{"id":2382,"date":"2013-03-29T13:32:57","date_gmt":"2013-03-29T04:32:57","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=2382"},"modified":"2013-03-29T13:32:57","modified_gmt":"2013-03-29T04:32:57","slug":"how-to-calculate-sensitivity-specificity-positive-predictive-value-negative-predictive-value-positive-likelihood-ratio-and-negative-likelihood-ratio-and-their-95-confidence-interval-with-cross-ta","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=2382","title":{"rendered":"How to calculate sensitivity, specificity, positive predictive value, negative predictive value, positive likelihood ratio and negative likelihood ratio and their 95 % confidence interval with cross tabulation?"},"content":{"rendered":"

You can calculate 95 % confidence interval of probability as formula below. <\/p>\n

\\displaystyle p \\pm 1.96 \\sqrt{\\frac{p(1 - p)}{n}}<\/p>\n<\/p>\n

In this article, I’d like to describe how to calculate sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), positive likelihood ratio (LR+) and negative likelihood ratio (LR-) and their 95 % confidence interval with cross tabulation. <\/p>\n\n\n\n\n\n\n
\u00a0<\/td>\nTRUE<\/span><\/strong><\/td>\nFALSE<\/span><\/strong><\/td>\nMarginal total<\/span><\/td>\n<\/tr>\n
POSITIVE<\/span><\/strong><\/td>\na<\/span><\/td>\nb<\/span><\/span><\/td>\na + b<\/span><\/td>\n<\/tr>\n
NEGATIVE<\/span><\/strong><\/td>\nc<\/span><\/td>\nd<\/span><\/td>\nc + d<\/span><\/td>\n<\/tr>\n
Marginal total<\/span><\/td>\na + c<\/span><\/td>\nb + d<\/span><\/td>\nN<\/span>\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Sensitivity, specificity, PPV, NPV, LR+ and LR- and their 95 % confidence interval are shown as following table. ‘Exp()’ means exponential with Napier’s constant and ‘LN()’ means natural logarithmic function, respectively. <\/p>\n\n\n\n\n\n\n\n\n\n
\u00a0<\/td>\n\u00a0Formula<\/span><\/strong><\/td>\n95% Confidence Interval<\/span><\/strong><\/td>\n<\/tr>\n
Sensitivity<\/span><\/strong><\/span><\/td>\n\\displaystyle \\frac{a}{a + c}<\/span><\/td>\n\\displaystyle Sensitivity\\pm1.96\\sqrt{\\frac{Sensitivity(1 - Sensitivity)}{a + c}}<\/span><\/td>\n<\/tr>\n
Specificity<\/span><\/strong><\/span><\/td>\n\\displaystyle \\frac{d}{b + d}<\/span><\/td>\n\\displaystyle Specificity\\pm1.96\\sqrt{\\frac{Specificity(1 - Specificity)}{b + d}}<\/span><\/td>\n<\/tr>\n
PPV<\/span><\/strong><\/span><\/td>\n\\displaystyle \\frac{a}{a + b}<\/span><\/td>\n\\displaystyle PPV \\pm 1.96\\sqrt{\\frac{PPV(1 - PPV)}{a + b}}<\/span><\/td>\n<\/tr>\n
NPV<\/span><\/strong><\/span><\/td>\n\\displaystyle \\frac{d}{c + d}<\/span><\/td>\n\\displaystyle NPV \\pm 1.96\\sqrt{\\frac{NPV(1 - NPV)}{c + d}}<\/span><\/td>\n<\/tr>\n
LR+<\/span><\/strong><\/span><\/td>\n\\displaystyle \\frac{a}{a + c}\\bigg\/\\frac{b}{b + d}<\/span><\/td>\n\\displaystyle Exp \\left[LN\\left( \\frac{Sensitivity}{1 - Specificity}\\right)\\pm1.96\\left(\\frac{1 - Sensitivity}{a} + \\frac{Specificity}{b}\\right) \\right]\u00a0<\/span><\/td>\n<\/tr>\n
LR-<\/span><\/strong><\/span><\/td>\n\\displaystyle \\frac{c}{a + c}\\bigg\/\\frac{d}{b + d}<\/span><\/td>\n\\displaystyle Exp\\left[ LN\\left(\\frac{1 - Sensitivity}{Specificity}\\right) \\pm1.96\\left( \\frac{Sensitivity}{c} + \\frac{1 - Specificity}{d} \\right)\\right]\u00a0<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>","protected":false},"excerpt":{"rendered":"

You can calculate 95 % confidence interval of probability as formula below. In this article, I’d like to … “How to calculate sensitivity, specificity, positive predictive value, negative predictive value, positive likelihood ratio and negative likelihood ratio and their 95 % confidence interval with cross tabulation?” \u306e<\/span>\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[7],"tags":[],"class_list":["post-2382","post","type-post","status-publish","format-standard","hentry","category-statistics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/2382","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2382"}],"version-history":[{"count":12,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/2382\/revisions"}],"predecessor-version":[{"id":2395,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/2382\/revisions\/2395"}],"wp:attachment":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2382"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2382"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2382"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}