Risk Ratios and Odds Ratiosfwhat Are They?

ARTICLE IN PRESS

Midwifery (2004) 20, 169–170

www.elsevier.com/locate/midw Risk ratios and odds ratiosFwhat are they?

Malcolm Campbell, BA (Hons) (Mathematics), MSc (Statistics), PhD (Statistics) (Lecturer in Statistics)

School of Nursing, Midwifery & Health Visiting, University of Manchester, Coupland III Building, Oxford Road, Manchester M13 9PL, UK

Downe et al. (2004) use relative risk How do you interpret probabilities, odds, ratios and odds ratios. What are they? relative risk and relative odds?

A risk ratio (sometimes called relative risk, both Probability takes values on a scale from 0 to 1, abbreviated to RR) and an odds ratio (OR) are ways where 0 is impossible, 0.5 is as likely as not, and 1 is of expressing a comparison between two propor- certain. The others take values from 0 to positive tions. For example, in this paper, there are two inﬁnity, where 1 has a special meaning. An odds of 1 randomised groups in the trial, women in the means that the event has the same chance of lateral position and women in the supported sitting occurring as not occurring (the probability of the position in the passive second stage of labour. The event is 0.5), while a risk ratio or odds ratio of 1 authors wanted to compare the proportions of means that in the two groups being compared, the instrumental births, episiotomies and perineal event has the same chance of occurring. Staying suturing in the two groups to see if there was any with our example of the event as ‘having an effect due to maternal position. A risk ratio gives instrumental delivery’, a risk ratio or odds ratio the relative probability or chance of something of 1 for the lateral group compared with the sitting happening in one group compared with the other, group would have meant that instrumental delivery while an odds ratio gives the relative odds. Do you was equally likely in the two groups (or equiva- know what the difference is between probability lently the groups would have the same proportion and odds? of instrumental deliveries). You could think of risk ratios and odds ratios as measures of clinical effect, Is probability an uncertainty and are odds a value of 1 indicating no intervention effect or no what you see at a bookmaker’s? difference between the groups.

Sort of. Probability or risk can be deﬁned as the So what about values in this study then? number of times some event happens divided by the total number of times it either does or does not Have a look at Table 3. In the lateral group, there happen. Odds are the number of times the event were 16 instrumental and 33 spontaneous births; in happens divided by the number of times it does not the sitting group, there were 30 and 28, respec- happen. If the event is ‘having an instrumental tively. So the probability or risk of an instrumental delivery’, the probability of an instrumental deliv- birth in the lateral group is 16/49, while that in the ery is the number of instrumental deliveries divided sitting group is 30/58. The risk ratio of instrumental by the total number of deliveries, while the odds of birth for the sitting group compared with the an instrumental delivery are the number of instru- lateral group as a reference group is the ratio of mental deliveries divided by the number of non- the two probabilities, 30/58 divided by 16/49, instrumental deliveries. Most people ﬁnd probabil- which is 1.58. This means that women in the sitting ity easier to understand but gamblers may think group are more than one and a half as likely as more naturally in odds. those in the lateral group to have an instrumental delivery. The odds of an instrumental birth for the E-mail address: [email protected] (M. Campbell). lateral group are 16/33, while those for the sitting

170 M. Campbell group are 30/28. The odds ratio for the sitting associated with instrumental birth. So the authors group compared with the lateral group is 30/28 fitted logistic regression models to predict whether divided by 16/33, or 2.20. This means that for a birth was instrumental or spontaneous from such women in the sitting group compared with women confounding variables together with position in the in the lateral group, the odds of an instrumental passive second stage of labour. These models birth are more than twice as high. allowed the authors to estimate an odds ratio for position adjusted for the confounding variables. Just a minuteFthe paper gives the risk ratio They found that the odds ratio of 2.2 for sitting of instrumental birth for the lateral group compared with lateral rose to 2.3 when adjusted compared with the sitting group as 0.63. for the other variables. Where did that come from? Where can I find out more about risk ratios Yes, it might be a little confusing as they are using and odds ratios? the sitting group as the reference group, but it has the same meaning. This risk ratio is the probability Simon’s website (STATSFSTeve’s Attempt to Teach of instrumental birth in the lateral group, 16/49, Statistics) shows how they are calculated and divided by the probability in the sitting group, 30/ interpreted with examples at 58, which is 0.63 (and this is just 1 over the risk http://www.childrensmercy.org/stats/definitions/ ratio for sitting compared with lateral). Women in or.htm (accessed 5 February 2004), while Kirkwood the lateral group are just under two-thirds as likely and Sterne (2003, pp. 148–164) give a highly as women in the sitting group to have an instru- detailed and readable description. mental delivery.

I think I can grasp the meaning of a risk ratio. Acknowledgements Why do we need odds ratios as well? I would like to thank an anonymous statistical Although odds ratios may seem harder to interpret, reviewer for helpful comments. they can be used in more complicated analyses to allow for the behaviour of other variables. As the authors point out, while the position of the women References may affect whether a birth is instrumental, so too might factors such as position of the fetal head at Downe, S., Gerret, D., Renfrew, M., 2004. A prospective trial on the diagnosis of full dilation, the use of oxytocin the effect of position in the passive second stage of labour on birth outcome in nulliparous women using epidural analgesia. during labour, or maternal BMI. If these factors Midwifery 20 (2), 157–168. differ between the groups, they may inﬂuence the Kirkwood, B.R., Sterne, J.A.C., 2003. Essential Medical Statistics observed probabilities, risk ratios and odds ratios 2nd Edition. Blackwell Science, Oxford.