M/Phqk :dZddlZddlmZgdZdZdddd d d d d dddd Zgdddgddgddgddgddggdgddd ggd!d"gg ZiZ eD]+Z e de e d<e d#dD] Z e de e <, d1d&Z d2d(Z d3d*Z d4d.ZGd/d0ZdS)5zQMultiple Testing and P-Value Correction Author: Josef Perktold License: BSD-3 N) RegressionFDR) fdrcorrectionfdrcorrection_twostage local_fdr multipletestsNullDistributionrcpt|}tjd|dzt|z S)z2no frills empirical cdf used in fdrcorrection )lennparangefloat)xnobss [/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/stats/multitest.py_ecdfrs0 q66D 9QtAv  uT{{ ** BonferroniSidakHolmz Holm-SidakzSimes-HochbergHommelzFDR Benjamini-HochbergzFDR Benjamini-YekutielizFDR 2-stage Benjamini-Hochbergz'FDR 2-stage Benjamini-Krieger-Yekutieliz&FDR adaptive Gavrilov-Benjamini-Sarkar) bshhsshhofdr_bhfdr_byfdr_tsbh fdr_tsbkyfdr_gbsrbonf bonferronirsidakrholmr holm-sidakrsimes-hochbergrhommelrfdr_ifdr_pfdrifdrprfdr_nfdr_cfdrnfdrcorrr fdr_2sbhr! fdr_2sbky fdr_twostager"r 皙?Fc  ddl}tj|}|}|s)tj|}tj||}t |} dtjd|z d| z z } |t| z } |dvr|| k} |t| z} nO|dvr3|| k} tj | tj | z } n|dvrdtjd|z dtj | ddz z }||k}~tj |d}|j dkrt |}ntj|}d ||d<|} ~tj tj | ddtj | z }tj|} ~n|d vr||tj | ddz k}tj |d}|j dkrt |}ntj|}d ||d<|} |tj | ddz}tj|} ~|n-|d vr|tj | ddz }||k} tj | }|dj dkr-tjtj | }d | d|<tj | dd|z}tj|dddddd} ~nY|d vr|}t+| ddD]}tj||| dztj d|dzz }tj|| d||| d<tj|d| tj||d| z||d| <|} ||k} nq|d vrt-||dd \} } nC|dvrt-||dd \} } n|dvr t/||d|d dd\} } n|dvr t/||d|d dd\} } n|dvrtj d| dz}| dz|z |z |zd|z z }tj|}tj|dddddd} ~| |k} nt1d| d| | dk<|s|r| | | | fStj| }| ||<~ tj| }| ||<||| | fS)aI Test results and p-value correction for multiple tests Parameters ---------- pvals : array_like, 1-d uncorrected p-values. Must be 1-dimensional. alpha : float FWER, family-wise error rate, e.g. 0.1 method : str Method used for testing and adjustment of pvalues. Can be either the full name or initial letters. Available methods are: - `bonferroni` : one-step correction - `sidak` : one-step correction - `holm-sidak` : step down method using Sidak adjustments - `holm` : step-down method using Bonferroni adjustments - `simes-hochberg` : step-up method (independent) - `hommel` : closed method based on Simes tests (non-negative) - `fdr_bh` : Benjamini/Hochberg (non-negative) - `fdr_by` : Benjamini/Yekutieli (negative) - `fdr_tsbh` : two stage fdr correction (non-negative) - `fdr_tsbky` : two stage fdr correction (non-negative) maxiter : int or bool Maximum number of iterations for two-stage fdr, `fdr_tsbh` and `fdr_tsbky`. It is ignored by all other methods. maxiter=1 (default) corresponds to the two stage method. maxiter=-1 corresponds to full iterations which is maxiter=len(pvals). maxiter=0 uses only a single stage fdr correction using a 'bh' or 'bky' prior fraction of assumed true hypotheses. is_sorted : bool If False (default), the p_values will be sorted, but the corrected pvalues are in the original order. If True, then it assumed that the pvalues are already sorted in ascending order. returnsorted : bool not tested, return sorted p-values instead of original sequence Returns ------- reject : ndarray, boolean true for hypothesis that can be rejected for given alpha pvals_corrected : ndarray p-values corrected for multiple tests alphacSidak : float corrected alpha for Sidak method alphacBonf : float corrected alpha for Bonferroni method Notes ----- There may be API changes for this function in the future. Except for 'fdr_twostage', the p-value correction is independent of the alpha specified as argument. In these cases the corrected p-values can also be compared with a different alpha. In the case of 'fdr_twostage', the corrected p-values are specific to the given alpha, see ``fdrcorrection_twostage``. The 'fdr_gbs' procedure is not verified against another package, p-values are derived from scratch and are not derived in the reference. In Monte Carlo experiments the method worked correctly and maintained the false discovery rate. All procedures that are included, control FWER or FDR in the independent case, and most are robust in the positively correlated case. `fdr_gbs`: high power, fdr control for independent case and only small violation in positively correlated case **Timing**: Most of the time with large arrays is spent in `argsort`. When we want to calculate the p-value for several methods, then it is more efficient to presort the pvalues, and put the results back into the original order outside of the function. Method='hommel' is very slow for large arrays, since it requires the evaluation of n partitions, where n is the number of p-values. rNr ?r#)rr&)rr(T)rr')rr))rr*r+indepalphamethod is_sortedr0nr6bky)r?r@maxiterrA)r r5bh)r"zmethod not recognized)gcr asarrayargsorttaker powerrlowerexpm1log1pr nonzerosizeminmaximum accumulatecollectmaxminimumcopyrangerr ValueError empty_like)pvalsr?r@rDrA returnsortedrGalphafsortindntests alphacSidak alphacBonfrejectpvals_correctedalphacSidak_all notrejectnr_index notrejectminpvals_corrected_rawalphashrejind rejectmaxamcimiiqpvals_corrected_reject_s rrr?shIII Ju  E F (*U##w'' ZZFbhV bi888K%--'J ||~~444*$%--/ > ) )+%8FRXuf-=-=$=>>> / / /bhV ')")FAr*B*B'BDDDO+ :i((+ =A  u::LL6(++L#' ,--   "x &!R(@(@(*%(8(8)9 : ::*//0CDD   = ( (FRYvq"%=%=== :i((+ =A  u::LL6(++L#' ,-- #bi2&>&>>*//0CDD  3 3 329VQ333'!F## !9>A  rz&1122I!%F:I:  i266>*//0CDDbD0IJJ44R4P   + + + JJLLvq"%% I IA&UA233Z")Aad*;*;;<3(G(GHHAcrcFFf G G G"/U8?;?#A#A#A J J J"/U8;;?#A#A#A E E E"8e@EAHCG#I#I#IJL!#M 3 3 3"8e@DAHCG#I#I#IJL!#M ; & &Yq&1* % % b[2 r !E )R%Z 8 j33A66*//0CDDbD0IJJ44R4P  E)0111"-.)*BLB Z??=99$3! -''!(+zAArr=c (tj|}|jdks Jd|s*tj|}tj||}n|}|dvrt |}n`|dvrMtjdtjdt|dzz }t ||z }ntd|||zk}| r.ttj |d} d|d | <||z } tj | d d d d d d } ~ d| | dk<|s7tj| } | | |<~ tj|} || |<| | fS|| fS) a pvalue correction for false discovery rate. This covers Benjamini/Hochberg for independent or positively correlated and Benjamini/Yekutieli for general or negatively correlated tests. Parameters ---------- pvals : array_like, 1d Set of p-values of the individual tests. alpha : float, optional Family-wise error rate. Defaults to ``0.05``. method : {'i', 'indep', 'p', 'poscorr', 'n', 'negcorr'}, optional Which method to use for FDR correction. ``{'i', 'indep', 'p', 'poscorr'}`` all refer to ``fdr_bh`` (Benjamini/Hochberg for independent or positively correlated tests). ``{'n', 'negcorr'}`` both refer to ``fdr_by`` (Benjamini/Yekutieli for general or negatively correlated tests). Defaults to ``'indep'``. is_sorted : bool, optional If False (default), the p_values will be sorted, but the corrected pvalues are in the original order. If True, then it assumed that the pvalues are already sorted in ascending order. Returns ------- rejected : ndarray, bool True if a hypothesis is rejected, False if not pvalue-corrected : ndarray pvalues adjusted for multiple hypothesis testing to limit FDR Notes ----- If there is prior information on the fraction of true hypothesis, then alpha should be set to ``alpha * m/m_0`` where m is the number of tests, given by the p-values, and m_0 is an estimate of the true hypothesis. (see Benjamini, Krieger and Yekuteli) The two-step method of Benjamini, Krieger and Yekutiel that estimates the number of false hypotheses will be available (soon). Both methods exposed via this function (Benjamini/Hochberg, Benjamini/Yekutieli) are also available in the function ``multipletests``, as ``method="fdr_bh"`` and ``method="fdr_by"``, respectively. See also -------- multipletests r z2pvals must be 1-dimensional, that is of shape (n,))ir=pposcorr)rBnegcorrr;z"only indep and negcorr implementedrTNr<)r rHndimrIrJrsumr r rYanyrUrOrVrSrZ)r[r?r@rA pvals_sortind pvals_sorted ecdffactorcmrbrkrhrcrqrrs rrrsf Ju  E :???P???  5)) wum44   ///<(( # # # VBryC $5$5a$7888 9 9<((2- =>>> Z- -F zz||" 6**1-.. !z z&3j++,?",EFFtttLO)*OOA%& '=99*9' -''!' (((&&rrCctj|}|!ddl}d}||t|durd}n|dus|dvrt |}|s)tj|}tj||}t |} |dkr d |z} || z } n|d krd } |} ntd | g} t|| d d \} }| }|dks|| kr | }|| z}|}n|x}}| }t|D]y}d | z|z }| | z|z }| |t||d d \} }| }||dz ks||krn||krtd|}z||d z| z z}|dkr|d |zz}d||dk<|sz oops - should not be here)r rHwarningswarn FutureWarningr rIrJrYrryrXappend RuntimeErrorrZ)r[r?r@rDiterrArmsgr{r_fact alpha_prime alpha_stagesrej pvalscorrr1rbriri_oldntests0it alpha_star pvalscorr_s rrrrs^ Ju  E H c=))) u}} J..e** . 5)) }-- ZZF 5dl 4 FGGG=L"5 G-1333NC B aR6\\T ..  BFlV+G$v-7J    + + +*5 759;;;NCBgk!!bFllf"#?@@@FF Ws]f,, U?? "u* %IIik 9]9-- $- =! s## #}z6B; <<Iv{L88rr;cddlm}ddlm}ddlm}t |} t |} tj| | |} tj || d} | dd| ddzdz } tj | |dz}| d}|d k}|dd|fxx||zcc<|tj d| z| j}|dkr7|| || d|| }n4|| ||  | }tj ||dz}|dd|fxx||zcc<||t%|| d| dz zz }|=tjd |dzztjdtjzz }n ||}||z|z }tj|dd}|S)a+ Calculate local FDR values for a list of Z-scores. Parameters ---------- zscores : array_like A vector of Z-scores null_proportion : float The assumed proportion of true null hypotheses null_pdf : function mapping reals to positive reals The density of null Z-scores; if None, use standard normal deg : int The maximum exponent in the polynomial expansion of the density of non-null Z-scores nbins : int The number of bins for estimating the marginal density of Z-scores. alpha : float Use Poisson ridge regression with parameter alpha to estimate the density of non-null Z-scores. Returns ------- fdr : array_like A vector of FDR values References ---------- B Efron (2008). Microarrays, Empirical Bayes, and the Two-Groups Model. Statistical Science 23:1, 1-22. Examples -------- Basic use (the null Z-scores are taken to be standard normal): >>> from statsmodels.stats.multitest import local_fdr >>> import numpy as np >>> zscores = np.random.randn(30) >>> fdr = local_fdr(zscores) Use a Gaussian null distribution estimated from the data: >>> null = EmpiricalNull(zscores) >>> fdr = local_fdr(zscores, null_pdf=null.pdf) r)GLM)families)OLSNr<r rEg:0yE>)family)L1_wtr? start_params)r)+statsmodels.genmod.generalized_linear_modelrr#statsmodels.regression.linear_modelrrQrUr linspace histogramvanderstdlogfitparamsPoissonfit_regularizedpredictr expsqrtpiclip)zscoresnull_proportionnull_pdfdegnbinsr?rrrminzmaxzbinszhistzbinsdmatsdrostartmd dmat_fullfzf0fdrs rrr sx`@?????DDDDDD777777 w<.xformsDBDB bza VF2J''a' 5Ar { 3 334T> !r)normc |\}}} |z |z  |z |z z }||z} tj|z z tjd|z zz}|z |z }|tj|dz dz  tj|zz z }| tj|zz}| S)a] Negative log-likelihood of z-scores. The function has three arguments, packed into a vector: mean : location parameter logscale : log of the scale parameter logitprop : logit of the proportion of true nulls The implementation follows section 4 from Efron 2008. r rE)cdfr rry)rdrru central_masscprvalzvn_zsn_zs0rnull_lbnull_ubrzscores0s rfunz&NullDistribution.__init__..funseFmmGAq!!HHgkQ%677 HHgkQ%6778L\!B26"::%B(GGDQ,!#B BFBE6A:&&):: :D EBF<000 0D5Lr)minimize)rrz Nelder-Mead)r@r) r flatnonzeror rscipy.stats.distributionsrscipy.optimizerr_rrr)selfrrrrrrrorrmzrrrrrrrrs ````` @@@@@r__init__zNullDistribution.__init__s>^W/Gw4FG H H r77a<<MNN N2;'llCMM e " " " " " " "& 322222           D ,+++++ Xc25?= A A Ar#wb$ #rc||jz |jz }tjd|dzztj|jz dtjdtjzzz S)a\ Evaluates the fitted empirical null Z-score density. Parameters ---------- zscores : scalar or array_like The point or points at which the density is to be evaluated. Returns ------- The empirical null Z-score density evaluated at the given points. rrEg?)rrr rrr)rrzvals rpdfzNullDistribution.pdfsV $)#tw.vd47lRVDG__4s26!BE'??7JJKKKrN)r<r TTF)__name__ __module__ __qualname____doc__rrrrrrpsV..`FJ?DM$M$M$M$bLLLLLrr)r9rr FF)r9r=F)r9rCr NF)r;Nrrr)rnumpyr statsmodels.stats._knockoffr__all__rmultitest_methods_names _alias_listmultitest_aliasrmrlrrrrrrrrrs 555555 A A A+++ !- ' &!-!1!)%=%>'G(Q&N  +**W~V}l#&'h;;;>>>J'999{   ""AaDOAaD qrrU""qT"-1!$VBVBVBVBrW'W'W'W't6;#$ $%*V9V9V9V9r@AbbbbJSLSLSLSLSLSLSLSLSLSLr