For a case-control study designed to investigate a possible association between endometriosis and systemic lupus erythematosus (SLE), 1,040 women with SLE and 1,260 women without SLE are selected. The investigators inquire about a history of endometriosis in both groups of women. Among women with SLE, 240 had a history of endometriosis; among women without SLE, 210 had a history of endometriosis. Which of the following is the estimated odds ratio of endometriosis in women with SLE compared to women without SLE?

Question

For a case-control study designed to investigate a possible association between endometriosis and systemic lupus erythematosus (SLE), 1,040 women with SLE and 1,260 women without SLE are selected.  The investigators inquire about a history of endometriosis in both groups of women.  Among women with SLE, 240 had a history of endometriosis; among women without SLE, 210 had a history of endometriosis.  Which of the following is the estimated odds ratio of endometriosis in women with SLE compared to women without SLE?

Quizplus · Accepted Answer

The odds of an event are related to the probability P of that event, with odds = P / (1 − P). For example, the probability of rolling a die and getting a 1 is 1/6, but the odds of rolling a 1 is 1/5. The odds ratio (OR) is a measure of association used in case-control studies to compare the odds of exposure in cases (ie, individuals with disease) relative to controls (ie, individuals without disease): OR = (odds of exposure in cases) / (odds of exposure in controls) A shortcut to calculate the OR when a contingency table has a standard format (ie, exposure of interest in the first row of exposure status and cases in the first column of disease status) is the following: OR = (a/c) / (b/d) In this study, the disease of interest is systemic lupus erythematosus (SLE), so cases are women with SLE, and controls are women without SLE. The exposure of interest is a history of endometriosis. Given that 240 of 1,040 women with SLE had a history of endometriosis, 1,040 − 240 = 800 of women with SLE had no history of endometriosis. Given that 210 of 1,260 without SLE had a history of endometriosis, 1,260 − 210 = 1,050 of women without SLE had no history of endometriosis. Based on these data, the standard contingency table is as follows: 11ec160b_3710_7749_9249_f7d106cb7d07_MD0001_00 The odds of endometriosis in women with SLE and women without SLE are: Odds of endometriosis in cases: a/c = 240/800 = 0.3 Odds of endometriosis in controls: b/d = 210/1,050 = 0.2 Therefore, the OR of endometriosis in women with SLE compared to women without SLE is: OR = (odds of endometriosis in cases) / (odds of endometriosis in controls) = (a/c) / (b/d) = 0.3/0.2 = 1.5 The estimated OR = 1.5 is >1 (ie, the null value for the OR); this indicates that a history of endometriosis acts as a risk factor for SLE. This example calculated the OR of exposure (ie, odds of exposure among cases relative to controls). The OR is sometimes described as the odds of disease among exposed individuals relative to nonexposed individuals, given by (a/b) / (c/d). Both OR definitions are mathematically equivalent and reduce to OR = (ad) / (bc). Educational objective: The odds ratio (OR) is a measure of association calculated as: OR = (odds of exposure in cases) / (odds of exposure in controls). For a contingency table in the standard format: OR = (ad) / (bc).

For a Case-Control Study Designed to Investigate a Possible Association