definitions of AP or PAF when positive, but is different when they are negative. We also allow for an arbitrary number of factors, both those of primary interest and confounders, and quantify interaction as departure from a given model, such as a multiplicative, additive odds or disjunctive one. In particular, this makes it possible to compare different types of threeway or higher order interactions. Effect parameters are estimated on a linear or logit scale in order to find point estimates and confidence intervals for the various versions of AP and PAF, for prospective or retrospective studies. We investigate the accuracy of three confidence intervals; two of which use the delta method and a third bootstrapped interval. It is found that the delta method with logit type transformations, and the bootstrap, perform well for a wide range of models. The methodology is also applied to a multiple sclerosis (MS) data set, with smoking and two genetic variables as risk factors.
摘要建立了因子间联合效应、边际效应或相互作用的归因比例(AP)和总体归因分数(PAF)的统一理论。我们使用了一种新的归一化,其范围在-1和1之间,当AP或PAF为正时给出了传统的定义,但当它们为负时则不同。我们还允许任意数量的因素,包括主要兴趣和混杂因素,并将相互作用量化为偏离给定模型,例如乘法,加性几率或分离性几率。特别是,这使得比较不同类型的三向或高阶相互作用成为可能。在前瞻性或回顾性研究中,以线性或logit量表估计效果参数,以便找到各种版本的AP和PAF的点估计和置信区间。我们研究了三个置信区间的准确性;其中两个使用delta方法,第三个使用自举区间。结果表明,具有logit类型转换的delta方法和自举法在广泛的模型中表现良好。该方法也适用于多发性硬化症(MS)的数据集,吸烟和两个遗传变量作为风险因素。
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引用次数: 5
Doubly Robust Estimator for Indirectly Standardized Mortality Ratios 间接标准化死亡率的双稳健估计
Q3 Mathematics Pub Date : 2017-09-01 DOI: 10.1515/em-2016-0016
Katherine Daignault, O. Saarela
Abstract Routinely collected administrative and clinical data are increasingly being utilized for comparing quality of care outcomes between hospitals. This problem can be considered in a causal inference framework, as such comparisons have to be adjusted for hospital-specific patient case-mix, which can be done using either an outcome or assignment model. It is often of interest to compare the performance of hospitals against the average level of care in the health care system, using indirectly standardized mortality ratios, calculated as a ratio of observed to expected quality outcome. A doubly robust estimator makes use of both outcome and assignment models in the case-mix adjustment, requiring only one of these to be correctly specified for valid inferences. Doubly robust estimators have been proposed for direct standardization in the quality comparison context, and for standardized risk differences and ratios in the exposed population, but as far as we know, not for indirect standardization. We present the causal estimand in indirect standardization in terms of potential outcome variables, propose a doubly robust estimator for this, and study its properties. We also consider the use of a modified assignment model in the presence of small hospitals.
常规收集的行政和临床数据越来越多地被用于比较医院之间的护理结果质量。这个问题可以在因果推理框架中考虑,因为这种比较必须根据医院特定的患者病例组合进行调整,这可以使用结果模型或分配模型来完成。将医院的表现与卫生保健系统的平均护理水平进行比较,通常是令人感兴趣的,使用间接标准化死亡率,计算为观察到的质量结果与预期质量结果的比率。双鲁棒估计器在病例组合调整中同时使用结果模型和分配模型,仅需要其中一个模型被正确指定以进行有效推断。双稳健估计已被提议用于质量比较背景下的直接标准化,以及暴露人群的标准化风险差异和比率,但据我们所知,不用于间接标准化。我们提出了间接标准化中潜在结果变量的因果估计,提出了一个双鲁棒估计,并研究了它的性质。我们还考虑在存在小医院的情况下使用改进的分配模型。
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引用次数: 6
A Bias in the Evaluation of Bias Comparing Randomized Trials with Nonexperimental Studies. 比较随机试验与非实验研究的偏倚评价中的偏倚。
Q3 Mathematics Pub Date : 2017-04-01 Epub Date: 2017-04-22 DOI: 10.1515/em-2016-0018
Jessica M Franklin, Sara Dejene, Krista F Huybrechts, Shirley V Wang, Martin Kulldorff, Kenneth J Rothman

In a recent BMJ article, the authors conducted a meta-analysis to compare estimated treatment effects from randomized trials with those derived from observational studies based on routinely collected data (RCD). They calculated a pooled relative odds ratio (ROR) of 1.31 (95% confidence interval [CI]: 1.03-1.65) and concluded that RCD studies systematically over-estimated protective effects. However, their meta-analysis inverted results for some clinical questions to force all estimates from RCD to be below 1. We evaluated the statistical properties of this pooled ROR, and found that the selective inversion rule employed in the original meta-analysis can positively bias the estimate of the ROR. We then repeated the random effects meta-analysis using a different inversion rule and found an estimated ROR of 0.98 (0.78-1.23), indicating the ROR is highly dependent on the direction of comparisons. As an alternative to the ROR, we calculated the observed proportion of clinical questions where the RCD and trial CIs overlap, as well as the expected proportion assuming no systematic difference between the studies. Out of 16 clinical questions, 50% CIs overlapped for 8 (50%; 25 to 75%) compared with an expected overlap of 60% assuming no systematic difference between RCD studies and trials. Thus, there was little evidence of a systematic difference in effect estimates between RCD and RCTs. Estimates of pooled RORs across distinct clinical questions are generally not interpretable and may be misleading.

在最近的一篇BMJ文章中,作者进行了一项荟萃分析,将随机试验的估计治疗效果与基于常规收集数据(RCD)的观察性研究的估计治疗效果进行比较。他们计算出的合并相对优势比(ROR)为1.31(95%可信区间[CI]: 1.03-1.65),并得出结论,RCD研究系统性地高估了保护作用。然而,他们的荟萃分析推翻了一些临床问题的结果,迫使RCD的所有估计都低于1。我们评估了该合并ROR的统计特性,发现原始荟萃分析中采用的选择性反转规则可以使ROR的估计正偏倚。然后,我们使用不同的反转规则重复随机效应荟萃分析,发现估计的ROR为0.98(0.78-1.23),表明ROR高度依赖于比较的方向。作为ROR的替代方法,我们计算了RCD和试验ci重叠的临床问题的观察比例,以及假设两项研究之间没有系统差异的预期比例。在16个临床问题中,50%的ci重叠8个(50%;25 - 75%),而假设RCD研究和试验之间没有系统差异,预期重叠率为60%。因此,几乎没有证据表明RCD和rct在效果估计上存在系统性差异。对不同临床问题的综合误差率的估计通常是不可解释的,可能会产生误导。
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引用次数: 19
Evaluating the Impact of a HIV Low-Risk Express Care Task-Shifting Program: A Case Study of the Targeted Learning Roadmap. 评估艾滋病低风险快速护理任务转移计划的影响:目标学习路线图案例研究》。
Q3 Mathematics Pub Date : 2016-12-01 Epub Date: 2016-11-10 DOI: 10.1515/em-2016-0004
Linh Tran, Constantin T Yiannoutsos, Beverly S Musick, Kara K Wools-Kaloustian, Abraham Siika, Sylvester Kimaiyo, Mark J van der Laan, Maya Petersen

In conducting studies on an exposure of interest, a systematic roadmap should be applied for translating causal questions into statistical analyses and interpreting the results. In this paper we describe an application of one such roadmap applied to estimating the joint effect of both time to availability of a nurse-based triage system (low risk express care (LREC)) and individual enrollment in the program among HIV patients in East Africa. Our study population is comprised of 16,513 subjects found eligible for this task-shifting program within 15 clinics in Kenya between 2006 and 2009, with each clinic starting the LREC program between 2007 and 2008. After discretizing follow-up into 90-day time intervals, we targeted the population mean counterfactual outcome (i. e. counterfactual probability of either dying or being lost to follow up) at up to 450 days after initial LREC eligibility under three fixed treatment interventions. These were (i) under no program availability during the entire follow-up, (ii) under immediate program availability at initial eligibility, but non-enrollment during the entire follow-up, and (iii) under immediate program availability and enrollment at initial eligibility. We further estimated the controlled direct effect of immediate program availability compared to no program availability, under a hypothetical intervention to prevent individual enrollment in the program. Targeted minimum loss-based estimation was used to estimate the mean outcome, while Super Learning was implemented to estimate the required nuisance parameters. Analyses were conducted with the ltmle R package; analysis code is available at an online repository as an R package. Results showed that at 450 days, the probability of in-care survival for subjects with immediate availability and enrollment was 0.93 (95% CI: 0.91, 0.95) and 0.87 (95% CI: 0.86, 0.87) for subjects with immediate availability never enrolling. For subjects without LREC availability, it was 0.91 (95% CI: 0.90, 0.92). Immediate program availability without individual enrollment, compared to no program availability, was estimated to slightly albeit significantly decrease survival by 4% (95% CI 0.03,0.06, p<0.01). Immediately availability and enrollment resulted in a 7 % higher in-care survival compared to immediate availability with non-enrollment after 450 days (95% CI-0.08,-0.05, p<0.01). The results are consistent with a fairly small impact of both availability and enrollment in the LREC program on incare survival.

在对感兴趣的暴露进行研究时,应采用系统的路线图将因果问题转化为统计分析并解释结果。在本文中,我们介绍了这样一种路线图的应用,它适用于估算东非艾滋病患者中护士分流系统(低风险快速护理(LREC))的可用时间和个人加入该计划的共同影响。我们的研究对象包括 2006 年至 2009 年间肯尼亚 15 家诊所中符合任务分流计划条件的 16513 名受试者,每家诊所都在 2007 年至 2008 年间启动了 LREC 计划。在将随访时间离散为 90 天的时间间隔后,我们将人群平均反事实结果(即死亡或失去随访机会的反事实概率)的目标设定为在最初获得 LREC 资格后的 450 天内,在三种固定的治疗干预下。这三种情况分别是:(i) 在整个随访期间没有提供计划;(ii) 在最初符合条件时立即提供计划,但在整个随访期间没有注册;(iii) 在最初符合条件时立即提供计划并注册。我们还进一步估算了在假定干预措施阻止个人参与计划的情况下,立即提供计划与不提供计划相比所产生的直接控制效果。我们使用基于最小损失的目标估计法来估计平均结果,同时使用超级学习法来估计所需的干扰参数。分析使用 ltmle R 软件包进行;分析代码作为 R 软件包可从在线存储库中获取。结果显示,在 450 天时,立即可用且注册的受试者的护理生存概率为 0.93(95% CI:0.91,0.95),而立即可用且从未注册的受试者的护理生存概率为 0.87(95% CI:0.86,0.87)。而对于没有 LREC 的受试者,这一比例为 0.91(95% CI:0.90,0.92)。据估计,与不提供项目相比,不进行个人注册但可立即提供项目的受试者的存活率会略微降低 4%(95% CI 0.03,0.06,P<0.05)。
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引用次数: 0
A Note on the Mantel-Haenszel Estimators When the Common Effect Assumptions Are Violated 关于违反共同效应假设时的Mantel-Haenszel估计量的注记
Q3 Mathematics Pub Date : 2016-12-01 DOI: 10.1515/em-2015-0004
H. Noma, K. Nagashima
Abstract The Mantel-Haenszel estimators for the common effect parameters of stratified 2×2 tables have been widely adopted in epidemiological and clinical studies for controlling the effects of confounding factors. Although the Mantel-Haenszel estimators are simple and effective estimating methods, the correctness of the common effect assumptions cannot be justified in general practices. Also then, the targeted “common effect parameters” do not exist. Under these settings, even if the Mantel-Haenszel estimators have desirable properties, it is quite uncertain what they estimate and how the estimates are interpreted. In this article, we conducted theoretical evaluations for their asymptotic behaviors when the common effect assumptions are violated. We explicitly showed that the Mantel-Haenszel estimators converge to weighted averages of stratum-specific effect parameters and they can be interpreted as intuitive summaries of the stratum-specific effect measures. Also, the Mantel-Haenszel estimators correspond to the standardized effect measures on standard distributions of stratification variables to be the total cohort, approximately. In addition, the ordinary sandwich-type variance estimators are still valid for quantifying variabilities of the Mantel-Haenszel estimators. We implemented numerical studies based on two epidemiologic studies of breast cancer and schizophrenia for evaluating empirical properties of these estimators, and confirmed general validities of these theoretical results.
摘要在流行病学和临床研究中,广泛采用分层2×2表共同效应参数的Mantel-Haenszel估计量来控制混杂因素的影响。尽管Mantel-Haenszel估计是一种简单有效的估计方法,但在一般实践中不能证明常见效果假设的正确性。同样,目标的“通用效果参数”也不存在。在这些情况下,即使Mantel-Haenszel估计器具有理想的性质,它们估计什么以及如何解释估计也是相当不确定的。在本文中,我们对它们在违反共同效应假设时的渐近行为进行了理论评价。我们明确地表明,Mantel-Haenszel估计收敛于层特异性效应参数的加权平均值,它们可以被解释为层特异性效应测度的直观总结。此外,Mantel-Haenszel估计量近似地对应于分层变量标准分布的标准化效应测度。此外,普通的三明治型方差估计量对于量化Mantel-Haenszel估计量的可变性仍然有效。我们基于两项乳腺癌和精神分裂症的流行病学研究实施了数值研究,以评估这些估计器的经验性质,并证实了这些理论结果的一般有效性。
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引用次数: 6
期刊
Epidemiologic Methods
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