Research Synthesis Methods

Meta‐analysis of test accuracy studies using imputation for partial reporting of multiple thresholds

Journal Article


For tests reporting continuous results, primary studies usually provide test performance at multiple but often different thresholds. This creates missing data when performing a meta‐analysis at each threshold. A standard meta‐analysis (no imputation [NI]) ignores such missing data. A single imputation (SI) approach was recently proposed to recover missing threshold results. Here, we propose a new method that performs multiple imputation of the missing threshold results using discrete combinations (MIDC).


The new MIDC method imputes missing threshold results by randomly selecting from the set of all possible discrete combinations which lie between the results for 2 known bounding thresholds. Imputed and observed results are then synthesised at each threshold. This is repeated multiple times, and the multiple pooled results at each threshold are combined using Rubin's rules to give final estimates. We compared the NI, SI, and MIDC approaches via simulation.


Both imputation methods outperform the NI method in simulations. There was generally little difference in the SI and MIDC methods, but the latter was noticeably better in terms of estimating the between‐study variances and generally gave better coverage, due to slightly larger standard errors of pooled estimates. Given selective reporting of thresholds, the imputation methods also reduced bias in the summary receiver operating characteristic curve. Simulations demonstrate the imputation methods rely on an equal threshold spacing assumption. A real example is presented.


The SI and, in particular, MIDC methods can be used to examine the impact of missing threshold results in meta‐analysis of test accuracy studies.

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Published features on are checked for statistical accuracy by a panel from the European Network for Business and Industrial Statistics (ENBIS)   to whom Wiley and express their gratitude. This panel are: Ron Kenett, David Steinberg, Shirley Coleman, Irena Ograjenšek, Fabrizio Ruggeri, Rainer Göb, Philippe Castagliola, Xavier Tort-Martorell, Bart De Ketelaere, Antonio Pievatolo, Martina Vandebroek, Lance Mitchell, Gilbert Saporta, Helmut Waldl and Stelios Psarakis.