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Measures of association as used to address therapy, harm, and aetiology questions
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1. Stuart Carney, MB, ChB, MPH, MRCPsych1,
2. Helen Doll, BSc, Dip App Stats, MSc2
1. 1Department of Psychiatry, University of Oxford, Oxford, UK
2. 2Department of Public Health, University of Oxford, Oxford, UK

## WHAT ARE MEASURES OF ASSOCIATION?

Measures of association describe the strength of the relationship between an exposure (or intervention) and an outcome in clinical studies (randomised controlled trials [RCTs], cohort studies, and case control studies). There are 2 types of measures: relative (relative risk, relative risk reduction, odds ratios) and absolute (absolute risk reduction, number needed to treat).

Confidence intervals (CI) should be given for each measure of association to quantify their uncertainty and are usually reported as 95% CI (ie, the interval has a 95% chance of including the true, but unknown, population value). If the 95% CI overlaps the value of no effect (see below), the result is not statistically significant at the 5% level (p<0.05). The use of p values and CIs to measure statistical uncertainty will be considered in a future statistics note.

The identification of a statistically significant association between an exposure and an outcome alone does not imply causation. Possible bias and consistency need to be considered.1–3 When addressing therapy, harm, or aetiology questions, a systematic review of ⩾2 double blind RCTs typically provides more convincing evidence than an individual RCT, which again provides more convincing evidence than an individual cohort or case control study.

## WHEN ARE THEY USED?

All of the absolute and relative measures of association described above can be used in RCTs and cohort studies. In case control studies, however, only odds ratios should be calculated because in such a study the prevalence of the outcome (eg, a disease) is not known as the groups are determined by outcome rather than exposure status.

## HOW ARE THEY CALCULATED?

The most common measures are calculated below using the results from probably the earliest RCT, which evaluated the role of streptomycin in the treatment of tuberculosis (TB):4

### Q: What proportion died on streptomycin?

• 4 out of 55 or 7.3%.

• This percentage is called the experimental event risk (EER).

### Q: What proportion died on placebo?

• 14 out of 52 or 26.9%.

• This percentage is called the control event risk (CER).

• Some authors call the EER and CER “rates” instead of risks, which is technically inaccurate as rates describe the number of events per person time.

## ABSOLUTE RISK REDUCTION (ARR)

### Q: What was the difference in risk of death between the two groups?

• 6% (95% CI 5.7% to 33.6%) more people died on placebo compared with streptomycin. This result is statistically significant at the 5% level because the 95% CI does not overlap the value of no effect (ARR  =  0%).

• This is called the absolute risk reduction (ARR) and is calculated by subtracting the EER from the CER.

• When positive outcomes are considered (eg, survival), and the intervention is more helpful than the control, this is called the absolute benefit increase (ABI).

## NUMBER NEEDED TO TREAT (NNT)

### Q: How many people with TB would I need to treat with streptomycin to prevent 1 additional death

• 6 (95% CI 3 to 18) patients with TB would need to be treated with streptomycin to prevent 1 additional person dying. This result is statistically significant at the 5% level because the 95% CI does not overlap the value of no effect (NNT  =  infinity when ARR  =  0%). The word “additional” is used to stress the fact that not everybody died on placebo.

• This measure is called the number needed to treat (NNT). The NNT is usually rounded up to the nearest whole number to provide a more conservative estimate of the added value of the intervention.

• The NNT is the reciprocal of the ARR.

• A negative NNT is also known as the number needed to harm (NNH).

## RELATIVE RISK (RR)

### Q: What was the risk of dying on streptomycin relative to placebo?

• The bar graph shows that for every 1 patient who died on streptomycin, approximately 4 patients died on placebo (27/7).

• This is called the relative risk (RR). The RR compares the risk of death in the intervention group (EER) with the risk of death in the control group (CER).

• The relative risk of dying on streptomycin compared with placebo was 0.27 (95% CI 0.10 to 0.77). This result is statistically significant at the 5% level because the 95% CI does not overlap the value of no effect (RR  =  1).

## RELATIVE RISK REDUCTION (RRR)

### Q: How much less common was death on streptomycin compared with placebo?

• Treatment with streptomycin was associated with a 73% (95% CI 23% to 90%) reduction in the risk of death compared with placebo. In other words, antibiotic treatment prevented approximately three quarters of the deaths that would have occurred on placebo. This result is statistically significant at the 5% level because the 95% CI does not overlap the value of no effect (RRR  =  0%).

• This is called the relative risk reduction (RRR) and is commonly used in promotional literature distributed by pharmaceutical companies.

• The RRR can be calculated by either dividing the ARR by the CER or subtracting the RR from 1.

• When positive outcomes are considered and the intervention is more helpful than the control, this is called the relative benefit increase (RBI).

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