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import operator
from dataclasses import dataclass
import numpy as np
from scipy.special import ndtri
from ._common import ConfidenceInterval
def _validate_int(n, bound, name):
msg = f'{name} must be an integer not less than {bound}, but got {n!r}'
try:
n = operator.index(n)
except TypeError:
raise TypeError(msg) from None
if n < bound:
raise ValueError(msg)
return n
@dataclass
class RelativeRiskResult:
"""
Result of `scipy.stats.contingency.relative_risk`.
Attributes
----------
relative_risk : float
This is::
(exposed_cases/exposed_total) / (control_cases/control_total)
exposed_cases : int
The number of "cases" (i.e. occurrence of disease or other event
of interest) among the sample of "exposed" individuals.
exposed_total : int
The total number of "exposed" individuals in the sample.
control_cases : int
The number of "cases" among the sample of "control" or non-exposed
individuals.
control_total : int
The total number of "control" individuals in the sample.
Methods
-------
confidence_interval :
Compute the confidence interval for the relative risk estimate.
"""
relative_risk: float
exposed_cases: int
exposed_total: int
control_cases: int
control_total: int
def confidence_interval(self, confidence_level=0.95):
"""
Compute the confidence interval for the relative risk.
The confidence interval is computed using the Katz method
(i.e. "Method C" of [1]_; see also [2]_, section 3.1.2).
Parameters
----------
confidence_level : float, optional
The confidence level to use for the confidence interval.
Default is 0.95.
Returns
-------
ci : ConfidenceInterval instance
The return value is an object with attributes ``low`` and
``high`` that hold the confidence interval.
References
----------
.. [1] D. Katz, J. Baptista, S. P. Azen and M. C. Pike, "Obtaining
confidence intervals for the risk ratio in cohort studies",
Biometrics, 34, 469-474 (1978).
.. [2] Hardeo Sahai and Anwer Khurshid, Statistics in Epidemiology,
CRC Press LLC, Boca Raton, FL, USA (1996).
Examples
--------
>>> from scipy.stats.contingency import relative_risk
>>> result = relative_risk(exposed_cases=10, exposed_total=75,
... control_cases=12, control_total=225)
>>> result.relative_risk
2.5
>>> result.confidence_interval()
ConfidenceInterval(low=1.1261564003469628, high=5.549850800541033)
"""
if not 0 <= confidence_level <= 1:
raise ValueError('confidence_level must be in the interval '
'[0, 1].')
# Handle edge cases where either exposed_cases or control_cases
# is zero. We follow the convention of the R function riskratio
# from the epitools library.
if self.exposed_cases == 0 and self.control_cases == 0:
# relative risk is nan.
return ConfidenceInterval(low=np.nan, high=np.nan)
elif self.exposed_cases == 0:
# relative risk is 0.
return ConfidenceInterval(low=0.0, high=np.nan)
elif self.control_cases == 0:
# relative risk is inf
return ConfidenceInterval(low=np.nan, high=np.inf)
alpha = 1 - confidence_level
z = ndtri(1 - alpha/2)
rr = self.relative_risk
# Estimate of the variance of log(rr) is
# var(log(rr)) = 1/exposed_cases - 1/exposed_total +
# 1/control_cases - 1/control_total
# and the standard error is the square root of that.
se = np.sqrt(1/self.exposed_cases - 1/self.exposed_total +
1/self.control_cases - 1/self.control_total)
delta = z*se
katz_lo = rr*np.exp(-delta)
katz_hi = rr*np.exp(delta)
return ConfidenceInterval(low=katz_lo, high=katz_hi)
def relative_risk(exposed_cases, exposed_total, control_cases, control_total):
"""
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_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.
See Also
--------
odds_ratio
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)
.. versionadded:: 1.7.0
References
----------
.. [1] Alan Agresti, An Introduction to Categorical Data Analysis
(second edition), Wiley, Hoboken, NJ, USA (2007).
.. [2] Hardeo Sahai and Anwer Khurshid, Statistics in Epidemiology,
CRC Press LLC, Boca Raton, FL, USA (1996).
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.
"""
# Relative risk is a trivial calculation. The nontrivial part is in the
# `confidence_interval` method of the RelativeRiskResult class.
exposed_cases = _validate_int(exposed_cases, 0, "exposed_cases")
exposed_total = _validate_int(exposed_total, 1, "exposed_total")
control_cases = _validate_int(control_cases, 0, "control_cases")
control_total = _validate_int(control_total, 1, "control_total")
if exposed_cases > exposed_total:
raise ValueError('exposed_cases must not exceed exposed_total.')
if control_cases > control_total:
raise ValueError('control_cases must not exceed control_total.')
if exposed_cases == 0 and control_cases == 0:
# relative risk is 0/0.
rr = np.nan
elif exposed_cases == 0:
# relative risk is 0/nonzero
rr = 0.0
elif control_cases == 0:
# relative risk is nonzero/0.
rr = np.inf
else:
p1 = exposed_cases / exposed_total
p2 = control_cases / control_total
rr = p1 / p2
return RelativeRiskResult(relative_risk=rr,
exposed_cases=exposed_cases,
exposed_total=exposed_total,
control_cases=control_cases,
control_total=control_total)
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