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## EVIDENCE-BASED-HEALTH@JISCMAIL.AC.UK

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Re: odds ratios

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Date:

Thu, 2 Aug 2001 11:27:37 +0100

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 ```On 02-Aug-01 Julie Clark wrote: > Dear colleagues, > I was wondering if you could help answer > what is probably a simple question. I have figures on newly acquired > HIV infection for a certain time period and also whether they have > high ( 19 cases ) or low risk partners (90 cases) . How should I > calculate a relationship between how much more likely you were to > acquire HIV infection through low risk as opposed to high risk partners > during this time period ? In the past odds ratios have been used, but > this has been queried. If odds-ratios have been queried, for data of that kind, it is likely to be on the following grounds (if other, please write back and let us know). The data you have is of the form: GIVEN an infected person, the probability that the person has a high-risk partner can be estimated as   P(HR | I) = 19/(90+19). Similarly   P(LR | I) = 90/109 The question you are asking is: GIVEN that a person has a high-risk/low-risk partner, what is the ratio of the probabilities of infection given the riskiness of the partner, and you can't get that from your data without knowing proportions of high and low risk partners in the population (including non-infecteds). Let HR and LR high and low risk partner, Let I denote infection, then what you're looking for is P(I | HR) / P(I | LR) = ( P(I & HR) / P(HR) ) / ( P(I & LR) / P(LR) ) = ( P(HR | I) * P(I) / P(HR) ) / ( P(LR | I) * P(I) / P(LR) ) = ( P(HR | I) * P(LR) ) / ( P(LR | I) * P(HR) ) Your data give you P(HR | I) and P(LR | I), but you can't complete the calculation until you have P(HR) and P(LR) as well; and it seems you don't. So I guess the answer to your question "How should I ..." is "You shouldn't". Not without supplementary data. Ted. -------------------------------------------------------------------- E-Mail: (Ted Harding) <[log in to unmask]> Fax-to-email: +44 (0)870 167 1972 Date: 02-Aug-01 Time: 11:27:37 ------------------------------ XFMail ------------------------------ ```