{"id":12669,"date":"2019-06-12T12:15:19","date_gmt":"2019-06-12T10:15:19","guid":{"rendered":"http:\/\/www.wjst.de\/blog\/?p=12669"},"modified":"2026-07-15T19:03:42","modified_gmt":"2026-07-15T17:03:42","slug":"how-to-interpret-an-odds-ratio-of-less-than-1","status":"publish","type":"post","link":"https:\/\/www.wjst.de\/blog\/sciencesurf\/2019\/06\/how-to-interpret-an-odds-ratio-of-less-than-1\/","title":{"rendered":"How to interpret an odds ratio of less than 1"},"content":{"rendered":"

In a recent paper \u00a0(see page 122<\/a> ) I have read that an odds ratio OR of 0.7 means a 30% risk reduction which is wrong.<\/p>\n

The OR is a measure of association not a risk ratio (which requires random sampling of the population and a slightly different formula).<\/p>\n

Let’s have a look on the following table to see why this is all wrong<\/p>\n\n\n\n\n\t\n\n\t\n\t
<\/td>Disease+<\/th>Disease-<\/th>\n<\/tr>\n<\/thead>\n
Exposure+<\/td>a=7<\/td>b=10<\/td>\n<\/tr>\n
Exposure-<\/td>c=10<\/td>d=10<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n

The odds of an event is the number of those who experience the event divided by the number of those who do not.<\/p>\n

Comparing the odds in an exposed and a not exposed group results in the simple odds ratio OR formula.<\/p>\n

\r\nOR = (a\/b) \/ (c\/d)\r\n<\/pre>\n
But the odds is not the risk. The risk (incidence proportion) of an event is the number who experience it divided by everyone<\/em> in that group – those who do and those who do not.<\/p>\n
Risk for the exposed is 42.7%, for the unexposed 50%.<\/p>\n
\r\n\r\nRR = ( a\/(a+b) \/ c\/c+b) )\r\n\r\n<\/pre>\n
Note the denominators: for the odds it was b<\/em> and d<\/em> (only the disease-free), for the risk it is the whole row (a+b<\/em> and c+d<\/em>). That single change is the whole difference between the two measures.<\/p>\n
The risk ratio is then RR= 0.82 and the risk reduction 18%.<\/p>\n\n
 <\/p>\n
\n  CC-BY-NC Science Surf , accessed 30.07.2026<\/span>\n <\/div>","protected":false},"excerpt":{"rendered":"
In a recent paper \u00a0(see page 122 ) I have read that an odds ratio OR of 0.7 means a 30% risk reduction which is wrong. The OR is a measure of association not a risk ratio (which requires random sampling of the population and a slightly different formula). Let’s have a look on the … Continue reading How to interpret an odds ratio of less than 1<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9],"tags":[],"class_list":["post-12669","post","type-post","status-publish","format-standard","hentry","category-computer-software"],"_links":{"self":[{"href":"https:\/\/www.wjst.de\/blog\/wp-json\/wp\/v2\/posts\/12669","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wjst.de\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wjst.de\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wjst.de\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wjst.de\/blog\/wp-json\/wp\/v2\/comments?post=12669"}],"version-history":[{"count":28,"href":"https:\/\/www.wjst.de\/blog\/wp-json\/wp\/v2\/posts\/12669\/revisions"}],"predecessor-version":[{"id":26569,"href":"https:\/\/www.wjst.de\/blog\/wp-json\/wp\/v2\/posts\/12669\/revisions\/26569"}],"wp:attachment":[{"href":"https:\/\/www.wjst.de\/blog\/wp-json\/wp\/v2\/media?parent=12669"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wjst.de\/blog\/wp-json\/wp\/v2\/categories?post=12669"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wjst.de\/blog\/wp-json\/wp\/v2\/tags?post=12669"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}