Meta-analysis of continuous outcomes combining individual patient data and aggregate data

Meta-analysis of individual patient data (IPD) is the gold-standard for synthesizing evidence across clinical studies. However, for some studies IPD may not be available and only aggregate data (AD), such as a treatment effect estimate and its standard error, may be obtained. In this situation, methods for combining IPD and AD are important to utilize all the available evidence. In this paper, we develop and assess a range of statistical methods for combining IPD and AD in meta-analysis of continuous outcomes from randomized controlled trials.The methods take either a one-step or a two-step approach. The latter is simple, with IPD reduced to AD so that standard AD meta-analysis techniques can be employed. The one-step approach is more complex but offers a flexible framework to include both patient-level and trial-level parameters. It uses a dummy variable to distinguish IPD trials from AD trials and to constrain which parameters the AD trials estimate. We show that this is important when assessing how patient-level covariates modify treatment effect, as aggregate-level relationships across trials are subject to ecological bias and confounding. We thus develop models to separate within-trial and across-trials treatment-covariate interactions; this ensures that only IPD trials estimate the former, whilst both IPD and AD trials estimate the latter in addition to the pooled treatment effect and any between-study heterogeneity. Extension to multiple correlated outcomes is also considered. Ten IPD trials in hypertension, with blood pressure the continuous outcome of interest, are used to assess the models and identify the benefits of utilizing AD alongside IPD.     

Meta-analysis of ordinal outcomes using individual patient data

Meta-analyses are being undertaken in an increasing diversity of diseases and conditions, some of which involve outcomes measured on an ordered categorical scale. We consider methodology for undertaking a meta-analysis on individual patient data for an ordinal response. The approach is based on the proportional odds model, in which the treatment effect is represented by the log-odds ratio. A general framework is proposed for fixed and random effect models. Tests of the validity of the various assumptions made in the meta-analysis models, such as a global test of the assumption of proportional odds between treatments, are presented. The combination of studies with different definitions or numbers of response categories is discussed. The methods are illustrated on two data sets, in a classical framework using SAS and MLn and in a Bayesian framework using BUGS. The relative merits of the three software packages for such meta-analyses are discussed.     

The meta-analysis of data from individual patients

- An IPD (Individual Participant Data) meta-analysis requires collecting original individual patient data and calculating an estimated effect based on these data.- The use of individual patient data has various advantages: the original data and the results of published analyses are verified, comparability between studies in terms of definitions, coding and analyses is increased, the number of options for performing sub-group analyses becomes greater, and it becomes possible to conduct more complex statistical analyses, such as the pooling of time-dependent data and multivariate regression analyses.- In an IPD meta-analysis, additional information can be used which was not mentioned in the original article, for example, data from long-term follow-up.- Improvements to this methodology are still possible; for example, to find the right balance between sufficient power to detect clinically relevant subgroup effects and minimizing the risk of false-positive findings.- Readers can evaluate an IPD meta-analysis on various factors, including the reason for the choice for an IPD meta-analysis, the method used to identify and select the studies, and the number of approached authors that made their data available.     

Meta-analysis of diagnostic test studies using individual patient data and aggregate data

A meta-analysis of diagnostic test studies provides evidence-based results regarding the accuracy of a particular test, and usually involves synthesizing aggregate data (AD) from each study, such as the 2 by 2 tables of diagnostic accuracy. A bivariate random-effects meta-analysis (BRMA) can appropriately synthesize these tables, and leads to clinical results, such as the summary sensitivity and specificity across studies. However, translating such results into practice may be limited by between-study heterogeneity and that they relate to some 'average' patient across studies.In this paper we describe how the meta-analysis of individual patient data (IPD) from diagnostic studies can lead to clinical results more tailored to the individual patient. We develop IPD models that extend the BRMA framework to include study-level covariates, which help explain the between-study heterogeneity, and also patient-level covariates, which allow one to assess the effect of patient characteristics on test accuracy. We show how the inclusion of patient-level covariates requires a careful separation of within-study and across-study accuracy-covariate effects, as the latter are particularly prone to confounding. Our models are assessed through simulation and extended to allow IPD studies to be combined with AD studies, as IPD are not always available for all studies. Application is made to 23 studies assessing the accuracy of ear thermometers for diagnosing fever in children, with 16 IPD and 7 AD studies. The models reveal that between-study heterogeneity is partly explained by the use of different measurement devices, but there is no evidence that being an infant modifies diagnostic accuracy.     

Meta‐analysis of randomised trials with a continuous outcome according to baseline imbalance and availability of individual participant data

We describe methods for meta‐analysis of randomised trials where a continuous outcome is of interest, such as blood pressure, recorded at both baseline (pre treatment) and follow‐up (post treatment). We used four examples for illustration, covering situations with and without individual participant data (IPD) and with and without baseline imbalance between treatment groups in each trial. Given IPD, meta‐analysts can choose to synthesise treatment effect estimates derived using analysis of covariance (ANCOVA), a regression of just final scores, or a regression of the change scores. When there is baseline balance in each trial, treatment effect estimates derived using ANCOVA are more precise and thus preferred. However, we show that meta‐analysis results for the summary treatment effect are similar regardless of the approach taken. Thus, without IPD, if trials are balanced, reviewers can happily utilise treatment effect estimates derived from any of the approaches. However, when some trials have baseline imbalance, meta‐analysts should use treatment effect estimates derived from ANCOVA, as this adjusts for imbalance and accounts for the correlation between baseline and follow‐up; we show that the other approaches can give substantially different meta‐analysis results. Without IPD and with unavailable ANCOVA estimates, reviewers should limit meta‐analyses to those trials with baseline balance. Trowman's method to adjust for baseline imbalance without IPD performs poorly in our examples and so is not recommended. Finally, we extend the ANCOVA model to estimate the interaction between treatment effect and baseline values and compare options for estimating this interaction given only aggregate data. Copyright © 2013 John Wiley & Sons, Ltd.     

Rare variants association testing for a binary outcome when pooling individual level data from heterogeneous studies

Whole genome sequencing (WGS) and whole exome sequencing studies are used to test the association of rare genetic variants with health traits. Many existing WGS efforts now aggregate data from heterogeneous groups, for example, combining sets of individuals of European and African ancestries. We here investigate the statistical implications on rare variant association testing with a binary trait when combining together heterogeneous studies, defined as studies with potentially different disease proportion and different frequency of variant carriers. We study and compare in simulations the Type 1 error control and power of the naïve score test, the saddlepoint approximation to the score test, and the BinomiRare test in a range of settings, focusing on low numbers of variant carriers. We show that Type 1 error control and power patterns depend on both the number of carriers of the rare allele and on disease prevalence in each of the studies. We develop recommendations for association analysis of rare genetic variants. (1) The Score test is preferred when the case proportion in the sample is 50%. (2) Do not down‐sample controls to balance case–control ratio, because it reduces power. Rather, use a test that controls the Type 1 error. (3) Conduct stratified analysis in parallel with combined analysis. Aggregated testing may have lower power when the variant effect size differs between strata.     

Estimating transformations for repeated measures modeling of continuous bounded outcome data

Continuous bounded outcome data are unlikely to meet the usual assumptions for mixed-effects models of normally distributed and independent subject-specific and residual random effects. Additionally, overly complicated model structures might be necessary to account adequately for non-drug (time-dependent) and drug treatment effects. A transformation strategy with a likelihood component for censoring is developed to promote the simplicity of model structures and to improve the plausibility of assumptions on the random effects. The approach is motivated by Health Assessment Questionnaire Disability Index (HAQ-DI) data from a study in subjects with rheumatoid arthritis and is evaluated using a simulation study.     

Analysis of an incomplete binary outcome derived from frequently recorded longitudinal continuous data: application to daily pain evaluation

Randomized clinical trials increasingly collect daily data, frequently using electronic diaries. Such data are usually summarized into an 'intermediate' continuous outcome (such as the mean of the daily values in a period before a scheduled clinic visit). These are in turn often summarized further into a binary outcome, for example, indicating whether the intermediate continuous outcome has improved by a prespecified amount from randomization. This article compares and contrasts statistical approaches for analyzing such binary outcomes when the underlying study is subject to dropout so that some of the underlying diary data are missing. Such analysis involves rigorous rules for the derivation of outcomes, a thorough data exploration for the selection of covariates, and an elucidation of the missingness mechanism. The investigated statistical methods for treatment-effect analysis are based on direct modeling and on multiple imputation and are applied either to the binary outcome or the intermediate continuous outcome or to the daily diary data. These are compared on the basis of criteria for inferences at prespecified times during the follow-up. We show that multiple-imputation methods are particularly well adapted to our context and that missing data imputation on the daily diary data, rather than the derived outcomes, makes best use of the available information. The data set, which motivated our investigation, comes from a placebo-controlled clinical trial to assess the effect on pain of a new compound.     

Meta-analysis when only the median survival times are known: a comparison with individual patient data results

BACKGROUND: The hazard ratio (HR) is the most appropriate measure for time to event outcomes such as survival. In systematic reviews, HRs can be calculated either from the raw trial data obtained as part of an individual patient data (IPD) meta-analysis or from the appropriate trial-level summary statistics. However, the information required for the latter are seldom reported in sufficient detail to allow reviewers to calculate HRs. In contrast, the median survival and survival rates at specific time points are frequently presented. We aimed to evaluate retrospectively the performance of meta-analyses using median survival times and survival rates by comparing them with meta-analyses using IPD to calculate HRs. METHODS: IPD from thirteen published meta-analyses (MAs) in cancers with high mortality rates were used. Median survival and survival rates were calculated from the IPD rather than taken from publications so that the same trials, patients, and extended follow-up are used in each analysis. RESULTS AND CONCLUSIONS: We show that using median survival times or survival rates at a particular point in time are not reasonable surrogate measures for meta-analyses of survival outcomes and that, wherever possible, HRs should be calculated. Individual trial publications reporting on time to event outcomes, therefore, should provide more detailed statistical information, preferably logHRs and their variances, or their estimators.     

Detecting pleiotropy in Mendelian randomisation studies with summary data and a continuous outcome

Mendelian randomisation (MR) estimates causal effects of modifiable phenotypes on an outcome by using genetic variants as instrumental variables, but its validity relies on the assumption of no pleiotropy, that is, genes influence the outcome only through the given phenotype. Excluding pleiotropy is difficult, but the use of multiple instruments can indirectly address the issue: if all genes represent valid instruments, their MR estimates should vary only by chance. The Sargan test detects pleiotropy when individual phenotype, outcome and genotype data are measured in the same subjects. We propose an alternative approach to be used when only summary genetic data are available or data on gene‐phenotype and gene‐outcome come from different subjects. The presence of pleiotropy is investigated using the between‐instrument heterogeneity Q test (together with the I² index) in a meta‐analysis of MR Wald estimates, derived separately from each instrument. For a continuous outcome, we evaluate the approach through simulations and illustrate it using published data. For the scenario where all data come from the same subjects, we compare it with the Sargan test. The Q test tends to be conservative in small samples. Its power increases with the degree of pleiotropy and the sample size, as does the precision of the I² index, in which case results are similar to those of the Sargan test. In MR studies with large sample sizes based on summary data, the between‐instrument Q test represents a useful tool to explore the presence of heterogeneity due to pleiotropy or other causes. Copyright © 2015 John Wiley & Sons, Ltd.     

Handling incomplete correlated continuous and binary outcomes in meta‐analysis of individual participant data

Meta‐analysis of individual participant data (IPD) is increasingly utilised to improve the estimation of treatment effects, particularly among different participant subgroups. An important concern in IPD meta‐analysis relates to partially or completely missing outcomes for some studies, a problem exacerbated when interest is on multiple discrete and continuous outcomes. When leveraging information from incomplete correlated outcomes across studies, the fully observed outcomes may provide important information about the incompleteness of the other outcomes. In this paper, we compare two models for handling incomplete continuous and binary outcomes in IPD meta‐analysis: a joint hierarchical model and a sequence of full conditional mixed models. We illustrate how these approaches incorporate the correlation across the multiple outcomes and the between‐study heterogeneity when addressing the missing data. Simulations characterise the performance of the methods across a range of scenarios which differ according to the proportion and type of missingness, strength of correlation between outcomes and the number of studies. The joint model provided confidence interval coverage consistently closer to nominal levels and lower mean squared error compared with the fully conditional approach across the scenarios considered. Methods are illustrated in a meta‐analysis of randomised controlled trials comparing the effectiveness of implantable cardioverter‐defibrillator devices alone to implantable cardioverter‐defibrillator combined with cardiac resynchronisation therapy for treating patients with chronic heart failure. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.     

Meta-analysis of individual- and aggregate-level data

The methodology described here was developed for a systematic review and individual participant-level meta-analysis of home safety education and the provision of safety equipment for the prevention of childhood accidents. This review had a particular emphasis on exploring whether effectiveness was related to socio-demographic characteristics previously shown to be associated with injury risk. Individual participant data were only made available to us for a proportion of the included studies. This resulted in the need for developing a new methodology to combine the available data most efficiently.Our objective was to develop a (random effects) meta-analysis model that could synthesize both individual-level and aggregate-level binary outcome data while exploring the effects of binary covariates also available in a combination of individual participant and aggregate level data. To add further complication, the studies to be combined were a mixture of cluster and individual participant-allocated designs.A Bayesian model using Markov chain Monte Carlo methods to estimate parameters is described which efficiently synthesizes the data by allowing different models to be fitted to the different study design and data format combinations available. Initially we describe a model to estimate mean effects ignoring the influence of the covariates, and then extend it to include a binary covariate. The application of the method is illustrated by application to one outcome from the motivating home safety meta-analysis for illustration. Using the same general approach, it would be possible to develop further 'tailor made' evidence synthesis models to synthesize all available evidence most effectively.     

Meta-analysis of summary survival curve data

The use of standard univariate fixed- and random-effects models in meta-analysis has become well known in the last 20 years. However, these models are unsuitable for meta-analysis of clinical trials that present multiple survival estimates (usually illustrated by a survival curve) during a follow-up period. Therefore, special methods are needed to combine the survival curve data from different trials in a meta-analysis. For this purpose, only fixed-effects models have been suggested in the literature. In this paper, we propose a multivariate random-effects model for joint analysis of survival proportions reported at multiple time points and in different studies, to be combined in a meta-analysis. The model could be seen as a generalization of the fixed-effects model of Dear (Biometrics 1994; 50:989-1002). We illustrate the method by using a simulated data example as well as using a clinical data example of meta-analysis with aggregated survival curve data. All analyses can be carried out with standard general linear MIXED model software. Copyright (c) 2008 John Wiley & Sons, Ltd.     

不良妊娠结局危险因素的Meta分析

目的:利用Meta分析方法探讨影响我国妇女不良妊娠结局的危险因素,为制定预防措施提供依据。方法:通过文献检索收集不良妊娠结局病例对照研究的相关文献,应用严格的纳入和剔除标准进行筛检,采用随机效应模型和固定效应模型通过Review Manager4.2软件进行分析评价。结果:纳入文献21篇,累计病例3298例,对照27886例。解脲脲原体感染合并OR值为5.57(1.66,18.63);沙眼衣原体感染合并OR值为4.15(1.95,8.87);多胎妊娠合并OR值为6.42(2.06,19.99);妊娠期高血压疾病合并OR值2.87(1.68,4.91):胎位异常合并OR值为3.46(2.71,4.42);流产史合并OR值为1.15(0.91,91.45)。结论:本研究分析显示不良妊娠结局的危险因素由强到弱依次为:多胎妊娠,解脲脲原体感染,沙眼衣原体感染,胎位异常和妊娠期高血压疾病。     

2001—2005年中国大学生心理调查结果的meta分析

[目的] 比较不同地区大学生群体症状自评量表（SCL-90）各因子与全国青年组的差异,为促进中国大学生心理健康提供参考。[方法] 收集筛选2001—2005年关于不同地区大学生群体的SCL-90研究成果,与常模进行比较,分析年度效应报告质量效应。[结果] 不同地区大学生SCL-90的10项研究与全国常模比较的平均效应量值d为0.31;与1986年全国青年组比较,躯体化、焦虑、偏执和精神病性有显著性差异;大学生心理健康躯体化、偏执因子存在显著的性别差异;SCL-90因子得分与发表年度呈负相关。[结论] 与1986年青年组相比,躯体化、焦虑、偏执、和精神病性有显著性差异,提示我们在进行大学生心理健康教育的时候应该有所侧重;大学生心理健康躯体化、偏执因子存在显著的性别差异,在进行心理健康教育时要注意性别差异;SCL-90因子得分存在年度效应,得分随发表年代降低,提示大学生心理健康有好转的趋势。     

人体蠕形螨感染与个人卫生习惯关系的Meta分析

目的探讨人体蠕形螨感染与个人卫生习惯的关系。方法采用Meta分析方法对1994年1月1日至2006年12月31日在中国期刊网上检索到的有关混用生活用品者和使用洁面用品者与蠕形螨感染关系的文献进行综合定量评价。结果检索到有关生活用品混用的文献11篇，累计调查人数为9356人，其中经常混用生活用品者5447人，蠕形螨平均感染率为45．82％；不常混用生活用品者3909人，蠕形螨平均感染率为27．71％，二者间的差异有统计学意义（X^2=316．28，P〈0．05），生活用品混用者蠕形螨感染率明显高于不混用者，OR合并为2．49，95％可信区间（95％CI）为[1．94，3.20]。检索到符合使用洁面用品纳入标准的相关文献7篇，总调查人数3230人，其中纳入不使用洁面用品者1476人，蠕形螨的平均感染率为31．44％；使用洁面用品者1754人，蠕形螨的平均感染率为27．25％，二者之间的差异亦有统计学意义（X^2=6．79，P〈0．05），经常使用洁面用品者蠕形螨的感染率显著低于不常使用洁面用品者，OR合并为0.70，95％CI为[0．52，0．93]。结论人体蠕形螨感染与个人卫生习惯有一定的关联性，混用生活用品是蠕形螨感染的危险因素，而使用洁面用品则是蠕形螨感染的保护因素。     

Computerization of data from continuous and sequential air monitoring systems.

Continuous and sequential area air monitoring systems are more frequently becoming a necessity in both new and existing chemical manufacturing and processing plants. While these systems have most frequently been installed to alert employees to conditions of possible acute overexposure, they generate a wealth of data valuable in documenting employee exposures over extended period of time. Within the Dow Chemical Company, use of a dedicated microcomputer with area air monitoring systems has proven helful in summarizing each days' data and in calculating month-to-date totals for use in employee exposure documentation over long time periods.     

Allowing for uncertainty due to missing continuous outcome data in pairwise and network meta‐analysis

Missing outcome data are commonly encountered in randomized controlled trials and hence may need to be addressed in a meta‐analysis of multiple trials. A common and simple approach to deal with missing data is to restrict analysis to individuals for whom the outcome was obtained (complete case analysis). However, estimated treatment effects from complete case analyses are potentially biased if informative missing data are ignored. We develop methods for estimating meta‐analytic summary treatment effects for continuous outcomes in the presence of missing data for some of the individuals within the trials. We build on a method previously developed for binary outcomes, which quantifies the degree of departure from a missing at random assumption via the informative missingness odds ratio. Our new model quantifies the degree of departure from missing at random using either an informative missingness difference of means or an informative missingness ratio of means, both of which relate the mean value of the missing outcome data to that of the observed data. We propose estimating the treatment effects, adjusted for informative missingness, and their standard errors by a Taylor series approximation and by a Monte Carlo method. We apply the methodology to examples of both pairwise and network meta‐analysis with multi‐arm trials. © 2014 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.     

Case-control analysis with a continuous outcome variable

It is not uncommon for a continuous outcome variable Y to be dichotomized and analysed using logistic regression. Moser and Coombs (Statist. Med. 2004; 23:1843-1860) provide a method for converting the output from a standard linear regression analysis using the original continuous outcome Y to give much more efficient inferences about the same odds-ratio parameters being estimated by the logistic regression. However, these results apply only to prospective studies. This paper follows up Moser and Coombs by providing an efficient linear-model-based solution for data collected using case-control studies. Gains in statistical efficiency of up to 240 per cent are obtained even with small to moderate odds ratios. Differences in design efficiency between case-control and prospective sampling designs are found to be much smaller, however, when linear-model-based analyses are being used than they are when logistic regression analyses are being used.