84 lines
2.7 KiB
Python
84 lines
2.7 KiB
Python
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"""
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Created on Mar 30, 2022 1:21:54 PM
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Author: Josef Perktold
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License: BSD-3
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"""
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import numpy as np
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from numpy.testing import assert_allclose
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def _mover_confint(stat1, stat2, ci1, ci2, contrast="diff"):
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"""
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References
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----------
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.. [#] Krishnamoorthy, K., Jie Peng, and Dan Zhang. 2016. “Modified Large
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Sample Confidence Intervals for Poisson Distributions: Ratio, Weighted
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Average, and Product of Means.” Communications in Statistics - Theory
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and Methods 45 (1): 83–97. https://doi.org/10.1080/03610926.2013.821486.
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.. [#] Li, Yanhong, John J. Koval, Allan Donner, and G. Y. Zou. 2010.
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“Interval Estimation for the Area under the Receiver Operating
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Characteristic Curve When Data Are Subject to Error.” Statistics in
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Medicine 29 (24): 2521–31. https://doi.org/10.1002/sim.4015.
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.. [#] Zou, G. Y., and A. Donner. 2008. “Construction of Confidence Limits
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about Effect Measures: A General Approach.” Statistics in Medicine 27
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(10): 1693–1702. https://doi.org/10.1002/sim.3095.
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"""
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if contrast == "diff":
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stat = stat1 - stat2
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low_half = np.sqrt((stat1 - ci1[0])**2 + (stat2 - ci2[1])**2)
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upp_half = np.sqrt((stat1 - ci1[1])**2 + (stat2 - ci2[0])**2)
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ci = (stat - low_half, stat + upp_half)
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elif contrast == "sum":
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stat = stat1 + stat2
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low_half = np.sqrt((stat1 - ci1[0])**2 + (stat2 - ci2[0])**2)
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upp_half = np.sqrt((stat1 - ci1[1])**2 + (stat2 - ci2[1])**2)
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ci = (stat - low_half, stat + upp_half)
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elif contrast == "ratio":
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# stat = stat1 / stat2
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prod = stat1 * stat2
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term1 = stat2**2 - (ci2[1] - stat2)**2
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term2 = stat2**2 - (ci2[0] - stat2)**2
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low_ = (prod -
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np.sqrt(prod**2 - term1 * (stat1**2 - (ci1[0] - stat1)**2))
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) / term1
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upp_ = (prod +
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np.sqrt(prod**2 - term2 * (stat1**2 - (ci1[1] - stat1)**2))
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) / term2
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# method 2 Li, Tang, Wong 2014
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low1, upp1 = ci1
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low2, upp2 = ci2
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term1 = upp2 * (2 * stat2 - upp2)
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term2 = low2 * (2 * stat2 - low2)
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low = (prod -
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np.sqrt(prod**2 - term1 * low1 * (2 * stat1 - low1))
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) / term1
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upp = (prod +
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np.sqrt(prod**2 - term2 * upp1 * (2 * stat1 - upp1))
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) / term2
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assert_allclose((low_, upp_), (low, upp), atol=1e-15, rtol=1e-10)
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ci = (low, upp)
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return ci
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def _mover_confint_sum(stat, ci):
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stat_ = stat.sum(0)
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low_half = np.sqrt(np.sum((stat_ - ci[0])**2))
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upp_half = np.sqrt(np.sum((stat_ - ci[1])**2))
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ci = (stat - low_half, stat + upp_half)
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return ci
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