Evidence synthesis from aggregate recurrent event data for clinical trial design and analysis

Information from historical trials is important for the design, interim monitoring, analysis, and interpretation of clinical trials. Meta‐analytic models can be used to synthesize the evidence from historical data, which are often only available in aggregate form. We consider evidence synthesis methods for trials with recurrent event endpoints, which are common in many therapeutic areas. Such endpoints are typically analyzed by negative binomial regression. However, the individual patient data necessary to fit such a model are usually unavailable for historical trials reported in the medical literature. We describe approaches for back‐calculating model parameter estimates and their standard errors from available summary statistics with various techniques, including approximate Bayesian computation. We propose to use a quadratic approximation to the log‐likelihood for each historical trial based on 2 independent terms for the log mean rate and the log of the dispersion parameter. A Bayesian hierarchical meta‐analysis model then provides the posterior predictive distribution for these parameters. Simulations show this approach with back‐calculated parameter estimates results in very similar inference as using parameter estimates from individual patient data as an input. We illustrate how to design and analyze a new randomized placebo‐controlled exacerbation trial in severe eosinophilic asthma using data from 11 historical trials.     

Mixed treatment comparison of repeated measurements of a continuous endpoint: an example using topical treatments for primary open‐angle glaucoma and ocular hypertension

Mixed treatment comparison (MTC) meta‐analyses estimate relative treatment effects from networks of evidence while preserving randomisation. We extend the MTC framework to allow for repeated measurements of a continuous endpoint that varies over time. We used, as a case study, a systematic review and meta‐analysis of intraocular pressure (IOP) measurements from randomised controlled trials evaluating topical ocular hypotensives in primary open‐angle glaucoma or ocular hypertension because IOP varies over the day and over the treatment course, and repeated measurements are frequently reported. We adopted models for conducting MTC in W inBUGS (The BUGS Project, Cambridge, UK) to allow for repeated IOP measurements and to impute missing standard deviations of the raw data using the predictive distribution from observations with standard deviations. A flexible model with an unconstrained baseline for IOP variations over time and time‐invariant random treatment effects fitted the data well. We also adopted repeated measures models to allow for class effects; assuming treatment effects to be exchangeable within classes slightly improved model fit but could bias estimated treatment effects if exchangeability assumptions were not valid. We enabled all timepoints to be included in the analysis, allowing for repeated measures to increase precision around treatment effects and avoid bias associated with selecting timepoints for meta‐analysis.The methods we developed for modelling repeated measures and allowing for missing data may be adapted for use in other MTC meta‐analyses. Copyright © 2011 John Wiley & Sons, Ltd.     

Using historical control information for the design and analysis of clinical trials with overdispersed count data

Results from clinical trials are never interpreted in isolation. Previous studies in a similar setting provide valuable information for designing a new trial. For the analysis, however, the use of trial‐external information is challenging and therefore controversial, although it seems attractive from an ethical or efficiency perspective. Here, we consider the formal use of historical control data on lesion counts in a multiple sclerosis trial. The approach to incorporating historical data is Bayesian, in that historical information is captured in a prior that accounts for between‐trial variability and hence leads to discounting of historical data. We extend the meta‐analytic‐predictive approach, a random‐effects meta‐analysis of historical data combined with the prediction of the parameter in the new trial, from normal to overdispersed count data of individual‐patient or aggregate‐trial format. We discuss the prior derivation for the lesion mean count in the control group of the new trial for two populations. For the general population (without baseline enrichment), with 1936 control patients from nine historical trials, between‐trial variability was moderate to substantial, leading to a prior effective sample size of about 45 control patients. For the more homogenous population (with enrichment), with 412 control patients from five historical trials, the prior effective sample size was approximately 63 patients. Although these numbers are small relative to the historical data, they are fairly typical in settings where between‐trial heterogeneity is moderate. For phase II, reducing the number of control patients by 45 or by 63 may be an attractive option in many multiple sclerosis trials. Copyright © 2013 John Wiley & Sons, Ltd.     

Testing moderation in network meta‐analysis with individual participant data

Meta‐analytic methods for combining data from multiple intervention trials are commonly used to estimate the effectiveness of an intervention. They can also be extended to study comparative effectiveness, testing which of several alternative interventions is expected to have the strongest effect. This often requires network meta‐analysis (NMA), which combines trials involving direct comparison of two interventions within the same trial and indirect comparisons across trials. In this paper, we extend existing network methods for main effects to examining moderator effects, allowing for tests of whether intervention effects vary for different populations or when employed in different contexts. In addition, we study how the use of individual participant data may increase the sensitivity of NMA for detecting moderator effects, as compared with aggregate data NMA that employs study‐level effect sizes in a meta‐regression framework. A new NMA diagram is proposed. We also develop a generalized multilevel model for NMA that takes into account within‐trial and between‐trial heterogeneity and can include participant‐level covariates. Within this framework, we present definitions of homogeneity and consistency across trials. A simulation study based on this model is used to assess effects on power to detect both main and moderator effects. Results show that power to detect moderation is substantially greater when applied to individual participant data as compared with study‐level effects. We illustrate the use of this method by applying it to data from a classroom‐based randomized study that involved two sub‐trials, each comparing interventions that were contrasted with separate control groups. Copyright © 2016 John Wiley & Sons, Ltd.     

Meta‐analysis using individual participant data: one‐stage and two‐stage approaches,and why they may differ

Meta‐analysis using individual participant data (IPD) obtains and synthesises the raw, participant‐level data from a set of relevant studies. The IPD approach is becoming an increasingly popular tool as an alternative to traditional aggregate data meta‐analysis, especially as it avoids reliance on published results and provides an opportunity to investigate individual‐level interactions, such as treatment‐effect modifiers. There are two statistical approaches for conducting an IPD meta‐analysis: one‐stage and two‐stage. The one‐stage approach analyses the IPD from all studies simultaneously, for example, in a hierarchical regression model with random effects. The two‐stage approach derives aggregate data (such as effect estimates) in each study separately and then combines these in a traditional meta‐analysis model. There have been numerous comparisons of the one‐stage and two‐stage approaches via theoretical consideration, simulation and empirical examples, yet there remains confusion regarding when each approach should be adopted, and indeed why they may differ. In this tutorial paper, we outline the key statistical methods for one‐stage and two‐stage IPD meta‐analyses, and provide 10 key reasons why they may produce different summary results. We explain that most differences arise because of different modelling assumptions, rather than the choice of one‐stage or two‐stage itself. We illustrate the concepts with recently published IPD meta‐analyses, summarise key statistical software and provide recommendations for future IPD meta‐analyses. © 2016 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.     

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

In meta‐analyses, where a continuous outcome is measured with different scales or standards, the summary statistic is the mean difference standardised to a common metric with a common variance. Where trial treatment is delivered by a person, nesting of patients within care providers leads to clustering that may interact with, or be limited to, one or more of the arms. Assuming a common standardising variance is less tenable and options for scaling the mean difference become numerous. Metrics suggested for cluster‐randomised trials are within, between and total variances and for unequal variances, the control arm or pooled variances. We consider summary measures and individual‐patient‐data methods for meta‐analysing standardised mean differences from trials with two‐level nested clustering, relaxing independence and common variance assumptions, allowing sample sizes to differ across arms. A general metric is proposed with comparable interpretation across designs. The relationship between the method of standardisation and choice of model is explored, allowing for bias in the estimator and imprecision in the standardising metric. A meta‐analysis of trials of counselling in primary care motivated this work. Assuming equal clustering effects across trials, the proposed random‐effects meta‐analysis model gave a pooled standardised mean difference of ?0.27 (95% CI ?0.45 to ?0.08) using summary measures and ?0.26 (95% CI ?0.45 to ?0.09) with the individual‐patient‐data. While treatment‐related clustering has rarely been taken into account in trials, it is now recommended that it is considered in trials and meta‐analyses. This paper contributes to the uptake of this guidance. Copyright © 2016 John Wiley & Sons, Ltd.     

The Role of Environmental Heterogeneity in Meta‐Analysis of Gene–Environment Interactions With Quantitative Traits

With challenges in data harmonization and environmental heterogeneity across various data sources, meta‐analysis of gene–environment interaction studies can often involve subtle statistical issues. In this paper, we study the effect of environmental covariate heterogeneity (within and between cohorts) on two approaches for fixed‐effect meta‐analysis: the standard inverse‐variance weighted meta‐analysis and a meta‐regression approach. Akin to the results in Simmonds and Higgins ( 2007 ), we obtain analytic efficiency results for both methods under certain assumptions. The relative efficiency of the two methods depends on the ratio of within versus between cohort variability of the environmental covariate. We propose to use an adaptively weighted estimator (AWE), between meta‐analysis and meta‐regression, for the interaction parameter. The AWE retains full efficiency of the joint analysis using individual level data under certain natural assumptions. Lin and Zeng (2010a, b) showed that a multivariate inverse‐variance weighted estimator retains full efficiency as joint analysis using individual level data, if the estimates with full covariance matrices for all the common parameters are pooled across all studies. We show consistency of our work with Lin and Zeng (2010a, b). Without sacrificing much efficiency, the AWE uses only univariate summary statistics from each study, and bypasses issues with sharing individual level data or full covariance matrices across studies. We compare the performance of the methods both analytically and numerically. The methods are illustrated through meta‐analysis of interaction between Single Nucleotide Polymorphisms in FTO gene and body mass index on high‐density lipoprotein cholesterol data from a set of eight studies of type 2 diabetes.     

Meta‐analysis of Gaussian individual patient data: Two‐stage or not two‐stage?

Quantitative evidence synthesis through meta‐analysis is central to evidence‐based medicine. For well‐documented reasons, the meta‐analysis of individual patient data is held in higher regard than aggregate data. With access to individual patient data, the analysis is not restricted to a “two‐stage” approach (combining estimates and standard errors) but can estimate parameters of interest by fitting a single model to all of the data, a so‐called “one‐stage” analysis. There has been debate about the merits of one‐ and two‐stage analysis. Arguments for one‐stage analysis have typically noted that a wider range of models can be fitted and overall estimates may be more precise. The two‐stage side has emphasised that the models that can be fitted in two stages are sufficient to answer the relevant questions, with less scope for mistakes because there are fewer modelling choices to be made in the two‐stage approach. For Gaussian data, we consider the statistical arguments for flexibility and precision in small‐sample settings. Regarding flexibility, several of the models that can be fitted only in one stage may not be of serious interest to most meta‐analysis practitioners. Regarding precision, we consider fixed‐ and random‐effects meta‐analysis and see that, for a model making certain assumptions, the number of stages used to fit this model is irrelevant; the precision will be approximately equal. Meta‐analysts should choose modelling assumptions carefully. Sometimes relevant models can only be fitted in one stage. Otherwise, meta‐analysts are free to use whichever procedure is most convenient to fit the identified model.     

A Bayesian framework to account for uncertainty due to missing binary outcome data in pairwise meta‐analysis

Missing outcome data are a common threat to the validity of the results from randomised controlled trials (RCTs), which, if not analysed appropriately, can lead to misleading treatment effect estimates. Studies with missing outcome data also threaten the validity of any meta‐analysis that includes them. A conceptually simple Bayesian framework is proposed, to account for uncertainty due to missing binary outcome data in meta‐analysis. A pattern‐mixture model is fitted, which allows the incorporation of prior information on a parameter describing the missingness mechanism. We describe several alternative parameterisations, with the simplest being a prior on the probability of an event in the missing individuals. We describe a series of structural assumptions that can be made concerning the missingness parameters. We use some artificial data scenarios to demonstrate the ability of the model to produce a bias‐adjusted estimate of treatment effect that accounts for uncertainty. A meta‐analysis of haloperidol versus placebo for schizophrenia is used to illustrate the model. We end with a discussion of elicitation of priors, issues with poor reporting and potential extensions of the framework. Our framework allows one to make the best use of evidence produced from RCTs with missing outcome data in a meta‐analysis, accounts for any uncertainty induced by missing data and fits easily into a wider evidence synthesis framework for medical decision making. © 2015 The Authors. Statistics in MedicinePublished by John Wiley & Sons Ltd.     

One‐stage individual participant data meta‐analysis models: estimation of treatment‐covariate interactions must avoid ecological bias by separating out within‐trial and across‐trial information

Stratified medicine utilizes individual‐level covariates that are associated with a differential treatment effect, also known as treatment‐covariate interactions. When multiple trials are available, meta‐analysis is used to help detect true treatment‐covariate interactions by combining their data. Meta‐regression of trial‐level information is prone to low power and ecological bias, and therefore, individual participant data (IPD) meta‐analyses are preferable to examine interactions utilizing individual‐level information. However, one‐stage IPD models are often wrongly specified, such that interactions are based on amalgamating within‐ and across‐trial information. We compare, through simulations and an applied example, fixed‐effect and random‐effects models for a one‐stage IPD meta‐analysis of time‐to‐event data where the goal is to estimate a treatment‐covariate interaction. We show that it is crucial to centre patient‐level covariates by their mean value in each trial, in order to separate out within‐trial and across‐trial information. Otherwise, bias and coverage of interaction estimates may be adversely affected, leading to potentially erroneous conclusions driven by ecological bias. We revisit an IPD meta‐analysis of five epilepsy trials and examine age as a treatment effect modifier. The interaction is ?0.011 (95% CI: ?0.019 to ?0.003; p = 0.004), and thus highly significant, when amalgamating within‐trial and across‐trial information. However, when separating within‐trial from across‐trial information, the interaction is ?0.007 (95% CI: ?0.019 to 0.005; p = 0.22), and thus its magnitude and statistical significance are greatly reduced. We recommend that meta‐analysts should only use within‐trial information to examine individual predictors of treatment effect and that one‐stage IPD models should separate within‐trial from across‐trial information to avoid ecological bias. © 2016 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.     

A tutorial on Bayesian bivariate meta‐analysis of mixed binary‐continuous outcomes with missing treatment effects

Bivariate random‐effects meta‐analysis (BVMA) is a method of data synthesis that accounts for treatment effects measured on two outcomes. BVMA gives more precise estimates of the population mean and predicted values than two univariate random‐effects meta‐analyses (UVMAs). BVMA also addresses bias from incomplete reporting of outcomes. A few tutorials have covered technical details of BVMA of categorical or continuous outcomes. Limited guidance is available on how to analyze datasets that include trials with mixed continuous‐binary outcomes where treatment effects on one outcome or the other are not reported. Given the advantages of Bayesian BVMA for handling missing outcomes, we present a tutorial for Bayesian BVMA of incompletely reported treatment effects on mixed bivariate outcomes. This step‐by‐step approach can serve as a model for our intended audience, the methodologist familiar with Bayesian meta‐analysis, looking for practical advice on fitting bivariate models. To facilitate application of the proposed methods, we include our WinBUGS code. As an example, we use aggregate‐level data from published trials to demonstrate the estimation of the effects of vitamin K and bisphosphonates on two correlated bone outcomes, fracture, and bone mineral density. We present datasets where reporting of the pairs of treatment effects on both outcomes was ‘partially’ complete (i.e., pairs completely reported in some trials), and we outline steps for modeling the incompletely reported data. To assess what is gained from the additional work required by BVMA, we compare the resulting estimates to those from separate UVMAs. We discuss methodological findings and make four recommendations. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Investigation of 2‐stage meta‐analysis methods for joint longitudinal and time‐to‐event data through simulation and real data application

Background

Joint modelling of longitudinal and time‐to‐event data is often preferred over separate longitudinal or time‐to‐event analyses as it can account for study dropout, error in longitudinally measured covariates, and correlation between longitudinal and time‐to‐event outcomes. The joint modelling literature focuses mainly on the analysis of single studies with no methods currently available for the meta‐analysis of joint model estimates from multiple studies.

Methods

We propose a 2‐stage method for meta‐analysis of joint model estimates. These methods are applied to the INDANA dataset to combine joint model estimates of systolic blood pressure with time to death, time to myocardial infarction, and time to stroke. Results are compared to meta‐analyses of separate longitudinal or time‐to‐event models. A simulation study is conducted to contrast separate versus joint analyses over a range of scenarios.

Results

Using the real dataset, similar results were obtained by using the separate and joint analyses. However, the simulation study indicated a benefit of use of joint rather than separate methods in a meta‐analytic setting where association exists between the longitudinal and time‐to‐event outcomes.

Conclusions

Where evidence of association between longitudinal and time‐to‐event outcomes exists, results from joint models over standalone analyses should be pooled in 2‐stage meta‐analyses.     

A Bayesian sensitivity model for intention‐to‐treat analysis on binary outcomes with dropouts

Intention‐to‐treat (ITT) analysis is commonly used in randomized clinical trials. However, the use of ITT analysis presents a challenge: how to deal with subjects who drop out. Here we focus on randomized trials where the primary outcome is a binary endpoint. Several approaches are available for including the dropout subject in the ITT analysis, mainly chosen prior to unblinding the study. These approaches reduce the potential bias due to breaking the randomization code. However, the validity of the results will highly depend on untestable assumptions about the dropout mechanism. Thus, it is important to evaluate the sensitivity of the results across different missing‐data mechanisms. We propose here a Bayesian pattern‐mixture model for ITT analysis of binary outcomes with dropouts that applies over different types of missing‐data mechanisms. We introduce a new parameterization to identify the model, which is then used for sensitivity analysis. The parameterization is defined as the odds ratio of having an endpoint between the subjects who dropped out and those who completed the study. Such parameterization is intuitive and easy to use in sensitivity analysis; it also incorporates most of the available methods as special cases. The model is applied to TRial Of Preventing HYpertension. Copyright © 2008 John Wiley & Sons, Ltd.     

A pattern‐mixture model approach for handling missing continuous outcome data in longitudinal cluster randomized trials

We extend the pattern‐mixture approach to handle missing continuous outcome data in longitudinal cluster randomized trials, which randomize groups of individuals to treatment arms, rather than the individuals themselves. Individuals who drop out at the same time point are grouped into the same dropout pattern. We approach extrapolation of the pattern‐mixture model by applying multilevel multiple imputation, which imputes missing values while appropriately accounting for the hierarchical data structure found in cluster randomized trials. To assess parameters of interest under various missing data assumptions, imputed values are multiplied by a sensitivity parameter, k, which increases or decreases imputed values. Using simulated data, we show that estimates of parameters of interest can vary widely under differing missing data assumptions. We conduct a sensitivity analysis using real data from a cluster randomized trial by increasing k until the treatment effect inference changes. By performing a sensitivity analysis for missing data, researchers can assess whether certain missing data assumptions are reasonable for their cluster randomized trial.     

Meta‐STEPP: subpopulation treatment effect pattern plot for individual patient data meta‐analysis

We have developed a method, called Meta‐STEPP (subpopulation treatment effect pattern plot for meta‐analysis), to explore treatment effect heterogeneity across covariate values in the meta‐analysis setting for time‐to‐event data when the covariate of interest is continuous. Meta‐STEPP forms overlapping subpopulations from individual patient data containing similar numbers of events with increasing covariate values, estimates subpopulation treatment effects using standard fixed‐effects meta‐analysis methodology, displays the estimated subpopulation treatment effect as a function of the covariate values, and provides a statistical test to detect possibly complex treatment‐covariate interactions. Simulation studies show that this test has adequate type‐I error rate recovery as well as power when reasonable window sizes are chosen. When applied to eight breast cancer trials, Meta‐STEPP suggests that chemotherapy is less effective for tumors with high estrogen receptor expression compared with those with low expression. Copyright © 2016 John Wiley & Sons, Ltd.     

Network meta‐analysis of longitudinal data using fractional polynomials

Network meta‐analysis of randomized controlled trials (RCTs) are often based on one treatment effect measure per study. However, many studies report data at multiple time points. Furthermore, not all studies measure the outcomes at the same time points. As an alternative to a network meta‐analysis based on a synthesis of the results at one time point, a network meta‐analysis method is presented that allows for the simultaneous analysis of outcomes at multiple time points. The development of outcomes over time of interventions compared in an RCT is modeled with fractional polynomials, and the differences between the parameters of these polynomials within a trial are synthesized across studies with a Bayesian network meta‐analysis. The proposed models are illustrated with an analysis of RCTs evaluating interventions for osteoarthritis of the knee. Fixed and random effects second order fractional polynomials were applied to the case study. Network meta‐analysis with models that represent the treatment effects in terms of several parameters using fractional polynomials can be considered a useful addition to models for network meta‐analysis of repeated measures previously proposed. When RCTs report treatment effects at multiple follow‐up times, these models can be used to synthesize the results even if reporting times differ across the studies. Copyright © 2015 John Wiley & Sons, Ltd.     

Implementing informative priors for heterogeneity in meta‐analysis using meta‐regression and pseudo data

Many meta‐analyses combine results from only a small number of studies, a situation in which the between‐study variance is imprecisely estimated when standard methods are applied. Bayesian meta‐analysis allows incorporation of external evidence on heterogeneity, providing the potential for more robust inference on the effect size of interest. We present a method for performing Bayesian meta‐analysis using data augmentation, in which we represent an informative conjugate prior for between‐study variance by pseudo data and use meta‐regression for estimation. To assist in this, we derive predictive inverse‐gamma distributions for the between‐study variance expected in future meta‐analyses. These may serve as priors for heterogeneity in new meta‐analyses. In a simulation study, we compare approximate Bayesian methods using meta‐regression and pseudo data against fully Bayesian approaches based on importance sampling techniques and Markov chain Monte Carlo (MCMC). We compare the frequentist properties of these Bayesian methods with those of the commonly used frequentist DerSimonian and Laird procedure. The method is implemented in standard statistical software and provides a less complex alternative to standard MCMC approaches. An importance sampling approach produces almost identical results to standard MCMC approaches, and results obtained through meta‐regression and pseudo data are very similar. On average, data augmentation provides closer results to MCMC, if implemented using restricted maximum likelihood estimation rather than DerSimonian and Laird or maximum likelihood estimation. The methods are applied to real datasets, and an extension to network meta‐analysis is described. The proposed method facilitates Bayesian meta‐analysis in a way that is accessible to applied researchers. © 2016 The Authors. Statistics in Medicine Published by 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.     

Multiple imputation for IPD meta‐analysis: allowing for heterogeneity and studies with missing covariates

Recently, multiple imputation has been proposed as a tool for individual patient data meta‐analysis with sporadically missing observations, and it has been suggested that within‐study imputation is usually preferable. However, such within study imputation cannot handle variables that are completely missing within studies. Further, if some of the contributing studies are relatively small, it may be appropriate to share information across studies when imputing. In this paper, we develop and evaluate a joint modelling approach to multiple imputation of individual patient data in meta‐analysis, with an across‐study probability distribution for the study specific covariance matrices. This retains the flexibility to allow for between‐study heterogeneity when imputing while allowing (i) sharing information on the covariance matrix across studies when this is appropriate, and (ii) imputing variables that are wholly missing from studies. Simulation results show both equivalent performance to the within‐study imputation approach where this is valid, and good results in more general, practically relevant, scenarios with studies of very different sizes, non‐negligible between‐study heterogeneity and wholly missing variables. We illustrate our approach using data from an individual patient data meta‐analysis of hypertension trials. © 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.