{"id":429,"date":"2015-07-27T22:03:46","date_gmt":"2015-07-27T21:03:46","guid":{"rendered":"http:\/\/pcool.dyndns.org:8080\/statsbook\/?page_id=429"},"modified":"2025-06-24T00:17:57","modified_gmt":"2025-06-23T23:17:57","slug":"answers-epidemiology","status":"publish","type":"page","link":"https:\/\/pcool.dyndns.org\/index.php\/answers-epidemiology\/","title":{"rendered":"Answers Epidemiology"},"content":{"rendered":"\n<ol class=\"wp-block-list\">\n<li>There were 1000 people with osteosarcoma and the population at risk was 50 million:<\/li>\n<\/ol>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">Prevalence =\\( \\frac{1,000}{50{,}000,000} \\) =  \\(\\frac{20}{1,000000} \\) = 20 per million<script src=\"https:\/\/pcool.dyndns.org\/wp-includes\/js\/dist\/hooks.min.js?ver=dd5603f07f9220ed27f1\" id=\"wp-hooks-js\"><\/script>\n<script src=\"https:\/\/pcool.dyndns.org\/wp-includes\/js\/dist\/i18n.min.js?ver=c26c3dc7bed366793375\" id=\"wp-i18n-js\"><\/script>\n<script id=\"wp-i18n-js-after\">\nwp.i18n.setLocaleData( { 'text direction\\u0004ltr': [ 'ltr' ] } );\n\/\/# sourceURL=wp-i18n-js-after\n<\/script>\n<script  async src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-MML-AM_CHTML\" id=\"mathjax-js\"><\/script>\n<\/div>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li>At the start of the year there were 1000 cases of osteosarcoma. 200 new cases were diagnosed and 75 patients with osteosarcoma died. On 1<sup>st<\/sup> January 2001 there were therefore: <\/li>\n<\/ol>\n\n\n\n<p>1000 + 200 \u2013 75 = 1125 patients with osteosarcoma. So:<\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">Prevalence = \\( \\frac{1,125}{50{,}000,000} \\) = \\(\\frac{22.5}{1,000,000}\\) = 22.5 per million<\/div>\n\n\n\n<ol start=\"3\" class=\"wp-block-list\">\n<li>There were 200 new cases of osteosarcoma in the year. The Incidence is therefore:<\/li>\n<\/ol>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">Incidence = \\(\\frac{200}{50,000,000}\\) = \\(\\frac{4}{1,000,000}\\) = 4 per million<\/div>\n\n\n\n<ol start=\"4\" class=\"wp-block-list\">\n<li>The two by two table is as follows:\n<table id=\"tablepress-7\" class=\"tablepress tablepress-id-7\">\n<thead>\n<tr class=\"row-1\">\n\t<td class=\"column-1\"><\/td><th class=\"column-2\">Kienb\u00f6ck\u2019s<\/th><th class=\"column-3\">No Kienb\u00f6ck\u2019s<\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"row-striping row-hover\">\n<tr class=\"row-2\">\n\t<td class=\"column-1\">Neg Ulnar Var<\/td><td class=\"column-2\">12<\/td><td class=\"column-3\">138<\/td>\n<\/tr>\n<tr class=\"row-3\">\n\t<td class=\"column-1\">No Neg Ulnar Var<\/td><td class=\"column-2\">3<\/td><td class=\"column-3\">347<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-7 from cache --><\/li>\n\n\n\n<li>The relative risk is:<\/li>\n<\/ol>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">Absolute Risk 1 = \\(\\frac{12}{150}\\) = 0.08<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">Absolute Risk 1 = \\(\\frac{3}{350}\\) ~ 0.00857<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">Relative Risk = \\(\\frac{12 \\over 150}{3 \\over 350}\\) ~ 9.33<\/div>\n\n\n\n<ol start=\"6\" class=\"wp-block-list\">\n<li>The odds ratio is:<\/li>\n<\/ol>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">Odds Ratio = \\(\\frac{12 \\times 347}{138 \\times 3} \\) ~ 10.06<\/div>\n\n\n\n<ol start=\"7\" class=\"wp-block-list\">\n<li>First construct a two by two table:<\/li>\n<\/ol>\n\n\n\n<table id=\"tablepress-30\" class=\"tablepress tablepress-id-30\">\n<thead>\n<tr class=\"row-1\">\n\t<td class=\"column-1\"><\/td><th class=\"column-2\">Died<\/th><th class=\"column-3\">Survived<\/th><td class=\"column-4\"><\/td>\n<\/tr>\n<\/thead>\n<tbody class=\"row-striping row-hover\">\n<tr class=\"row-2\">\n\t<td class=\"column-1\">Men<\/td><td class=\"column-2\">1347<\/td><td class=\"column-3\">336<\/td><td class=\"column-4\">1683<\/td>\n<\/tr>\n<tr class=\"row-3\">\n\t<td class=\"column-1\">Women &amp; Children<\/td><td class=\"column-2\">170<\/td><td class=\"column-3\">370<\/td><td class=\"column-4\">540<\/td>\n<\/tr>\n<tr class=\"row-4\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">1517<\/td><td class=\"column-3\">706<\/td><td class=\"column-4\">2223<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-30 from cache -->\n\n\n<p>In the R console<sup class='sup-ref-note' id='note-zotero-ref-p429-r1-o1'><a class='sup-ref-note' href='#zotero-ref-p429-r1'>1<\/a><\/sup> :<\/p>\n\n\n\n<pre class=\"wp-block-code has-small-font-size\"><code><code><mark style=\"background-color:rgba(0, 0, 0, 0);color:#fa0000\" class=\"has-inline-color\"><em>library(epiR)<\/em>\n<em>mat&lt;-matrix(c(1347,170,336,370),ncol=2)<\/em>\n<em>mat<\/em><\/mark>\n<mark style=\"background-color:rgba(0, 0, 0, 0);color:#011df7\" class=\"has-inline-color\"><em>\u00a0\u00a0\u00a0\u00a0 &#091;,1] &#091;,2]<\/em>\n<em>&#091;1,] 1347\u00a0 336<\/em>\n<em>&#091;2,]\u00a0 170\u00a0 370<\/em>\n<em>epi.2by2(mat)<\/em>\n<em>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Outcome +\u00a0\u00a0Outcome \u2013\u00a0\u00a0\u00a0\u00a0\u00a0 Total\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Inc risk *\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Odds<\/em>\n<em>Exposed +\u00a0\u00a0\u00a0\u00a0\u00a01347\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0  336\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1683\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<strong>80.0\u00a0<\/strong>\u00a0\u00a0 \u00a0 \u00a0<strong>4.009<\/strong><\/em>\n<em>Exposed \u2013\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0170\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 370\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0  540\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<strong>31.5\u00a0\u00a0<\/strong>\u00a0\u00a0 \u00a0 <strong>0.459<\/strong><\/em>\n<em>Total\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a01517\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 706\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2223\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a068.2\u00a0\u00a0\u00a0\u00a0 \u00a0 2.149<\/em><\/mark><\/code>\n<code><mark style=\"background-color:rgba(0, 0, 0, 0);color:#0048fe\" class=\"has-inline-color\"><em>Point estimates and 95 % CIs:<\/em>\n<em>\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014<\/em>\n<em>Inc risk ratio\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2.54 (2.24, 2.89)<\/em>\n<em>Odds ratio\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<strong>\u00a0 8.71 (6.98, 10.91)<\/strong><\/em>\n<em>Attrib risk *\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 48.55 (44.20, 52.91)<\/em>\n<em>Attrib risk in population *\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 36.76 (32.39, 41.13)<\/em>\n<em>Attrib fraction in exposed (%)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 60.67 (55.35, 65.35)<\/em>\n<em>Attrib fraction in population (%)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 53.87 (48.34, 58.81)<\/em>\n<em>\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014<\/em>\n<em>\u00a0* Cases per 100 population units<\/em><\/mark><\/code><\/code><\/pre>\n\n\n\n<p>The package epiR<sup class='sup-ref-note' id='note-zotero-ref-p429-r2-o1'><a class='sup-ref-note' href='#zotero-ref-p429-r2'>2<\/a><\/sup> should be <a href=\"https:\/\/pcool.dyndns.org\/index.php\/packages\/\" data-type=\"page\" data-id=\"22\">installed<\/a>.<\/p>\n\n\n\n<p>Or a summary:<\/p>\n\n\n\n<pre class=\"wp-block-code has-small-font-size\"><code><code><span style=\"color: #ff0000;\"><em>summary(epi.tests(mat))<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 est\u00a0\u00a0\u00a0\u00a0 lower\u00a0\u00a0\u00a0\u00a0\u00a0 upper<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>aprev\u00a0\u00a0\u00a0 0.7570850 0.7387012\u00a0 0.7747887<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>tprev\u00a0\u00a0\u00a0 0.6824112 0.6626028\u00a0 0.7017375<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>se\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.8879367 0.8709769\u00a0 0.9033774<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>sp\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.5240793 0.4864967\u00a0 0.5614599<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>diag.acc 0.7723797 0.7543719\u00a0 0.7896666<\/em><\/span>\n<span style=\"color: #0000ff;\"><em><strong>diag.or\u00a0 8.7253151 7.0204403 10.8442094<\/strong><\/em><\/span>\n<span style=\"color: #0000ff;\"><em>nnd\u00a0\u00a0\u00a0\u00a0\u00a0 2.4270900 2.1512902\u00a0 2.7974095<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>youden\u00a0\u00a0 0.4120160 0.3574736\u00a0 0.4648373<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>ppv\u00a0\u00a0\u00a0\u00a0\u00a0 0.8003565 0.7804454\u00a0 0.8192143<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>npv\u00a0\u00a0\u00a0\u00a0\u00a0 0.6851852 0.6441513\u00a0 0.7241780<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>plr\u00a0\u00a0\u00a0\u00a0\u00a0 1.8657242 1.7232384\u00a0 2.0199914<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>nlr\u00a0\u00a0\u00a0\u00a0\u00a0 0.2138289 0.1825536\u00a0 0.2504622<\/em><\/span><\/code><\/code><\/pre>\n\n\n\n<p>The absolute risk for men dying is <strong>80 %<\/strong><\/p>\n\n\n\n<p>The absolute risk for women and children dying is <strong>31.5 %<\/strong><\/p>\n\n\n\n<p>The odds for men dying is <strong>4.009<\/strong><\/p>\n\n\n\n<p>The odds for women and children dying is <strong>0.459<\/strong><\/p>\n\n\n\n<p>The odds ratio is <strong>8.73 ; 95% confidence interval: 7.02 &#8211; 10.84<\/strong><\/p>\n\n\n\n<p>Or a summary:<\/p>\n\n\n\n<pre class=\"wp-block-code has-small-font-size\"><code><code><span style=\"color: #ff0000;\"><em>summary(epi.tests(mat,<strong>conf.level=0.99<\/strong>))<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 est\u00a0\u00a0\u00a0\u00a0 lower\u00a0\u00a0\u00a0\u00a0\u00a0 upper<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>aprev\u00a0\u00a0\u00a0 0.7570850 0.7328916\u00a0 0.7801648<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>tprev\u00a0\u00a0\u00a0 0.6824112 0.6563789\u00a0 0.7076541<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>se\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.8879367 0.8655122\u00a0 0.9078798<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>sp\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.5240793 0.4749263\u00a0 0.5729024<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>diag.acc 0.7723797 0.7486736\u00a0 0.7949055<\/em><\/span>\n<strong><span style=\"color: #0000ff;\"><em>diag.or\u00a0 8.7253151 6.5568681 11.6108976<\/em><\/span><\/strong>\n<span style=\"color: #0000ff;\"><em>nnd\u00a0\u00a0\u00a0\u00a0\u00a0 2.4270900 2.0799435\u00a0 2.9373883<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>youden\u00a0\u00a0 0.4120160 0.3404385\u00a0 0.4807823<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>ppv\u00a0\u00a0\u00a0\u00a0\u00a0 0.8003565 0.7741208\u00a0 0.8248692<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>npv\u00a0\u00a0\u00a0\u00a0\u00a0 0.6851852 0.6312886\u00a0 0.7357534<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>plr\u00a0\u00a0\u00a0\u00a0\u00a0 1.8657242 1.6807535\u00a0 2.0710513<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>nlr\u00a0\u00a0\u00a0\u00a0\u00a0 0.2138289 0.1737045\u00a0 0.2632217<\/em><\/span><\/code><\/code><\/pre>\n\n\n\n<p>The odds ratio is <strong>8.73 ; 99% confidence interval: 6.56 &#8211; 11.61<\/strong><\/p>\n\n\n\n<ol start=\"8\" class=\"wp-block-list\">\n<li>First construct the two by two table:<\/li>\n<\/ol>\n\n\n\n<table id=\"tablepress-31\" class=\"tablepress tablepress-id-31\">\n<thead>\n<tr class=\"row-1\">\n\t<td class=\"column-1\"><\/td><th class=\"column-2\">Died<\/th><th class=\"column-3\">Survived<\/th><td class=\"column-4\"><\/td>\n<\/tr>\n<\/thead>\n<tbody class=\"row-striping row-hover\">\n<tr class=\"row-2\">\n\t<td class=\"column-1\">1st \/ 2nd Class<\/td><td class=\"column-2\">296<\/td><td class=\"column-3\">318<\/td><td class=\"column-4\">614<\/td>\n<\/tr>\n<tr class=\"row-3\">\n\t<td class=\"column-1\">3rd Class<\/td><td class=\"column-2\">536<\/td><td class=\"column-3\">174<\/td><td class=\"column-4\">710<\/td>\n<\/tr>\n<tr class=\"row-4\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">832<\/td><td class=\"column-3\">492<\/td><td class=\"column-4\">1324<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-31 from cache -->\n\n\n<pre class=\"wp-block-code has-small-font-size\"><code><code><span style=\"color: #ff0000;\"><em>library(epiR)<\/em><\/span>\n<span style=\"color: #ff0000;\"><em>mat&lt;-matrix(c(296,536,318,174),ncol=2)<\/em><\/span>\n<span style=\"color: #ff0000;\"><em>mat<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>\u00a0\u00a0\u00a0\u00a0 &#091;,1] &#091;,2]<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>&#091;1,]\u00a0 296\u00a0 318<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>&#091;2,]\u00a0 536\u00a0 174<\/em><\/span>\n<span style=\"color: #ff0000;\"><em>epi.2by2(mat)<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Outcome +\u00a0\u00a0\u00a0 Outcome -\u00a0\u00a0\u00a0\u00a0\u00a0 Total\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Inc risk *\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Odds<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>Exposed +\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 296\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 318\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 614\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <strong>48.2\u00a0<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0<strong> 0.931<\/strong><\/em><\/span>\n<span style=\"color: #0000ff;\"><em>Exposed -\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 \u00a0536\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 174\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 710\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <strong>75.5<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <strong>3.080<\/strong><\/em><\/span>\n<span style=\"color: #0000ff;\"><em>Total\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0832\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 492\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1324\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 62.8\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1.691<\/em><\/span><\/code>\n<code><span style=\"color: #0000ff;\"><em>Point estimates and 95 % CIs:<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>---------------------------------------------------------<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>Inc risk ratio\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.64 (0.58, 0.70)<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>Odds ratio\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.30 (0.24, 0.38)<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>Attrib risk *\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -27.28 (-32.35, -22.22)<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>Attrib risk in population *\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -12.65 (-16.75, -8.56)<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>Attrib fraction in exposed (%)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -56.60 (-71.70, -42.82)<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>Attrib fraction in population (%)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -20.14 (-24.39, -16.03)<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>---------------------------------------------------------<\/em><\/span>\n<em><span style=\"color: #0000ff;\">\u00a0* Cases per 100 population units<\/span><\/em><\/code><\/code><\/pre>\n\n\n\n<p>The absolute risk for third class passengers dying is <strong>75.5 %<\/strong><\/p>\n\n\n\n<p>The absolute risk for first and second class passengers dying is <strong>48.2 %<\/strong><\/p>\n\n\n\n<p>The odds for third class passengers dying is <strong>3.08<\/strong><\/p>\n\n\n\n<p>The odds for first and second class passengers dying is <strong>0.93<\/strong><\/p>\n\n\n\n<p>The odds ratio is <strong>0.3 ; 95% confidence interval: 0.24 &#8211; 0.38<\/strong><\/p>\n\n\n\n<p>The package epiR<sup class='sup-ref-note' id='note-zotero-ref-p429-r3-o1'><a class='sup-ref-note' href='#zotero-ref-p429-r3'>3<\/a><\/sup> should be <a href=\"https:\/\/pcool.dyndns.org\/index.php\/packages\/\">installed<\/a>.<\/p>\n\n\n\n<pre class=\"wp-block-code has-small-font-size\"><code><code><span style=\"color: #ff0000;\"><em>summary(epi.tests(mat))<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 est\u00a0\u00a0\u00a0\u00a0\u00a0 lower\u00a0\u00a0\u00a0\u00a0\u00a0 upper<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>aprev\u00a0\u00a0\u00a0\u00a0 0.4637462\u00a0 0.4366131\u00a0 0.4910407<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>tprev\u00a0\u00a0\u00a0\u00a0 0.6283988\u00a0 0.6017300\u00a0 0.6544962<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>se\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.3557692\u00a0 0.3231978\u00a0 0.3893667<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>sp\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.3536585\u00a0 0.3113859\u00a0 0.3977019<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>diag.acc\u00a0 0.3549849\u00a0 0.3291785\u00a0 0.3814368<\/em><\/span>\n<strong><span style=\"color: #0000ff;\"><em>diag.or\u00a0\u00a0 0.3021684\u00a0 0.2393570\u00a0 0.3814626<\/em><\/span><\/strong>\n<span style=\"color: #0000ff;\"><em>nnd\u00a0\u00a0\u00a0\u00a0\u00a0 -3.4414851 -4.6963489 -2.7366048<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>youden\u00a0\u00a0 -0.2905722 -0.3654163 -0.2129314<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>ppv\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.4820847\u00a0 0.4419150\u00a0 0.5224274<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>npv\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.2450704\u00a0 0.2138415\u00a0 0.2784340<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>plr\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.5504354\u00a0 0.4919185\u00a0 0.6159133<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>nlr\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1.8216180\u00a0 1.6000518\u00a0 2.0738655<\/em><\/span><\/code><\/code><\/pre>\n\n\n\n<ol start=\"9\" class=\"wp-block-list\">\n<li>First construct a two by two table:<\/li>\n<\/ol>\n\n\n\n<table id=\"tablepress-32\" class=\"tablepress tablepress-id-32\">\n<thead>\n<tr class=\"row-1\">\n\t<td class=\"column-1\"><\/td><th class=\"column-2\">Prostate Cancer<\/th><th class=\"column-3\">Control<\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"row-striping row-hover\">\n<tr class=\"row-2\">\n\t<td class=\"column-1\">Bald<\/td><td class=\"column-2\">46<\/td><td class=\"column-3\">72<\/td>\n<\/tr>\n<tr class=\"row-3\">\n\t<td class=\"column-1\">Hairy<\/td><td class=\"column-2\">103<\/td><td class=\"column-3\">53<\/td>\n<\/tr>\n<tr class=\"row-4\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">149<\/td><td class=\"column-3\">125<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-32 from cache -->\n\n\n<pre class=\"wp-block-code has-small-font-size\"><code><code><span style=\"color: #ff0000;\"><em>library(epiR)<\/em><\/span>\n<span style=\"color: #ff0000;\"><em>mat&lt;-matrix(c(46,103,72,53),ncol=2)<\/em><\/span>\n<span style=\"color: #ff0000;\"><em>mat<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>\u00a0\u00a0\u00a0\u00a0 &#091;,1] &#091;,2]<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>&#091;1,]\u00a0\u00a0 46\u00a0\u00a0 72<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>&#091;2,]\u00a0 103\u00a0\u00a0 53<\/em><\/span>\n<em><span style=\"color: #ff0000;\">epi.2by2(mat)<\/span><\/em>\n<em><span style=\"color: #0000ff;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Outcome +\u00a0\u00a0\u00a0 Outcome -\u00a0\u00a0\u00a0\u00a0\u00a0 Total\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Inc risk *\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Odds<\/span><\/em>\n<em><span style=\"color: #0000ff;\">Exposed +\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 46\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 72\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 118\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 39.0\u00a0\u00a0\u00a0<strong>\u00a0\u00a0\u00a0 0.639<\/strong><\/span><\/em>\n<em><span style=\"color: #0000ff;\">Exposed -\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 103\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 53\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 156\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 66.0\u00a0\u00a0\u00a0\u00a0<strong>\u00a0\u00a0 1.943<\/strong><\/span><\/em>\n<em><span style=\"color: #0000ff;\">Total\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0149\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 125\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 274\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 54.4\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1.192<\/span><\/em><\/code>\n<code><em><span style=\"color: #0000ff;\">Point estimates and 95 % CIs:<\/span><\/em>\n<em><span style=\"color: #0000ff;\">---------------------------------------------------------<\/span><\/em>\n<em><span style=\"color: #0000ff;\">Inc risk ratio\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.59 (0.46, 0.76)<\/span><\/em>\n<em><span style=\"color: #0000ff;\">Odds ratio\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<strong> 0.33 (0.19, 0.56)<\/strong><\/span><\/em>\n<em><span style=\"color: #0000ff;\">Attrib risk *\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -27.04 (-38.56, -15.52)<\/span><\/em>\n<em><span style=\"color: #0000ff;\">Attrib risk in population *\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -11.65 (-21.13, -2.16)<\/span><\/em>\n<em><span style=\"color: #0000ff;\">Attrib fraction in exposed (%)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -69.37 (-117.96, -31.61)<\/span><\/em>\n<em><span style=\"color: #0000ff;\">Attrib fraction in population (%)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -21.42 (-31.94, -11.73)<\/span><\/em>\n<em><span style=\"color: #0000ff;\">---------------------------------------------------------<\/span><\/em>\n<em><span style=\"color: #0000ff;\">\u00a0* Cases per 100 population units<\/span><\/em><\/code><\/code><\/pre>\n\n\n\n<p>The odds of developing prostate cancer for bald patients is <strong>0.639<\/strong><\/p>\n\n\n\n<p>The odds of developing prostate cancer for hairy patients is <strong>1.943<\/strong><\/p>\n\n\n\n<p>The odds ratio is <strong>0.33 ; 95% confidence interval: 0.2 &#8211; 0.54<\/strong><\/p>\n\n\n\n<p>The package epiR<sup class='sup-ref-note' id='note-zotero-ref-p429-r4-o1'><a class='sup-ref-note' href='#zotero-ref-p429-r4'>4<\/a><\/sup> should be <a href=\"https:\/\/pcool.dyndns.org\/index.php\/packages\/\">installed<\/a>.<\/p>\n\n\n\n<pre class=\"wp-block-code has-small-font-size\"><code><code><em><span style=\"color: #ff0000;\">summary(epi.tests(mat))<\/span><\/em>\n<span style=\"color: #0000ff;\"><em>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 est\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 lower\u00a0\u00a0\u00a0\u00a0\u00a0 upper<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>aprev\u00a0\u00a0\u00a0\u00a0 0.4306569\u00a0\u00a0 0.3712342\u00a0 0.4915959<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>tprev\u00a0\u00a0\u00a0\u00a0 0.5437956\u00a0\u00a0 0.4827946\u00a0 0.6038392<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>se\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.3087248\u00a0\u00a0 0.2356959\u00a0 0.3895415<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>sp\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.4240000\u00a0\u00a0 0.3361237\u00a0 0.5155619<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>diag.acc\u00a0 0.3613139\u00a0\u00a0 0.3043858\u00a0 0.4212781<\/em><\/span>\n<span style=\"color: #0000ff;\"><em><strong>diag.or\u00a0\u00a0 0.3287487\u00a0\u00a0 0.2000696\u00a0 0.5401904<\/strong><\/em><\/span>\n<span style=\"color: #0000ff;\"><em>nnd\u00a0\u00a0\u00a0\u00a0\u00a0 -3.7414624 -10.5377855 -2.3354642<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>youden\u00a0\u00a0 -0.2672752\u00a0 -0.4281804 -0.0948966<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>ppv\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.3898305\u00a0\u00a0 0.3014051\u00a0 0.4839246<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>npv\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.3397436\u00a0\u00a0 0.2659238\u00a0 0.4197827<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>plr\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.5359806\u00a0\u00a0 0.4036857\u00a0 0.7116308<\/em><\/span>\n<span style=\"color: #0000ff;\"><em>nlr\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1.6303660\u00a0\u00a0 1.2943610\u00a0 2.0535949<\/em><\/span><\/code><\/code><\/pre>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>1000 + 200 \u2013 75 = 1125 patients with osteosarcoma. So: In the R console : The package epiR should be installed. Or a summary: The absolute risk for men dying is 80 % The absolute risk for women and children dying is 31.5 % The odds for men dying is 4.009 The odds for [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-429","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/pages\/429","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/comments?post=429"}],"version-history":[{"count":60,"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/pages\/429\/revisions"}],"predecessor-version":[{"id":4349,"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/pages\/429\/revisions\/4349"}],"wp:attachment":[{"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/media?parent=429"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}