Relative risks versus odds ratios

Researchers investigated the effectiveness of a probiotic drink containing Lactobacillus for the prevention of any diarrhoea associated with antibiotic use in hospital. A randomised double blind placebo controlled trial study design was used. The intervention consisted of the probiotic drink twice a day during a course of antibiotics and for one week afterwards. The control group received a placebo drink consisting of a longlife sterile milkshake. The primary outcome was the occurrence of antibiotic associated diarrhoea during follow-up.1

Participants were hospital patients aged over 50 years. In total, 135 patients were recruited to the trial and randomised to the intervention (n=69) or placebo (n=66). Twelve patients receiving the intervention and 10 in the placebo group did not complete their treatment protocol or were lost to follow-up. A smaller proportion of the probiotic group developed diarrhoea associated with antibiotic use compared with the placebo group (7 (12%) v 19 (34%); relative risk 0.36, 95% confidence interval 017 to 0.79). When adjusted using logistic regression to control for other factors, the effects of the probiotic drink in reducing antibiotic associated diarrhoea remained (odds ratio 0.25, 95% CI 0.07 to 0.85). The researchers concluded that consumption of the probiotic drink reduced the incidence of antibiotic associated diarrhoea.

Which of the following statements, if any, are true?

• a) It was possible to estimate the population at risk

• b) It was not possible to derive an adjusted relative risk

• c) The odds ratio is an estimate of the population relative risk

• d) The odds ratio is a measure …