scipy.stats.contingency.relative_risk(exposed_cases, exposed_total, control_cases, control_total)[source]

Compute the relative risk (also known as the risk ratio).

This function computes the relative risk associated with a 2x2 contingency table ([1], section 2.2.3; [2], section 3.1.2). Instead of accepting a table as an argument, the individual numbers that are used to compute the relative risk are given as separate parameters. This is to avoid the ambiguity of which row or column of the contingency table corresponds to the “exposed” cases and which corresponds to the “control” cases. Unlike, say, the odds ratio, the relative risk is not invariant under an interchange of the rows or columns.

exposed_casesnonnegative int

The number of “cases” (i.e. occurrence of disease or other event of interest) among the sample of “exposed” individuals.

exposed_totalpositive int

The total number of “exposed” individuals in the sample.

control_casesnonnegative int

The number of “cases” among the sample of “control” or non-exposed individuals.

control_totalpositive int

The total number of “control” individuals in the sample.

resultinstance of RelativeRiskResult

The object has the float attribute relative_risk, which is:

rr = (exposed_cases/exposed_total) / (control_cases/control_total)

The object also has the method confidence_interval to compute the confidence interval of the relative risk for a given confidence level.


The R package epitools has the function riskratio, which accepts a table with the following layout:

                disease=0   disease=1
exposed=0 (ref)    n00         n01
exposed=1          n10         n11

With a 2x2 table in the above format, the estimate of the CI is computed by riskratio when the argument method=”wald” is given, or with the function riskratio.wald.

For example, in a test of the incidence of lung cancer among a sample of smokers and nonsmokers, the “exposed” category would correspond to “is a smoker” and the “disease” category would correspond to “has or had lung cancer”.

To pass the same data to relative_risk, use:

relative_risk(n11, n10 + n11, n01, n00 + n01)

New in version 1.7.0.



Alan Agresti, An Introduction to Categorical Data Analysis (second edition), Wiley, Hoboken, NJ, USA (2007).


Hardeo Sahai and Anwer Khurshid, Statistics in Epidemiology, CRC Press LLC, Boca Raton, FL, USA (1996).


>>> from scipy.stats.contingency import relative_risk

This example is from Example 3.1 of [2]. The results of a heart disease study are summarized in the following table:

         High CAT   Low CAT    Total
         --------   -------    -----
CHD         27         44        71
No CHD      95        443       538

Total      122        487       609

CHD is coronary heart disease, and CAT refers to the level of circulating catecholamine. CAT is the “exposure” variable, and high CAT is the “exposed” category. So the data from the table to be passed to relative_risk is:

exposed_cases = 27
exposed_total = 122
control_cases = 44
control_total = 487
>>> result = relative_risk(27, 122, 44, 487)
>>> result.relative_risk

Find the confidence interval for the relative risk.

>>> result.confidence_interval(confidence_level=0.95)
ConfidenceInterval(low=1.5836990926700116, high=3.7886786315466354)

The interval does not contain 1, so the data supports the statement that high CAT is associated with greater risk of CHD.