# Odds and odds ratio relative odds in order to

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Odds and Odds Ratio (Relative Odds)In order to calculate a relative risk, we must have values for the incidenceof the disease in the exposedand the incidence in the nonexposed. In a case-controlstudy, we cannot calculate incidence in exposed and nonexposed. Case-control study Cases Controls Exposed a b Non- exposed c d Cohort study Disease Not Disease Exposed a b Non- exposed c d
Odds and Odds RatioTherefore, in a case-controlstudy, we cannot calculate the relative risk directly! We have to consider other type of measurement of association in a case-control study. Case-control study Cases Controls Exposed a b Non- exposed c d Cohort study Disease Not Disease Exposed a b Non- exposed c d
Odds and Odds RatioCase-control study Cases Controls Exposed a b Non- exposed c d Cohort study Disease Not Disease Exposed a b Non-exposed c d In a cohort study, we calculate the proportion of the exposed population in whom disease develops and the proportion of the nonexposed population in whom disease develops; In a case-control study, we calculate proportion of the cases who were exposed and the proportion of the controls who were exposed.
Odds The ratio of the number of ways the event can occur to the number of ways the event cannot occur. The probability of event occur: P The probability of event cannot occur: 1-P The odds of occurrence of the event:
The Odds Ratio in Cohort StudiesProbability of developing disease in exposed=a/(a+b) Probability of not developing disease in exposed=b/(a+b) Odds of developing disease in exposed=(a/(a+b))/(b/(a+b))=a/b Cohort study Disease Not Disease Exposed a b Non- exposed c d
The Odds Ratio in Cohort Studies (cont)Probability of developing disease in non exposed=c/(c+d) Probability of not developing disease in non exposed=d/(c+d) Odds of developing disease in Non- exposed=(c/c+d))/(d/(c+d))=c/d Cohort study Disease Not Disease Exposed a b Non- exposed c d
The Odds Ratio in Cohort StudiesOdd ratio in a cohort study is equal to the ratio of the odds that an exposed person develops disease to the odds that a non-exposed person develops disease. Cohort study Disease Not Disease Exposed a b Non- exposed c d
The Odds Ratio in a Case-Control StudyCase-control study Cases Controls Exposed a b Non- exposed c d Proportion of exposed in cases=a/(a+c) (proportion of cases who were exposed) Proportion of non-exposed in cases=c/(a+c) (proportion of cases who were unexposed) Odds of a case was exposed=(a(a+c))/(c/(a+c))=a/c
The Odds Ratio in a Case-Control StudyCase-control study Cases Controls Exposed a b Non- exposed c d Proportion exposed in controls=b/(b+d) (proportion of controls who were exposed) Proportion non-exposed in controls=d/(b+d) (proportion of controls who were exposed) Odds of a control was exposed=(b(b+d))/(d/(b+d))=b/d
The Odds Ratio in a Case-Control StudyOdds ratio in a case-control study is defined as the ratio of the odds that the cases were exposed to the odds that the controls were exposed.
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