Evaluation of various estimators for standardized mean difference in meta‐analysis

Meta‐analyses of a treatment's effect compared with a control frequently calculate the meta‐effect from standardized mean differences (SMDs). SMDs are usually estimated by Cohen's d or Hedges' g. Cohen's d divides the difference between sample means of a continuous response by the pooled standard deviation, but is subject to nonnegligible bias for small sample sizes. Hedges' g removes this bias with a correction factor. The current literature (including meta‐analysis books and software packages) is confusingly inconsistent about methods for synthesizing SMDs, potentially making reproducibility a problem. Using conventional methods, the variance estimate of SMD is associated with the point estimate of SMD, so Hedges' g is not guaranteed to be unbiased in meta‐analyses. This article comprehensively reviews and evaluates available methods for synthesizing SMDs. Their performance is compared using extensive simulation studies and analyses of actual datasets. We find that because of the intrinsic association between point estimates and standard errors, the usual version of Hedges' g can result in more biased meta‐estimation than Cohen's d. We recommend using average‐adjusted variance estimators to obtain an unbiased meta‐estimate, and the Hartung‐Knapp‐Sidik‐Jonkman method for accurate estimation of its confidence interval.     

Expressing findings from meta-analyses of continuous outcomes in terms of risks

Meta-analyses of clinical trials with continuous outcome data typically report the effect of an intervention as either a mean difference or a standardized mean difference. These results can be difficult to interpret, and re-expressing the effect size in terms of risk may facilitate understanding and applicability. We describe three methods for obtaining risks in such situations. Two of these methods involve direct transformation of a standardized mean difference to an odds ratio. The third entails estimation of risks in the two groups for a specific cut point. We extend this third approach to a completed meta-analysis by expressing the finding in the format of a single 'meta-study'. We compare the methods in two examples of meta-analyses and in a series of simulation studies that examine their properties in individual studies and in meta-analyses. These simulations show that the methods for expressing meta-analysis results from continuous outcomes are sensitive to underlying distributions, sample sizes and cut points but are remarkably robust to the presence of heterogeneity across studies. We offer suggestions of situations in which the various methods may safely be applied. In particular, if the underlying distribution is approximately normal, then estimation of risks for a specific cut point may be used for large sample sizes; direct transformations may be preferable otherwise. However, if the standard deviations in the two groups are notably different, then none of the methods have good properties. Furthermore, absolute risks are safely estimated after direct transformation only if they are in the region of 20% to 80%.     

A note on the empirical Bayes heterogeneity variance estimator in meta-analysis

This paper focuses on the empirical Bayes (EB) or Mandel-Paule estimator of the heterogeneity variance in meta-analysis, which was discussed by Morris and proposed in earlier publications by Mandel and Paule in an inter-laboratory context. The relationship of the EB estimator to other heterogeneity variance estimators typically used in meta-analysis is explored, and approximate variance estimators for the EB estimate of the heterogeneity variance are proposed based on the M-estimation method. Statistical inference for the overall treatment effect using the EB estimator and the proposed standard errors is discussed using two example data sets from meta-analysis applications.     

Clinical heterogeneity in random-effect meta-analysis: Between-study boundary estimate problem

Random-effect meta-analysis is commonly applied to estimate overall effects with unexplained heterogeneity across studies. However, standard methods, including (restricted) maximum likelihood (ML or REML), frequently produce (near) zero estimates for between-study variance parameters. Consequently, these methods are reduced to simple and unrealistic fixed-effect models, resulting in an ignorance of the substantial clinical heterogeneity and sometimes leading to incorrect conclusions. To solve the boundary estimate problem, we propose (1) an adjusted maximum likelihood method for the between-study variance that maximizes a likelihood defined as a product of a standard likelihood and a Gaussian class of adjustment factor and (2) a framework using sensitivity analysis by developing a new criterion to check for the occurrence of the boundary estimate. Although the adjustment introduces bias to the overall effects to ensure strictly positive estimates of the between-study variance when the number of studies K is small, the bias asymptotically approaches zero, resulting in the same estimates derived from the REML method. Moreover, the adjusted maximum likelihood estimator of the between-study variance is consistent for large K, and interestingly, the REML method and our method are equivalent in terms of mean squared error criterion, up to O(K⁻¹). We illustrate our approach with a motivating example to examine the controversial result of a meta-analysis for 24 randomized controlled trials of human albumin. Numerical evaluations show that our approach produces no boundary estimates but similar synthesized results with the standard maximum likelihood methods as those produced by conventional methods, especially with a small number of studies.     

Statistical methodology for estimating the mean difference in a meta‐analysis without study‐specific variance information

Statistical inference for analyzing the results from several independent studies on the same quantity of interest has been investigated frequently in recent decades. Typically, any meta‐analytic inference requires that the quantity of interest is available from each study together with an estimate of its variability. The current work is motivated by a meta‐analysis on comparing two treatments (thoracoscopic and open) of congenital lung malformations in young children. Quantities of interest include continuous end‐points such as length of operation or number of chest tube days. As studies only report mean values (and no standard errors or confidence intervals), the question arises how meta‐analytic inference can be developed. We suggest two methods to estimate study‐specific variances in such a meta‐analysis, where only sample means and sample sizes are available in the treatment arms. A general likelihood ratio test is derived for testing equality of variances in two groups. By means of simulation studies, the bias and estimated standard error of the overall mean difference from both methodologies are evaluated and compared with two existing approaches: complete study analysis only and partial variance information. The performance of the test is evaluated in terms of type I error. Additionally, we illustrate these methods in the meta‐analysis on comparing thoracoscopic and open surgery for congenital lung malformations and in a meta‐analysis on the change in renal function after kidney donation. Copyright © 2017 John Wiley & Sons, Ltd.     

Ratio of means for analyzing continuous outcomes in meta-analysis performed as well as mean difference methods

Objective

Meta-analyses of continuous outcomes typically use mean differences (MDs) or standardized mean differences (SMDs) (MD in pooled standard deviation units). Ratio of means (RoM) is an alternative effect measure that performs comparably in simulation. We compared treatment effects and heterogeneity for RoM, MD, and SMD using empiric data.

Study Design and Setting

From the Cochrane Database (2008, issue 1), we included systematic reviews reporting continuous outcomes, selected the meta-analysis with the most (and ≥five) trials, and calculated MD (where possible), SMD, and RoM. For each pair of effect measures, we compared P-values separately for treatment effect and heterogeneity and assessed asymmetry of discordant pairs (statistically significant result for only one of two measures).

Results

Two hundred thirty-two of 5,053 reviews were included. Measures demonstrated similar treatment effects, with ≤6% discordant pairs and no asymmetry. A 0.5 SMD increase corresponded to 22 (95% confidence interval: 19, 24)% increase using RoM. There was less heterogeneity in RoM vs. MD (n = 143, P = 0.007), SMD vs. RoM (n = 232, P = 0.005), and SMD vs. MD (n = 143, P = 0.004). Comparing discordant pairs, fewer meta-analyses showed significant heterogeneity with SMD vs. RoM (P = 0.04), consistent with the known bias of SMD.

Conclusion

Empiric data from diverse meta-analyses demonstrate similar treatment effects and no large differences in heterogeneity of RoM compared with difference-based methods.     

Estimating restricted mean treatment effects with stacked survival models

The difference in restricted mean survival times between two groups is a clinically relevant summary measure. With observational data, there may be imbalances in confounding variables between the two groups. One approach to account for such imbalances is estimating a covariate‐adjusted restricted mean difference by modeling the covariate‐adjusted survival distribution and then marginalizing over the covariate distribution. Because the estimator for the restricted mean difference is defined by the estimator for the covariate‐adjusted survival distribution, it is natural to expect that a better estimator of the covariate‐adjusted survival distribution is associated with a better estimator of the restricted mean difference. We therefore propose estimating restricted mean differences with stacked survival models. Stacked survival models estimate a weighted average of several survival models by minimizing predicted error. By including a range of parametric, semi‐parametric, and non‐parametric models, stacked survival models can robustly estimate a covariate‐adjusted survival distribution and, therefore, the restricted mean treatment effect in a wide range of scenarios. We demonstrate through a simulation study that better performance of the covariate‐adjusted survival distribution often leads to better mean squared error of the restricted mean difference although there are notable exceptions. In addition, we demonstrate that the proposed estimator can perform nearly as well as Cox regression when the proportional hazards assumption is satisfied and significantly better when proportional hazards is violated. Finally, the proposed estimator is illustrated with data from the United Network for Organ Sharing to evaluate post‐lung transplant survival between large‐volume and small‐volume centers. Copyright © 2016 John Wiley & Sons, Ltd.     

Simulation and data-generation for random-effects network meta-analysis of binary outcome

The performance of statistical methods is frequently evaluated by means of simulation studies. In case of network meta-analysis of binary data, however, available data-generating models (DGMs) are restricted to either inclusion of two-armed trials or the fixed-effect model. Based on data-generation in the pairwise case, we propose a framework for the simulation of random-effect network meta-analyses including multiarm trials with binary outcome. The only one of the common DGMs used in the pairwise case, which is directly applicable to a random-effects network setting uses strongly restrictive assumptions. To overcome these limitations, we modify this approach and derive a related simulation procedure using odds ratios as effect measure. The performance of this procedure is evaluated with synthetic data and in an empirical example.     

Variance estimation and confidence intervals for the standardized mortality ratio with application to the assessment of a cancer screening program

The effect of a cancer screening program can be measured through the standardized mortality ratio (SMR) statistic. The numerator of the SMR is the observed number of deaths from the screened disease among participants in the screening program, whereas the denominator of the SMR is an estimate of the expected number of deaths in these participants under the assumption that the screening program has no effect. In this article, we propose a variance estimator for the denominator of the SMR when this expected number of deaths is estimated with Sasieni's method. We give both a general formula for this variance as well as formulas for specific disease incidence and survival estimators. We show how this new variance estimator can be used to build confidence intervals for the SMR. We investigate the coverage properties of various types of confidence intervals by simulation and find that intervals that make use of the proposed variance estimator perform well. We illustrate the method by applying it to the Québec Breast Cancer Screening program.     

An Updated Method for Risk Adjustment in Outcomes Research

ObjectiveTo demonstrate why meta-analytic methods need modification before they can be used to aggregate rates or effect sizes in outcomes research, under the constraint of no common underlying effect or rate.MethodsStudies are presented that require different types of risk adjustment. First, we demonstrate using rates that external risk adjustment through standardization can be achieved using modified meta-analytic methods, but only with a model that allows input of user-defined weights. Next, we extend these observations to internal risk adjustment of comparative effect sizes.ResultsWe show that this procedure produces identical results to conventional age standardization if a rate is being standardized for age. We also demonstrate that risk adjustment of effect sizes can be achieved with this modified method but cannot be done using standard meta-analysis.ConclusionsWe conclude that this method allows risk adjustment to be performed in situations in which currently the fixed- or random-effects methods of meta-analysis are inappropriately used. The latter should be avoided when the underlying aim is risk adjustment rather than meta-analysis.     

Inconsistencies with formulas for the standard error of the standardized mean difference of repeated measures experiments

There are inconsistencies between the formulas for the variance of standardized mean difference (SMD ) in the Cochrane Handbook for Systematic Reviews and the variance reported in other sources. Instead of the variance appropriate for the SMD of a crossover experiment, the Cochrane Handbook uses the variance appropriate for a pre-test post-test experiment. This means that if there is a non-negligible time period effect, the formula reported by the Handbook will underestimate both the effect size and its variance. In addition, the formula for the standard error of SMD reported in the Cochrane Handbook (in section 23.2.7.2) is inconsistent with the variance derived from the variance of the related t− test. Even if the period effect is negligible, the Cochrane Handbook formula is biased toward underestimates. The difference between the estimates from the two formulas will be small if either the correlation between the repeated measures, or the magnitude of the SMD estimate, is small, or if the sample size is large. However, it can be can be quite substantial in other circumstances.     

Meta‐analysis of absolute mean differences from randomised trials with treatment‐related clustering associated with care providers

Nesting of patients within care providers in trials of physical and talking therapies creates an additional level within the design. The statistical implications of this are analogous to those of cluster randomised trials, except that the clustering effect may interact with treatment and can be restricted to one or more of the arms. The statistical model that is recommended at the trial level includes a random effect for the care provider but allows the provider and patient level variances to differ across arms. Evidence suggests that, while potentially important, such within‐trial clustering effects have rarely been taken into account in trials and do not appear to have been considered in meta‐analyses of these trials. This paper describes summary measures and individual‐patient‐data methods for meta‐analysing absolute mean differences from randomised trials with two‐level nested clustering effects, contrasting fixed and random effects meta‐analysis models. It extends methods for incorporating trials with unequal variances and homogeneous clustering to allow for between‐arm and between‐trial heterogeneity in intra‐class correlation coefficient estimates. The work is motivated by a meta‐analysis of trials of counselling in primary care, where the control is no counselling and the outcome is the Beck Depression Inventory. Assuming equal counsellor intra‐class correlation coefficients across trials, the recommended random‐effects heteroscedastic model gave a pooled absolute mean difference of ?2.53 (95% CI ?5.33 to 0.27) using summary measures and ?2.51 (95% CI ?5.35 to 0.33) with the individual‐patient‐data. Pooled estimates were consistently below a minimally important clinical difference of four to five points on the Beck Depression Inventory. Copyright © 2014 John Wiley & Sons, Ltd.     

提高标准化病人“标准化”程度的实践与思考

标准化病人（Standardized Patients，SP）目前在我国发展较快，很多医学院校已将SP应用于临床技能培训和考核，但是如何使SP真正达到“标准化”，目前依然缺乏统一的标准体系。文章根据SP的实施情况，结合文献报道，初步探讨如何对SP志愿者的招募、培训脚本撰写、培训流程、人员管理等各个环节进行标准化设置，并提出一些可行性方案和建议，以推进SP在我国的“标准化”进程。     

ISO质量管理体系与医疗设备的标准化管理

本文介绍医院医疗设备管理中贯彻ISO9000国际标准化质量管理的方法。     

规范化培训护士自主学习能力调查及影响因素分析

目的 调查规范化培训护士自主学习能力,并探讨临床教学因素对自主学习能力的影响.方法 采用《临床教学情况调查问卷》和《护理人员自主学习能力评价量表》对某院176名规范化培训护士进行问卷调查,并对结果进行分析.结果 规范化培训护士自主学习能力一般,总得分为(123.03±19.84)分;影响因素按照作用强度依次为专业兴趣、自我效能感、教学环境、学习目标和对教师的满意度.复相关系数R=0.357,R2=0.139.结论 护理教育工作者应针对规范化培训护士的特征,提高其自主学习能力,以保证规范化培训护士有能力按照工作岗位要求完成所承担或将要承担的工作和任务.     

Analysis of censored discrete longitudinal data: Estimation of mean response

The study of longitudinal data is usually concerned with one or several response variables measured, possibly along with some covariates, at different points in time. In real‐life situations this is often complicated by missing observations due to what we usually refer to as ‘censoring’. In this paper we consider missingness of a monotone kind; subjects that dropout, i.e. are censored, fail to participate in the study at any of the subsequent observation times. Our scientific objective is to make inference about the mean response in a hypothetical population without any dropouts. There are several methods and approaches that address this problem, and we will present two existing methods (the linear‐increments method and the inverse‐probability‐weighting method), as well as propose a new method, based on a discrete Markov process. We examine the performance of the corresponding estimators and compare these with respect to bias and variability. To demonstrate the effectiveness of the approaches in estimating the mean of a response variable, we analyse simulated data of different multistate models with a Markovian structure. Analyses of substantive data from (1) a study of symptoms experienced after a traumatic brain injury, and (2) a study of cognitive function among the elderly, are used as illustrations of the methods presented. Copyright © 2008 John Wiley & Sons, Ltd.     

安徽省1997～2001年食品卫生标化合格率分析

率的标准化法已广泛用于疾病统计 ,但用在食品卫生合格率的比较者甚少 ,大多用平均合格率 ,其结果常出现判断错误。本文对安徽省 1 997～ 2 0 0 1年食品监测的结果作了对比分析 ,各年度食品卫生平均合格率为 83 .62 %、84.99%、85 .72 %、87.0 8%、75 .76 % ;其标化合格率则分别为 83 .87%、84.74%、85 .79%、87.1 7%、81 .32 %。分析认为 ,标化合格率由于不受食品种类和构成的影响 ,因而较平均合格率更合理、准确 ,较能表明食品卫生的真实结果 ,亦符合我省实际情况。     

Meta-analysis on continuous outcomes in minimal important difference units: an application with appropriate variance calculations

ObjectiveTo compare results from meta-analyses for mean differences in minimal important difference (MID) units (MD_MID), when MID is treated as a random variable vs. a constant.Study Design and SettingMeta-analyses of published data. We calculated the variance of MD_MID as a random variable using the delta method and as a constant. We assessed performance under different assumptions. We compare meta-analysis results from data originally used to present the MD_MID and data from osteoarthritis studies using different domain instruments.ResultsDepending on the data set and depending on the values of rho and coefficient of variation of the MID (CoV_MID), estimates of treatment effect and P-values between an approach considering the MID as a constant vs. as a random variable may differ appreciably. Using our data sets, we provide examples of the potential magnitude. When rho = 0.5 and CoV_MID = 0.8, considering MID as a constant overestimated the treatment effect by 33–110% and decreased the P-value for heterogeneity from above 0.95 to below 0.08. When rho = 0.8 and CoV_MID = 0.5, the magnitude of the effects was similar.ConclusionsConsidering MID as a random variable avoids unrealistic assumptions and provides more appropriate treatment effect estimates.     

浙江省公共卫生医师规范化培训认知与需求分析

目的：了解浙江省公共卫生医师对其规范化培训的认知与需求情况,探讨基层公卫医师规范化培训必要性与可行性,为更好开展规范化培训提供科学依据。方法：选择整群抽样的方法,结合现场座谈和问卷调查对目标人群进行调查。结果：大多数调查对象认为公卫医师规范化培训重要且必要,但76.86%认为脱产参加公卫医师规范化培训困难很大或较大;培训对象：74.38%认为全部公共卫生医师不论学历都应该参加公卫医师规范化培训;培训期限：绝大多数认为无论本科还是硕士,以1年较为合适;培训内容：超过85.00%的调查对象认为传染病预防与控制、慢性病、健康教育、营养与食品卫生、环境卫生及职业卫生等16个专业需要和非常需要培训;福利保障：85.95%认为选派学员工资福利待遇应予以保障。结论：基层公卫医师脱产培训困难较大,需优化培训内容,灵活培训模式,避免增加基层公共卫生机构工学矛盾;同时增加培训投入,保障学员工资福利待遇,逐步建立并完善公共卫生医师培训体系。