97 lines
2.8 KiB
Python
97 lines
2.8 KiB
Python
# Authors: The MNE-Python contributors.
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# License: BSD-3-Clause
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# Copyright the MNE-Python contributors.
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import numpy as np
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def _ecdf(x):
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"""No frills empirical cdf used in fdrcorrection."""
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nobs = len(x)
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return np.arange(1, nobs + 1) / float(nobs)
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def fdr_correction(pvals, alpha=0.05, method="indep"):
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"""P-value correction with False Discovery Rate (FDR).
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Correction for multiple comparison using FDR :footcite:`GenoveseEtAl2002`.
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This covers Benjamini/Hochberg for independent or positively correlated and
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Benjamini/Yekutieli for general or negatively correlated tests.
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Parameters
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----------
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pvals : array_like
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Set of p-values of the individual tests.
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alpha : float
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Error rate.
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method : 'indep' | 'negcorr'
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If 'indep' it implements Benjamini/Hochberg for independent or if
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'negcorr' it corresponds to Benjamini/Yekutieli.
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Returns
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-------
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reject : array, bool
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True if a hypothesis is rejected, False if not.
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pval_corrected : array
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P-values adjusted for multiple hypothesis testing to limit FDR.
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References
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----------
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.. footbibliography::
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"""
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pvals = np.asarray(pvals)
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shape_init = pvals.shape
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pvals = pvals.ravel()
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pvals_sortind = np.argsort(pvals)
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pvals_sorted = pvals[pvals_sortind]
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sortrevind = pvals_sortind.argsort()
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if method in ["i", "indep", "p", "poscorr"]:
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ecdffactor = _ecdf(pvals_sorted)
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elif method in ["n", "negcorr"]:
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cm = np.sum(1.0 / np.arange(1, len(pvals_sorted) + 1))
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ecdffactor = _ecdf(pvals_sorted) / cm
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else:
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raise ValueError("Method should be 'indep' and 'negcorr'")
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reject = pvals_sorted < (ecdffactor * alpha)
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if reject.any():
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rejectmax = max(np.nonzero(reject)[0])
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else:
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rejectmax = 0
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reject[:rejectmax] = True
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pvals_corrected_raw = pvals_sorted / ecdffactor
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pvals_corrected = np.minimum.accumulate(pvals_corrected_raw[::-1])[::-1]
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pvals_corrected[pvals_corrected > 1.0] = 1.0
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pvals_corrected = pvals_corrected[sortrevind].reshape(shape_init)
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reject = reject[sortrevind].reshape(shape_init)
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return reject, pvals_corrected
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def bonferroni_correction(pval, alpha=0.05):
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"""P-value correction with Bonferroni method.
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Parameters
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----------
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pval : array_like
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Set of p-values of the individual tests.
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alpha : float
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Error rate.
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Returns
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-------
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reject : array, bool
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True if a hypothesis is rejected, False if not.
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pval_corrected : array
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P-values adjusted for multiple hypothesis testing to limit FDR.
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"""
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pval = np.asarray(pval)
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pval_corrected = pval * float(pval.size)
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# p-values must not be larger than 1.
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pval_corrected = pval_corrected.clip(max=1.0)
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reject = pval_corrected < alpha
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return reject, pval_corrected
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