`scipy.stats._relative_risk:relative_risk`

source: /scipy/stats/_relative_risk.py :125

Signature

   def     relative_risk (    exposed_cases    ,    exposed_total    ,    control_cases    ,    control_total      )

Summary

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

Extended Summary

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.

Parameters

exposed_cases : nonnegative int: The number of "cases" (i.e. occurrence of disease or other event of interest) among the sample of "exposed" individuals.
exposed_total : positive int: The total number of "exposed" individuals in the sample.
control_cases : nonnegative int: The number of "cases" among the sample of "control" or non-exposed individuals.
control_total : positive int: The total number of "control" individuals in the sample.

Returns

result : instance of `~scipy.stats._result_classes.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.

Notes

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)

Examples

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)

✗

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

Aliases

scipy.stats._relative_risk.relative_risk