265 lines
9.3 KiB
Python
265 lines
9.3 KiB
Python
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import operator
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from dataclasses import dataclass
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import numpy as np
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from scipy.special import ndtri
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from ._common import ConfidenceInterval
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def _validate_int(n, bound, name):
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msg = f'{name} must be an integer not less than {bound}, but got {n!r}'
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try:
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n = operator.index(n)
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except TypeError:
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raise TypeError(msg) from None
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if n < bound:
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raise ValueError(msg)
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return n
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@dataclass
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class RelativeRiskResult:
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"""
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Result of `scipy.stats.contingency.relative_risk`.
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Attributes
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----------
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relative_risk : float
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This is::
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(exposed_cases/exposed_total) / (control_cases/control_total)
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exposed_cases : int
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The number of "cases" (i.e. occurrence of disease or other event
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of interest) among the sample of "exposed" individuals.
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exposed_total : int
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The total number of "exposed" individuals in the sample.
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control_cases : int
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The number of "cases" among the sample of "control" or non-exposed
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individuals.
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control_total : int
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The total number of "control" individuals in the sample.
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Methods
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-------
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confidence_interval :
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Compute the confidence interval for the relative risk estimate.
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"""
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relative_risk: float
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exposed_cases: int
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exposed_total: int
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control_cases: int
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control_total: int
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def confidence_interval(self, confidence_level=0.95):
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"""
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Compute the confidence interval for the relative risk.
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The confidence interval is computed using the Katz method
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(i.e. "Method C" of [1]_; see also [2]_, section 3.1.2).
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Parameters
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----------
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confidence_level : float, optional
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The confidence level to use for the confidence interval.
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Default is 0.95.
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Returns
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-------
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ci : ConfidenceInterval instance
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The return value is an object with attributes ``low`` and
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``high`` that hold the confidence interval.
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References
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----------
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.. [1] D. Katz, J. Baptista, S. P. Azen and M. C. Pike, "Obtaining
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confidence intervals for the risk ratio in cohort studies",
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Biometrics, 34, 469-474 (1978).
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.. [2] Hardeo Sahai and Anwer Khurshid, Statistics in Epidemiology,
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CRC Press LLC, Boca Raton, FL, USA (1996).
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Examples
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--------
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>>> from scipy.stats.contingency import relative_risk
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>>> result = relative_risk(exposed_cases=10, exposed_total=75,
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... control_cases=12, control_total=225)
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>>> result.relative_risk
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2.5
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>>> result.confidence_interval()
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ConfidenceInterval(low=1.1261564003469628, high=5.549850800541033)
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"""
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if not 0 <= confidence_level <= 1:
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raise ValueError('confidence_level must be in the interval '
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'[0, 1].')
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# Handle edge cases where either exposed_cases or control_cases
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# is zero. We follow the convention of the R function riskratio
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# from the epitools library.
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if self.exposed_cases == 0 and self.control_cases == 0:
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# relative risk is nan.
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return ConfidenceInterval(low=np.nan, high=np.nan)
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elif self.exposed_cases == 0:
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# relative risk is 0.
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return ConfidenceInterval(low=0.0, high=np.nan)
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elif self.control_cases == 0:
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# relative risk is inf
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return ConfidenceInterval(low=np.nan, high=np.inf)
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alpha = 1 - confidence_level
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z = ndtri(1 - alpha/2)
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rr = self.relative_risk
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# Estimate of the variance of log(rr) is
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# var(log(rr)) = 1/exposed_cases - 1/exposed_total +
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# 1/control_cases - 1/control_total
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# and the standard error is the square root of that.
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se = np.sqrt(1/self.exposed_cases - 1/self.exposed_total +
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1/self.control_cases - 1/self.control_total)
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delta = z*se
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katz_lo = rr*np.exp(-delta)
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katz_hi = rr*np.exp(delta)
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return ConfidenceInterval(low=katz_lo, high=katz_hi)
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def relative_risk(exposed_cases, exposed_total, control_cases, control_total):
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"""
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Compute the relative risk (also known as the risk ratio).
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This function computes the relative risk associated with a 2x2
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contingency table ([1]_, section 2.2.3; [2]_, section 3.1.2). Instead
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of accepting a table as an argument, the individual numbers that are
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used to compute the relative risk are given as separate parameters.
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This is to avoid the ambiguity of which row or column of the contingency
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table corresponds to the "exposed" cases and which corresponds to the
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"control" cases. Unlike, say, the odds ratio, the relative risk is not
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invariant under an interchange of the rows or columns.
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Parameters
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----------
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exposed_cases : nonnegative int
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The number of "cases" (i.e. occurrence of disease or other event
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of interest) among the sample of "exposed" individuals.
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exposed_total : positive int
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The total number of "exposed" individuals in the sample.
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control_cases : nonnegative int
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The number of "cases" among the sample of "control" or non-exposed
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individuals.
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control_total : positive int
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The total number of "control" individuals in the sample.
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Returns
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-------
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result : instance of `~scipy.stats._result_classes.RelativeRiskResult`
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The object has the float attribute ``relative_risk``, which is::
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rr = (exposed_cases/exposed_total) / (control_cases/control_total)
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The object also has the method ``confidence_interval`` to compute
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the confidence interval of the relative risk for a given confidence
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level.
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See Also
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--------
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odds_ratio
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Notes
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-----
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The R package epitools has the function `riskratio`, which accepts
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a table with the following layout::
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disease=0 disease=1
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exposed=0 (ref) n00 n01
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exposed=1 n10 n11
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With a 2x2 table in the above format, the estimate of the CI is
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computed by `riskratio` when the argument method="wald" is given,
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or with the function `riskratio.wald`.
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For example, in a test of the incidence of lung cancer among a
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sample of smokers and nonsmokers, the "exposed" category would
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correspond to "is a smoker" and the "disease" category would
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correspond to "has or had lung cancer".
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To pass the same data to ``relative_risk``, use::
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relative_risk(n11, n10 + n11, n01, n00 + n01)
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.. versionadded:: 1.7.0
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References
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----------
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.. [1] Alan Agresti, An Introduction to Categorical Data Analysis
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(second edition), Wiley, Hoboken, NJ, USA (2007).
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.. [2] Hardeo Sahai and Anwer Khurshid, Statistics in Epidemiology,
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CRC Press LLC, Boca Raton, FL, USA (1996).
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Examples
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--------
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>>> from scipy.stats.contingency import relative_risk
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This example is from Example 3.1 of [2]_. The results of a heart
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disease study are summarized in the following table::
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High CAT Low CAT Total
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-------- ------- -----
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CHD 27 44 71
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No CHD 95 443 538
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Total 122 487 609
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CHD is coronary heart disease, and CAT refers to the level of
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circulating catecholamine. CAT is the "exposure" variable, and
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high CAT is the "exposed" category. So the data from the table
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to be passed to ``relative_risk`` is::
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exposed_cases = 27
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exposed_total = 122
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control_cases = 44
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control_total = 487
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>>> result = relative_risk(27, 122, 44, 487)
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>>> result.relative_risk
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2.4495156482861398
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Find the confidence interval for the relative risk.
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>>> result.confidence_interval(confidence_level=0.95)
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ConfidenceInterval(low=1.5836990926700116, high=3.7886786315466354)
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The interval does not contain 1, so the data supports the statement
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that high CAT is associated with greater risk of CHD.
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"""
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# Relative risk is a trivial calculation. The nontrivial part is in the
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# `confidence_interval` method of the RelativeRiskResult class.
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exposed_cases = _validate_int(exposed_cases, 0, "exposed_cases")
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exposed_total = _validate_int(exposed_total, 1, "exposed_total")
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control_cases = _validate_int(control_cases, 0, "control_cases")
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control_total = _validate_int(control_total, 1, "control_total")
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if exposed_cases > exposed_total:
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raise ValueError('exposed_cases must not exceed exposed_total.')
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if control_cases > control_total:
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raise ValueError('control_cases must not exceed control_total.')
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if exposed_cases == 0 and control_cases == 0:
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# relative risk is 0/0.
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rr = np.nan
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elif exposed_cases == 0:
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# relative risk is 0/nonzero
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rr = 0.0
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elif control_cases == 0:
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# relative risk is nonzero/0.
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rr = np.inf
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else:
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p1 = exposed_cases / exposed_total
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p2 = control_cases / control_total
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rr = p1 / p2
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return RelativeRiskResult(relative_risk=rr,
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exposed_cases=exposed_cases,
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exposed_total=exposed_total,
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control_cases=control_cases,
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control_total=control_total)
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