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.     

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.     

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.     

Combining individual patient data and aggregate data in mixed treatment comparison meta‐analysis: Individual patient data may be beneficial if only for a subset of trials

Background Individual patient data (IPD) meta‐analysis is the gold standard. Aggregate data (AD) and IPD can be combined using conventional pairwise meta‐analysis when IPD cannot be obtained for all relevant studies. We extend the methodology to combine IPD and AD in a mixed treatment comparison (MTC) meta‐analysis. Methods The proposed random‐effects MTC models combine IPD and AD for a dichotomous outcome. We study the benefits of acquiring IPD for a subset of trials when assessing the underlying consistency assumption by including treatment‐by‐covariate interactions in the model. We describe three different model specifications that make increasingly stronger assumptions regarding the interactions. We illustrate the methodology through application to real data sets to compare drugs for treating malaria by using the outcome unadjusted treatment success at day 28. We compare results from AD alone, IPD alone and all data. Results When IPD contributed (i.e. either using IPD alone or combining IPD and AD), the chains converged, and we identified statistically significant regression coefficients for the interactions. Using IPD alone, we were able to compare only three of the six treatments of interest. When models were fitted to AD, the treatment effects and regression coefficients for the interactions were far more imprecise, and the chains did not converge. Conclusions The models combining IPD and AD encapsulated all available evidence. When exploring interactions, it can be beneficial to obtain IPD for a subset of trials and to combine IPD with additional AD. Copyright © 2012 John Wiley & Sons, Ltd.     

A recursive partitioning approach for subgroup identification in individual patient data meta‐analysis

Background

Motivated by the setting of clinical trials in low back pain, this work investigated statistical methods to identify patient subgroups for which there is a large treatment effect (treatment by subgroup interaction). Statistical tests for interaction are often underpowered. Individual patient data (IPD) meta‐analyses provide a framework with improved statistical power to investigate subgroups. However, conventional approaches to subgroup analyses applied in both a single trial setting and an IPD setting have a number of issues, one of them being that factors used to define subgroups are investigated one at a time. As individuals have multiple characteristics that may be related to response to treatment, alternative exploratory statistical methods are required.

Methods

Tree‐based methods are a promising alternative that systematically searches the covariate space to identify subgroups defined by multiple characteristics. A tree method in particular, SIDES, is described and extended for application in an IPD meta‐analyses setting by incorporating fixed‐effects and random‐effects models to account for between‐trial variation. The performance of the proposed extension was assessed using simulation studies. The proposed method was then applied to an IPD low back pain dataset.

Results

The simulation studies found that the extended IPD‐SIDES method performed well in detecting subgroups especially in the presence of large between‐trial variation. The IPD‐SIDES method identified subgroups with enhanced treatment effect when applied to the low back pain data.

Conclusions

This work proposes an exploratory statistical approach for subgroup analyses applicable in any research discipline where subgroup analyses in an IPD meta‐analysis setting are of interest.     

Mixed treatment comparisons using aggregate and individual participant level data

Mixed treatment comparisons (MTC) extend the traditional pair‐wise meta‐analytic framework to synthesize information on more than two interventions. Although most MTCs use aggregate data (AD), a proportion of the evidence base might be available at the individual level (IPD). We develop a series of novel Bayesian statistical MTC models to allow for the simultaneous synthesis of IPD and AD, potentially incorporating study and individual level covariates. The effectiveness of different interventions to increase the provision of functioning smoke alarms in households with children was used as a motivating dataset. This included 20 studies (11 AD and 9 IPD), including 11 500 participants. Incorporating the IPD into the network allowed the inclusion of information on subject level covariates, which produced markedly more accurate treatment–covariate interaction estimates than an analysis solely on the AD from all studies. Including evidence at the IPD level in the MTC is desirable when exploring participant level covariates; even when IPD is available only for a fraction of the studies. Such modelling may not only reduce inconsistencies within networks of trials but also assist the estimation of intervention subgroup effects to guide more individualised treatment decisions. Copyright © 2012 John Wiley & Sons, Ltd.     

Multilevel mixed effects parametric survival models using adaptive Gauss–Hermite quadrature with application to recurrent events and individual participant data meta‐analysis

Multilevel mixed effects survival models are used in the analysis of clustered survival data, such as repeated events, multicenter clinical trials, and individual participant data (IPD) meta‐analyses, to investigate heterogeneity in baseline risk and covariate effects. In this paper, we extend parametric frailty models including the exponential, Weibull and Gompertz proportional hazards (PH) models and the log logistic, log normal, and generalized gamma accelerated failure time models to allow any number of normally distributed random effects. Furthermore, we extend the flexible parametric survival model of Royston and Parmar, modeled on the log‐cumulative hazard scale using restricted cubic splines, to include random effects while also allowing for non‐PH (time‐dependent effects). Maximum likelihood is used to estimate the models utilizing adaptive or nonadaptive Gauss–Hermite quadrature. The methods are evaluated through simulation studies representing clinically plausible scenarios of a multicenter trial and IPD meta‐analysis, showing good performance of the estimation method. The flexible parametric mixed effects model is illustrated using a dataset of patients with kidney disease and repeated times to infection and an IPD meta‐analysis of prognostic factor studies in patients with breast cancer. User‐friendly Stata software is provided to implement the methods. Copyright © 2014 John Wiley & Sons, Ltd.     

Assessing the consistency assumption by exploring treatment by covariate interactions in mixed treatment comparison meta‐analysis: individual patient‐level covariates versus aggregate trial‐level covariates

Mixed treatment comparison (MTC) meta‐analysis allows several treatments to be compared in a single analysis while utilising direct and indirect evidence. Treatment by covariate interactions can be included in MTC models to explore how the covariate modifies the treatment effects. If interactions exist, the assumptions underlying MTCs may be invalidated. For conventional pair‐wise meta‐analysis, important benefits regarding the investigation of such interactions, gained from using individual patient data (IPD) rather than aggregate data (AD), have been described. We aim to compare IPD MTC models including patient‐level covariates with AD MTC models including study‐level covariates. IPD and AD random‐effects MTC models for dichotomous outcomes are specified. Three assumptions are made regarding the interactions (i.e. independent, exchangeable and common interactions). The models are applied to a dataset to compare four drugs for treating malaria (i.e. amodiaquine‐artesunate, dihydroartemisinin‐piperaquine (DHAPQ), artemether‐lumefantrine and chlorproguanil‐dapsone plus artesunate) using the outcome unadjusted treatment success at day 28. The treatment effects and regression coefficients for interactions from the IPD models were more precise than those from AD models. Using IPD, assuming independent or exchangeable interactions, the regression coefficient for chlorproguanil‐dapsone plus artesunate versus DHAPQ was statistically significant and assuming common interactions, the common coefficient was significant; whereas using AD, no coefficients were significant. Using IPD, DHAPQ was the best drug; whereas using AD, the best drug varied. Using AD models, there was no evidence that the consistency assumption was invalid; whereas, the assumption was questionable based on the IPD models. The AD analyses were misleading. Copyright © 2012 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 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.     

Bayesian evidence synthesis for exploring generalizability of treatment effects: a case study of combining randomized and non‐randomized results in diabetes

In this paper, we present a unified modeling framework to combine aggregated data from randomized controlled trials (RCTs) with individual participant data (IPD) from observational studies. Rather than simply pooling the available evidence into an overall treatment effect, adjusted for potential confounding, the intention of this work is to explore treatment effects in specific patient populations reflected by the IPD. In this way, by collecting IPD, we can potentially gain new insights from RCTs' results, which cannot be seen using only a meta‐analysis of RCTs. We present a new Bayesian hierarchical meta‐regression model, which combines submodels, representing different types of data into a coherent analysis. Predictors of baseline risk are estimated from the individual data. Simultaneously, a bivariate random effects distribution of baseline risk and treatment effects is estimated from the combined individual and aggregate data. Therefore, given a subgroup of interest, the estimated treatment effect can be calculated through its correlation with baseline risk. We highlight different types of model parameters: those that are the focus of inference (e.g., treatment effect in a subgroup of patients) and those that are used to adjust for biases introduced by data collection processes (e.g., internal or external validity). The model is applied to a case study where RCTs' results, investigating efficacy in the treatment of diabetic foot problems, are extrapolated to groups of patients treated in medical routine and who were enrolled in a prospective cohort study. 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.     

A linearization approach for the model‐based analysis of combined aggregate and individual patient data

The application of model‐based meta‐analysis in drug development has gained prominence recently, particularly for characterizing dose‐response relationships and quantifying treatment effect sizes of competitor drugs. The models are typically nonlinear in nature and involve covariates to explain the heterogeneity in summary‐level literature (or aggregate data (AD)). Inferring individual patient‐level relationships from these nonlinear meta‐analysis models leads to aggregation bias. Individual patient‐level data (IPD) are indeed required to characterize patient‐level relationships but too often this information is limited. Since combined analyses of AD and IPD allow advantage of the information they share to be taken, the models developed for AD must be derived from IPD models; in the case of linear models, the solution is a closed form, while for nonlinear models, closed form solutions do not exist. Here, we propose a linearization method based on a second order Taylor series approximation for fitting models to AD alone or combined AD and IPD. The application of this method is illustrated by an analysis of a continuous landmark endpoint, i.e., change from baseline in HbA1c at week 12, from 18 clinical trials evaluating the effects of DPP‐4 inhibitors on hyperglycemia in diabetic patients. The performance of this method is demonstrated by a simulation study where the effects of varying the degree of nonlinearity and of heterogeneity in covariates (as assessed by the ratio of between‐trial to within‐trial variability) were studied. A dose‐response relationship using an Emax model with linear and nonlinear effects of covariates on the emax parameter was used to simulate data. The simulation results showed that when an IPD model is simply used for modeling AD, the bias in the emax parameter estimate increased noticeably with an increasing degree of nonlinearity in the model, with respect to covariates. When using an appropriately derived AD model, the linearization method adequately corrected for bias. It was also noted that the bias in the model parameter estimates decreased as the ratio of between‐trial to within‐trial variability in covariate distribution increased. Taken together, the proposed linearization approach allows addressing the issue of aggregation bias in the particular case of nonlinear models of aggregate data. Copyright © 2014 John Wiley & Sons, Ltd.     

A comparison of summary patient-level covariates in meta-regression with individual patient data meta-analysis.

OBJECTIVES: To compare meta-analysis of summary study level data with the equivalent individual patient data (IPD) analysis when interest lies in identification of binary patient characteristics related to treatment efficacy. DESIGN: A simulation study comparing meta-regression with IPD analyses of randomized controlled trials. METHODS: Twenty-seven different meta-analysis situations were simulated with 1000 repetitions in each case. The following parameters were varied: (1) the treatment effect magnitude for different patient risk groups; (2) sample sizes of individual studies; and (3) number of studies. The meta-regression and IPD results were then compared for each situation. RESULTS: The statistical power of meta-regression was dramatically and consistently lower than that of IPD analysis, with little agreement between the parameter estimates obtained from the two methods. Only in meta-analyses of large numbers of large trials, did meta-regression detect differential treatment effects between risk groups with any consistency. CONCLUSIONS: Meta-analysis of summary data may be adequate when estimating a single pooled treatment effect or investigating study level characteristics. However, when interest lies in investigating whether patient characteristics are related to treatment, IPD analysis will generally be necessary to discover any such relationships. In these situations practitioners should try to obtain individual-level data.     

A multivariate meta-analysis approach for reducing the impact of outcome reporting bias in systematic reviews

Multivariate meta‐analysis allows the joint synthesis of multiple correlated outcomes from randomised trials, and is an alternative to a separate univariate meta‐analysis of each outcome independently. Usually not all trials report all outcomes; furthermore, outcome reporting bias (ORB) within trials, where an outcome is measured and analysed but not reported on the basis of the results, may cause a biased set of the evidence to be available for some outcomes, potentially affecting the significance and direction of meta‐analysis results. The multivariate approach, however, allows one to ‘borrow strength’ across correlated outcomes, to potentially reduce the impact of ORB. Assuming ORB missing data mechanisms, we aim to investigate the magnitude of bias in the pooled treatment effect estimates for multiple outcomes using univariate meta‐analysis, and to determine whether the ‘borrowing of strength’ from multivariate meta‐analysis can reduce the impact of ORB. A simulation study was conducted for a bivariate fixed effect meta‐analysis of two correlated outcomes. The approach is illustrated by application to a Cochrane systematic review. Results show that the ‘borrowing of strength’ from a multivariate meta‐analysis can reduce the impact of ORB on the pooled treatment effect estimates. We also examine the use of the Pearson correlation as a novel approach for dealing with missing within‐study correlations, and provide an extension to bivariate random‐effects models that reduce ORB in the presence of heterogeneity. Copyright © 2012 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.     

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.     

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.     

A framework for developing,implementing, and evaluating clinical prediction models in an individual participant data meta‐analysis

The use of individual participant data (IPD) from multiple studies is an increasingly popular approach when developing a multivariable risk prediction model. Corresponding datasets, however, typically differ in important aspects, such as baseline risk. This has driven the adoption of meta‐analytical approaches for appropriately dealing with heterogeneity between study populations. Although these approaches provide an averaged prediction model across all studies, little guidance exists about how to apply or validate this model to new individuals or study populations outside the derivation data. We consider several approaches to develop a multivariable logistic regression model from an IPD meta‐analysis (IPD‐MA) with potential between‐study heterogeneity. We also propose strategies for choosing a valid model intercept for when the model is to be validated or applied to new individuals or study populations. These strategies can be implemented by the IPD‐MA developers or future model validators. Finally, we show how model generalizability can be evaluated when external validation data are lacking using internal–external cross‐validation and extend our framework to count and time‐to‐event data. In an empirical evaluation, our results show how stratified estimation allows study‐specific model intercepts, which can then inform the intercept to be used when applying the model in practice, even to a population not represented by included studies. In summary, our framework allows the development (through stratified estimation), implementation in new individuals (through focused intercept choice), and evaluation (through internal–external validation) of a single, integrated prediction model from an IPD‐MA in order to achieve improved model performance and generalizability. Copyright © 2013 John Wiley & Sons, Ltd.