Copas-like selection model to correct publication bias in systematic review of diagnostic test studies

The accuracy of a diagnostic test, which is often quantified by a pair of measures such as sensitivity and specificity, is critical for medical decision making. Separate studies of an investigational diagnostic test can be combined through meta-analysis; however, such an analysis can be threatened by publication bias. To the best of our knowledge, there is no existing method that accounts for publication bias in the meta-analysis of diagnostic tests involving bivariate outcomes. In this paper, we extend the Copas selection model from univariate outcomes to bivariate outcomes for the correction of publication bias when the probability of a study being published can depend on its sensitivity, specificity, and the associated standard errors. We develop an expectation-maximization algorithm for the maximum likelihood estimation under the proposed selection model. We investigate the finite sample performance of the proposed method through simulation studies and illustrate the method by assessing a meta-analysis of 17 published studies of a rapid diagnostic test for influenza.

[1]  C. Begg,et al.  Operating characteristics of a rank correlation test for publication bias. , 1994, Biometrics.

[2]  Nicky J Welton,et al.  A selection model for accounting for publication bias in a full network meta‐analysis , 2014, Statistics in medicine.

[3]  J. Copas,et al.  Meta-analysis, funnel plots and sensitivity analysis. , 2000, Biostatistics.

[4]  G. Smith,et al.  Bias in meta-analysis detected by a simple, graphical test , 1997, BMJ.

[5]  Haitao Chu,et al.  Bivariate Random Effects Meta-Analysis of Diagnostic Studies Using Generalized Linear Mixed Models , 2010 .

[6]  Haitao Chu,et al.  Bivariate meta-analysis of sensitivity and specificity with sparse data: a generalized linear mixed model approach. , 2006, Journal of clinical epidemiology.

[7]  Kay Dickersin,et al.  Publication Bias: Recognizing the Problem, Understanding Its Origins and Scope, and Preventing Harm , 2006 .

[8]  Paul-Christian Bürkner,et al.  Testing for publication bias in diagnostic meta‐analysis: a simulation study , 2014, Statistics in medicine.

[9]  S D Walter,et al.  A comparison of methods to detect publication bias in meta‐analysis , 2001, Statistics in medicine.

[10]  C M Rutter,et al.  A hierarchical regression approach to meta‐analysis of diagnostic test accuracy evaluations , 2001, Statistics in medicine.

[11]  D. Altman.  Summing up. The science of reviewing research, Richard J. Light and David B. Pillemer, Harvard University Press, Cambridge, Mass., 1984. No. of pages: x+191. Price: £6.25 (paperback); £14.95 (hardback) , 1986 .

[12]  Nandini Dendukuri,et al.  Bayesian Meta‐Analysis of the Accuracy of a Test for Tuberculous Pleuritis in the Absence of a Gold Standard Reference , 2012, Biometrics.

[13]  Alex J. Sutton,et al.  Publication and related biases: a review , 2000 .

[14]  J. Copas.  What works?: selectivity models and meta‐analysis , 1999 .

[15]  A. Sutton,et al.  Comparison of two methods to detect publication bias in meta-analysis. , 2006, JAMA.

[16]  J. Douglas,et al.  Confidence Regions for Parameter Pairs , 1993 .

[17]  Dimitris Mavridis,et al.  A fully Bayesian application of the Copas selection model for publication bias extended to network meta‐analysis , 2013, Statistics in medicine.

[18]  Madhukar Pai,et al.  Accuracy of Rapid Influenza Diagnostic Tests , 2012, Annals of Internal Medicine.

[19]  J Q Shi,et al.  A sensitivity analysis for publication bias in systematic reviews , 2001, Statistical methods in medical research.

[20]  Xiao-Hua Zhou,et al.  Sensitivity analysis for publication bias in meta‐analysis of diagnostic studies for a continuous biomarker , 2018, Statistics in medicine.

[21]  S Duval,et al.  Trim and Fill: A Simple Funnel‐Plot–Based Method of Testing and Adjusting for Publication Bias in Meta‐Analysis , 2000, Biometrics.

[22]  Jonathan J Deeks,et al.  The performance of tests of publication bias and other sample size effects in systematic reviews of diagnostic test accuracy was assessed. , 2005, Journal of clinical epidemiology.

[23]  Yan Xing,et al.  Contemporary diagnostic imaging modalities for the staging and surveillance of melanoma patients: a meta-analysis. , 2011, Journal of the National Cancer Institute.

[24]  Haitao Chu,et al.  A unification of models for meta‐analysis of diagnostic accuracy studies without a gold standard , 2015, Biometrics.

[25]  Jing Ning,et al.  Maximum likelihood estimation and EM algorithm of Copas-like selection model for publication bias correction. , 2017, Biostatistics.

[26]  Mohsen Sadatsafavi,et al.  A statistical method was used for the meta-analysis of tests for latent TB in the absence of a gold standard, combining random-effect and latent-class methods to estimate test accuracy. , 2010, Journal of clinical epidemiology.

[27]  M. Borenstein,et al.  Publication Bias in Meta-Analysis: Prevention, Assessment and Adjustments , 2006 .

[28]  Haitao Chu,et al.  Statistical methods for multivariate meta-analysis of diagnostic tests: An overview and tutorial , 2016, Statistical methods in medical research.

[29]  Thomas A Louis,et al.  Random Effects Models in a Meta-Analysis of the Accuracy of Two Diagnostic Tests Without a Gold Standard , 2009, Journal of the American Statistical Association.

[30]  T. Louis.  Finding the Observed Information Matrix When Using the EM Algorithm , 1982 .

[31]  P. Bossuyt,et al.  The diagnostic odds ratio: a single indicator of test performance. , 2003, Journal of clinical epidemiology.

[32]  Johannes B Reitsma,et al.  Bivariate analysis of sensitivity and specificity produces informative summary measures in diagnostic reviews. , 2005, Journal of clinical epidemiology.

[33]  J. Reitsma,et al.  Response to Chu and Cole: Bivariate meta-analysis of sensitivity and specificity with sparse data , 2006 .

[34]  J. Copas,et al.  Inference for Non‐random Samples , 1997 .

[35]  Haitao Chu,et al.  A unification of models for meta-analysis of diagnostic accuracy studies. , 2009, Biostatistics.

[36]  R. Tweedie,et al.  A Nonparametric “Trim and Fill” Method of Accounting for Publication Bias in Meta-Analysis , 2000 .