Statistical Risk Ratio (Relative Risk) Data Analysis

T. Dhasaratharaman*

Statistician, Kauvery Hospitals, India

*Correspondence: Tel +91 90037 84310    Email [email protected]

The relative risk (or risk ratio) is an intuitive way to compare the risks for the two groups. Simply divide the cumulative incidence in exposed group by the cumulative incidence in the unexposed group:

Risk Ratio= Cle/Clu

where, CIe is the cumulative incidence in the ‘exposed’ group and CIu is the cumulative incidence in the ‘unexposed’ group.

Risk is a relatively intuitive concept that we encounter every day, but interpretation of risk (especially low risk) is often inconsistent.

The risk of death while travelling to the shops to buy a lotto ticket can be higher than the risk of winning the jackpot!

Relative risk is used in “cohort studies”, prospective studies that follow a group (cohort) over a period of time and investigate the effect of a treatment or risk factor.

Interpretation

Risk is the probability that an event will happen. It is calculated by dividing the number of events by the number of people at risk.

One boy is born for every two births, so the probability (risk) of giving birth to a boy is

1⁄2 = 0.5

If one in every 100 patients suffers a side-effect from a treatment, the risk is

1⁄100 = 0.01

Risk ratios are calculated by dividing the risk in the treated or exposed group by the risk in the control or unexposed group.

A risk ratio of one indicates no difference in risk between the groups.

If the risk ratio of an event is >1, the rate of that event is increased compared to controls.

If < 1, the rate of that event is reduced.

Risk ratios are frequently given with their 95% CIs – if the CI for a risk ratio does not include one (no difference in risk), it is statistically significant.

Risk ratio < 1

It is also possible for the risk ratio to be less than 1; this would suggest that the exposure being considered is associated with a reduction in risk. A randomized clinical trial was begun in order to test whether low-dose aspirin was beneficial in reducing myocardial infarctions (heart attacks). The study population consisted of over 22,000 male physicians who were randomly assigned to either low-dose aspirin or a placebo (an identical looking pill that was inert). They followed these physicians for about five years. Some of the data is summarized in the 2 × 2 table shown below.

Treatment Myocardial Infarction No Infarction Total Cumulative Incidence
Aspirin 139 10,898 11,037 139/11,037 = 0.0126
Placebo 239 10,795 11,034 239/11,034 = 0.0217

Risk Ratio = 0.0126/0.0217 = 0.58

Note that the “exposure” of interest was low-dose aspirin, and the aspirin group is summarized in the top row. The group assigned to take aspirin had an incidence of 1.26%, while the placebo (unexposed) group had an incidence of about 2.17%. The cumulative incidence in the aspirin group was divided by the cumulative incidence in the placebo group, and RR = 0.58. An appropriate interpretation of this would be:

Those who take low dose aspirin regularly have 0.58 times the risk of myocardial infarction compared to those who do not take aspirin.

Note also that the unexposed (comparison, reference) group must be specified. For example, if we simply said, “Those who take low dose aspirin regularly have 0.58 times the risk of myocardial infarction”, the question is “compared to what?” Is it those who didn’t take any aspirin, those who took low-dose aspirin but used it irregularly, those who took high dose aspirin, those who took acetaminophen…?

In general

  • If the risk ratio is 1 (or close to 1), it suggests no difference or little difference in risk (incidence in each group is the same).
  • A risk ratio > 1 suggests an increased risk of that outcome in the exposed group.
  • A risk ratio < 1 suggests a reduced risk in the exposed group.

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