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>\n TRUE<\/span><\/strong><\/td>\n FALSE<\/span><\/strong><\/td>\n Marginal total<\/span><\/td>\n<\/tr>\n
POSITIVE<\/span><\/strong><\/td>\n a<\/span><\/td>\n b<\/span><\/span><\/td>\n a + b<\/span><\/td>\n<\/tr>\n
NEGATIVE<\/span><\/strong><\/td>\n c<\/span><\/td>\n d<\/span><\/td>\n c + d<\/span><\/td>\n<\/tr>\n
Marginal total<\/span><\/td>\n a + c<\/span><\/td>\n b + d<\/span><\/td>\n N<\/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>\n 95% 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":{"_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":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t