Intended for healthcare professionals

Endgames Statistical Question

# Incidence rate ratio

BMJ 2010; 341 (Published 08 September 2010) Cite this as: BMJ 2010;341:c4804
1. Philip Sedgwick, senior lecturer in medical statistics
1. p.sedgwick{at}sgul.ac.uk

Researchers evaluated whether a community falls prevention service reduced the rate of falls in older people. They used a randomised controlled trial design. Participants were recruited if they were aged over 60 years, had experienced a fall while living at home or in residential care, and an emergency ambulance had been called but had not taken them to hospital. Participants were randomised to the community falls prevention service or standard medical and social care (control treatment).1

The primary outcome was rate of falls in one year of follow-up, as recorded in monthly diaries. Analysis was by intention to treat. After randomisation, 99 participants were offered the community falls prevention service and 102 participants were offered the control treatment. Diaries for the intervention group contributed 88.6 person years and those for the control group contributed 84.5 person years. The incidence rates of falls per year were 3.46 in the intervention group and 7.68 in the control group, with an incidence rate ratio equal to 0.45 (95% confidence interval 0.35 to 0.58).

Which of the following, if any, are true?

• a) Follow-up for all participants ended when they experienced their first fall after recruitment

• b) Participants completed different lengths of follow-up

• c) The intervention reduced the number of falls per year of follow-up compared with the control

• d) The result was statistically significant at the 5% level of significance

b, c, and d are all true; a is false.

The aim was to establish whether the community falls prevention service reduced falls in older people. The primary outcome was rate of falls averaged across treatment groups. It was originally intended that all people would complete monthly diaries for a year regardless of the number of falls experienced (a is false). Participants were still followed even if they had experienced a fall.

For each group, the sum of person years of follow-up was less than the number of participants. Therefore, not all people were followed for a full year (b is true). Not everyone completed all their monthly diaries for a variety of reasons, including withdrawal or death. Because participants were followed for different lengths of time, the opportunity for experiencing falls varied. Therefore, for each group the rate of falls was expressed as an incidence rate. Incidence rates were described in last week’s question.2 For each group, the total number of falls reported by all people was divided by the sum of person years of follow-up, giving the mean number of falls per person year of follow-up. When calculating the incidence rates, no distinction was made between people who provided different lengths of follow-up or experienced different numbers of falls.

The incidence rate ratio provides a relative measure of the effect of the community falls protection service—it was derived as the incidence rate for the intervention divided by the incidence rate for the control. An incidence rate ratio is interpreted in a similar fashion to an odds ratio. People randomised to the community falls prevention service had 0.49 times as many falls per year of follow-up compared with controls (c is true). Therefore, compared with the control treatment, the community falls protection service roughly halved the mean number of falls per year of follow-up. This reduction was across all participants and not for an individual.

Statistical hypothesis testing and the P value have been described in previous questions.3 4 The null and alternative hypotheses were stated before data were collected. The null hypothesis specifies no difference between the groups—that is, that the incidence rate is the same for the intervention and control groups and the incidence rate ratio equals 1.0. The alternative hypothesis specifies that the population incidence rate ratio is less than or greater than unity. The aim was to establish whether the sample data supported the null hypothesis or lent support to the alternative. Traditionally, the null hypothesis is rejected in favour of the alternative if P is less than 0.05.

The 95% confidence interval quantifies the uncertainty of the sample incidence rate ratio as an estimate of the population parameter. The amount of confidence—namely, 95%—indicates how sure we are that the interval will contain the population incidence rate ratio. The relation between the 95% confidence interval for a ratio and the size of the P value for the test of statistical hypotheses was described for a relative risk in a previous question.5 If the 95% confidence interval for the population incidence rate ratio does not include unity, the state of equipoise, then the resulting P value for the associated statistical hypothesis test will be less than 0.05. Therefore, for the above result the null hypothesis would be rejected in favour of the alternative at the 5% level of significance (d is true). Conversely if the 95% confidence interval had not included unity, then P would have been greater than 0.05.

## Notes

Cite this as: BMJ 2010;341:c4804

## Footnotes

• Competing interests: None declared.

## References

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