scipy.stats.contingency.relative_risk#
- 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.
- Parameters:
- 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.
- Returns:
- 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.
- resultinstance of
See also
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)
New in version 1.7.0.
References
[1]Alan Agresti, An Introduction to Categorical Data Analysis (second edition), Wiley, Hoboken, NJ, USA (2007).
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 2.4495156482861398
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.