Question:

The aim of a case-control study is to investigate the association between probiotic yogurt intake before and during pregnancy and gestational diabetes mellitus (GDM) in women age >18 during their 24 to 28 weeks of a singleton pregnancy. The investigators obtain a history of probiotic yogurt intake between cases and controls. Results of the study are shown below.

Probiotic yogurt intake during pregnancy	GDM +	GDM −	Total
Low	82	60	142
High	41	66	107
Total	123	126	249

Which of the following best represents the odds of high probiotic yogurt intake in women with GDM compared to women without GDM?

0.17

0.45

0.66

1.51

2.20

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Explanation:

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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 single 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)

In this study, the disease of interest is gestational diabetes mellitus (GDM), so cases are women with GDM, and controls are women without GDM. The exposure of interest is probiotic yogurt intake before or during pregnancy. More specifically, the OR of interest is the odds of high intake of yogurt in cases (ie, women with GDM) relative to the odds of high intake of yogurt in controls (ie, women without GDM).

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)

The given table is incorrectly formatted (ie, high intake should be in the first row rather than in the second row of exposure status), so it is necessary to reformat the table.

Probiotic yogurt intake during pregnancy	GDM +	GDM −	Total
High	41	66	107
	(a)	(b)	107
Low	82	60	142
	(c)	(d)	142
Total	123	126	249

The odds of high intake of yogurt in women with GDM and women without GDM are:

Odds of high intake of yogurt in cases: a/c = 41/82 = 0.50
Odds of high intake of yogurt in controls: b/d = 66/60 = 1.10

Therefore, the OR is:

OR = (odds of exposure in cases) / (odds of exposure in controls) = (a/c) / (b/d) = 0.50 / 1.10 = 0.45

The OR is <1: this indicates that a high intake of probiotic yogurt during pregnancy has a protective effect against GDM.

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 correctly formatted contingency table: OR = (ad) / (bc).