Efficient integration of aggregate data and individual participant data in one‐way mixed models

Often both aggregate data (AD) studies and individual participant data (IPD) studies are available for specific treatments. Combining these two sources of data could improve the overall meta-analytic estimates of treatment effects. Moreover, often for some studies with AD, the associated IPD maybe available, albeit at some extra effort or cost to the analyst. We propose a method for combining treatment effects across trials when the response is from the exponential family of distribution and hence a generalized linear model structure can be used. We consider the case when treatment effects are fixed and common across studies. Using the proposed combination method, we study the relative efficiency of analyzing all IPD studies vs combining various percentages of AD and IPD studies. For many different models, design constraints under which the AD estimators are the IPD estimators, and hence fully efficient, are known. For such models, we advocate a selection procedure that chooses AD studies over IPD studies in a manner that force least departure from design constraints and hence ensures an efficient combined AD and IPD estimator.

[1]  Minge Xie,et al.  A Split-and-Conquer Approach for Analysis of Extraordinarily Large Data , 2014 .

[2]  Richard D Riley,et al.  Evidence synthesis combining individual patient data and aggregate data: a systematic review identified current practice and possible methods. , 2007, Journal of clinical epidemiology.

[3]  R. Riley.  Commentary: like it and lump it? Meta-analysis using individual participant data. , 2010, International journal of epidemiology.

[4]  Richard D Riley,et al.  Meta‐analysis of diagnostic test studies using individual patient data and aggregate data , 2008, Statistics in medicine.

[5]  Richard D Riley,et al.  Meta‐analysis of a binary outcome using individual participant data and aggregate data , 2010, Research synthesis methods.

[6]  Andrea Benedetti,et al.  A comparison of analytic approaches for individual patient data meta-analyses with binary outcomes , 2017, BMC Medical Research Methodology.

[7]  A J Sutton,et al.  Meta‐analysis of individual‐ and aggregate‐level data , 2008, Statistics in medicine.

[8]  Wolfgang Viechtbauer,et al.  Bias and Efficiency of Meta-Analytic Variance Estimators in the Random-Effects Model , 2005 .

[9]  A. Sutton,et al.  Mixed treatment comparisons using aggregate and individual participant level data , 2012, Statistics in medicine.

[10]  Theo Stijnen,et al.  Advanced methods in meta‐analysis: multivariate approach and meta‐regression , 2002, Statistics in medicine.

[11]  Anne Whitehead,et al.  Meta-analysis of individual patient data versus aggregate data from longitudinal clinical trials , 2009, Clinical trials.

[12]  N. Laird,et al.  Meta-analysis in clinical trials. , 1986, Controlled clinical trials.

[13]  Xiao-Hua Zhou,et al.  Statistical Methods for Meta‐Analysis , 2008 .

[14]  N. Laird,et al.  Meta-analysis in clinical trials revisited. , 2015, Contemporary clinical trials.

[15]  Sylvia Richardson,et al.  Improving ecological inference using individual‐level data , 2006, Statistics in medicine.

[16]  D. Zeng,et al.  On the relative efficiency of using summary statistics versus individual-level data in meta-analysis. , 2010, Biometrika.

[17]  H Tunstall-Pedoe,et al.  Systematically missing confounders in individual participant data meta-analysis of observational cohort studies , 2009, Statistics in medicine.

[18]  Thomas Mathew,et al.  Comparison of One‐Step and Two‐Step Meta‐Analysis Models Using Individual Patient Data , 2010, Biometrical journal. Biometrische Zeitschrift.

[19]  C D Naylor,et al.  Meta-analysis of controlled clinical trials. , 1989, The Journal of rheumatology.

[20]  Kurex Sidik,et al.  A comparison of heterogeneity variance estimators in combining results of studies , 2007, Statistics in medicine.

[21]  Richard D Riley,et al.  Meta‐analysis of a continuous outcome combining individual patient data and aggregate data: a method based on simulated individual patient data , 2014, Research synthesis methods.

[22]  B. Sinha,et al.  Statistical Meta-Analysis with Applications , 2008 .

[23]  Minge Xie,et al.  Multivariate Meta-Analysis of Heterogeneous Studies Using Only Summary Statistics: Efficiency and Robustness , 2015, Journal of the American Statistical Association.

[24]  Eugene Demidenko,et al.  Multivariate meta-analysis for data consortia, individual patient meta-analysis, and pooling projects , 2008 .

[25]  N. Chatterjee,et al.  Generalized meta-analysis for multiple regression models across studies with disparate covariate information. , 2017, Biometrika.

[26]  I. Chalmers.  The Cochrane Collaboration: Preparing, Maintaining, and Disseminating Systematic Reviews of the Effects of Health Care , 1993, Annals of the New York Academy of Sciences.

[27]  Mats O Karlsson,et al.  A linearization approach for the model‐based analysis of combined aggregate and individual patient data , 2014, Statistics in medicine.

[28]  Anne Whitehead,et al.  Meta-Analysis of Controlled Clinical Trials , 2002 .

[29]  A. Sutton,et al.  Assessment of publication bias, selection bias, and unavailable data in meta-analyses using individual participant data: a database survey , 2012, BMJ : British Medical Journal.

[30]  Ralf Bender,et al.  Methods to estimate the between‐study variance and its uncertainty in meta‐analysis† , 2015, Research synthesis methods.

[31]  C. McCulloch,et al.  Generalized Linear Mixed Models , 2005 .

[32]  L. Ryan,et al.  Sufficiency Revisited: Rethinking Statistical Algorithms in the Big Data Era , 2017 .

[33]  Harris Cooper,et al.  The relative benefits of meta-analysis conducted with individual participant data versus aggregated data. , 2009, Psychological methods.

[34]  Mike W.-L. Cheung,et al.  Analyzing Big Data in Psychology: A Split/Analyze/Meta-Analyze Approach , 2016, Front. Psychol..

[35]  Wolfgang Viechtbauer,et al.  Conducting Meta-Analyses in R with the metafor Package , 2010 .

[36]  Guido Knapp,et al.  On Estimating Residual Heterogeneity in Random-Effects Meta-Regression: A Comparative Study , 2013, J. Stat. Theory Appl..

[37]  I Olkin,et al.  Comparison of meta-analysis versus analysis of variance of individual patient data. , 1998, Biometrics.

[38]  Richard D Riley,et al.  Meta‐analysis of continuous outcomes combining individual patient data and aggregate data , 2008, Statistics in medicine.

[39]  N. Reid,et al.  AN OVERVIEW OF COMPOSITE LIKELIHOOD METHODS , 2011 .

[40]  R. Peto,et al.  Beta blockade during and after myocardial infarction: an overview of the randomized trials. , 1985, Progress in cardiovascular diseases.

[41]  Catrin Tudur Smith,et al.  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 , 2013, Statistics in medicine.

[42]  T. Mathew,et al.  On the Equivalence of Meta‐Analysis Using Literature and Using Individual Patient Data , 1999, Biometrics.

[43]  Nicky J Welton,et al.  Enhanced secondary analysis of survival data: reconstructing the data from published Kaplan-Meier survival curves , 2012, BMC Medical Research Methodology.