{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T16:08:11Z","timestamp":1791389291898,"version":"4.3.3"},"reference-count":16,"publisher":"Wiley","issue":"14","license":[{"start":{"date-parts":[[2007,3,14]],"date-time":"2007-03-14T00:00:00Z","timestamp":1173830400000},"content-version":"vor","delay-in-days":4975,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[1993,7,30]]},"abstract":"Abstract<\/jats:title>\n \n We consider how to combine several independent studies of the same diagnostic test, where each study reports an estimated false positive rate )FPR( and an estimated true positive rate )TPR(. We propose constructing a summary receiver operating characteristic )ROC( curve by the following steps. )i( Convert each FPR to its logistic transform\n U<\/jats:italic>\n and each TPR to its logistic transform\n V<\/jats:italic>\n after increasing each observed frequency by adding 1\/2. )ii( For each study calculate\n D<\/jats:italic>\n =\n V \u2013 U<\/jats:italic>\n , which is the log odds ratio of TPR and FPR, and\n S<\/jats:italic>\n =\n V<\/jats:italic>\n +\n U<\/jats:italic>\n , an implied function of test threshold; then plot each study's point\n \n )S\n i<\/jats:sub>\n , D\n i<\/jats:sub>\n (\n <\/jats:italic>\n . )iii( Fit a robust\u2010resistant regression line to these points )or an equally weighted least\u2010squares regression line(, with\n V \u2013 U<\/jats:italic>\n as the dependent variable. )iv( Back\u2010transform the line to ROC space. To avoid model\u2010dependent extrapolation from irrelevant regions of ROC space we propose defining\n a priori<\/jats:italic>\n a value of FPR so large that the test simply would not be used at that FPR, and a value of TPR so low that the test would not be used at that TPR. Then )a( only data points lying in the thus defined north\u2010west rectangle of the unit square are used in the data analysis, and )b( the estimated summary ROC is depicted only within that subregion of the unit square. We illustrate the methods using simulated and real data sets, and we point to ways of comparing different tests and of taking into account the effects of covariates.\n <\/jats:p>","DOI":"10.1002\/sim.4780121403","type":"journal-article","created":{"date-parts":[[2007,4,27]],"date-time":"2007-04-27T10:18:14Z","timestamp":1177669094000},"page":"1293-1316","source":"Crossref","is-referenced-by-count":1134,"title":["Combining independent studies of a diagnostic test into a summary roc curve: Data\u2010analytic approaches and some additional considerations"],"prefix":"10.1002","volume":"12","author":[{"given":"Lincoln E.","family":"Moses","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"Shapiro","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Benjamin","family":"Littenberg","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2007,3,14]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1001\/jama.248.5.548"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.7326\/0003-4819-105-6-906"},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1055\/s-0038-1634759","article-title":"Comparative diagnostic performance of three radiological procedures for the detection of lumbar disk herniation","volume":"29","author":"Kardaun J. W. P. F.","year":"1990","journal-title":"Methods of Information in Medicine"},{"key":"e_1_2_1_5_2","unstructured":"Hall W. J.Efficiency of Weighted Averages Technical Report 92\/02 Department of Statistics and Biostatistics University of Rochester 1992."},{"key":"e_1_2_1_6_2","volume-title":"The Analysis of Binary Data","author":"Cox D. R.","year":"1970"},{"key":"e_1_2_1_7_2","unstructured":"Kafadar K.\u2018Robust\u2010resistant line\u2019 in Kotz S. and Johnson N. L. (eds.) Encyclopedia of Statistical Sciences vol. 8 1988 pp.169\u2013170."},{"key":"e_1_2_1_8_2","unstructured":"Emerson J. D.andHoaglin D. C.Resistant lines foryvsx' in Hoaglin D. C. Mosteller F. and Tukey J. W. (eds.) Understanding Robust and Exploratory Data Analysis Chapter 5 1983 pp.129\u2013165."},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1002\/bimj.4710280414"},{"key":"e_1_2_1_10_2","first-page":"719","article-title":"Statistical aspects of the analysis of data from retrospective studies of disease","volume":"22","author":"Mantel N.","year":"1959","journal-title":"Journal of the National Cancer Institute"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.2307\/2288562"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.2307\/2684185"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1137\/0904024"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4780100908"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.2307\/2347977"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.2307\/2346353"},{"key":"e_1_2_1_17_2","first-page":"144","article-title":"Extra\u2010Poisson variation in log\u2010linear models","volume":"31","author":"Breslow N. E.","year":"1984","journal-title":"Applied Statistics"}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fsim.4780121403","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.4780121403","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T18:41:58Z","timestamp":1698259318000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.4780121403"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,7,30]]},"references-count":16,"journal-issue":{"issue":"14","published-print":{"date-parts":[[1993,7,30]]}},"alternative-id":["10.1002\/sim.4780121403"],"URL":"https:\/\/doi.org\/10.1002\/sim.4780121403","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,7,30]]}}}