In order to quantify the association between the exposure and the outcome of interest the incidence of disease in a group of individuals exposed to the supposed risk factor must be compared with the incidence in a group of persons not exposed. This comparison can be summarized by calculating either the ratio of the measures of disease occurrence for the two groups, which indicates the likelihood of developing the disease in the exposed individuals relative to those unexposed.In case-control studies, it is not possible to directly estimate disease incidence in those exposed and those unexposed, since people are selected on the basis of having or not having the condition of interest, not on the basis of their exposure status. It is however, possible to calculate the odds of exposure in the cases and in the controls.The odds ratio (OR) estimates the magnitude of association between the exposure and outcome. It is defined as the ratio of odds of an event occurring in one group to the odds of it occurring in another group, or to a sample-based estimate of that ratio. These groups might be an experimental group and control group.The 2x2 contingency table showing the relationship between the exposure and the disease is presented as follows:
Probability of being exposed among cases=a/(a+c)Probability of being non-exposed among cases=c/(a+c)Odds of being exposed among cases=a/cProbability of being exposed among controls=b/(b+d)Probability of being non-exposed among controls=d/(b+d)Odds of being exposed among controls=b/dOdds ratio = (odds of being exposed among cases)/ (odds of being exposed among controls)= (a/c)/ (b/d)= (a*d)/ (b*c)
In strict terms, the odds ratio obtained tells us how many more (or less, if the exposure is associated with a reduced risk) times likely the cases are to have been exposed to the factor under study compared with the controls.
In strict terms, the odds ratio obtained tells us how many more (or less, if the exposure is associated with a reduced risk) times likely the cases are to have been exposed to the factor under study compared with the controls.
If odds ratio is equal to 1 then this implies that the condition or event under study is equally likely in both groups. An odds ratio greater than 1 indicates that the condition or event is more likely in the first group. An odds ratio less than 1 indicate that the condition or event is less likely in the first group. The odds ratio can vary from zero to infinity.
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