labs.utils.reproducibility_measures

Module: labs.utils.reproducibility_measures

Functions for computing reproducibility measures.

General procedure is:

• dataset is subject to jacknife subampling (‘splitting’),

• each subsample being analysed independently,

• a reproducibility measure is then derived;

It is used to produce the work described in Analysis of a large fMRI cohort:

Statistical and methodological issues for group analyses. Thirion B, Pinel P, Meriaux S, Roche A, Dehaene S, Poline JB. Neuroimage. 2007 Mar;35(1):105-20.

Bertrand Thirion, 2009-2010

Functions

nipy.labs.utils.reproducibility_measures.bootstrap_group(nsubj, ngroups)

Split the proposed group into redundant subgroups by bootstrap

Parameters

nsubj (int) the number of subjects in the population

ngroups(int) Number of subbgroups to be drawn

Returns

samples: a list of ngroups arrays containing

the indexes of the subjects in each subgroup

nipy.labs.utils.reproducibility_measures.cluster_reproducibility(data, vardata, domain, ngroups, sigma, method='crfx', swap=False, verbose=0, **kwargs)

Returns a measure of cluster-level reproducibility of activation patterns (i.e. how far clusters are from each other)

Parameters

data: array of shape (nvox,nsubj)

the input data from which everything is computed

vardata: array of shape (nvox,nsubj)

the variance of the data that is also available

domain: referential- and domain- defining image instance

ngroups (int),

Number of subbgroups to be drawn

sigma (float): parameter that encodes how far far is

threshold (float):

binarization threshold

method=’crfx’, string to be chosen among ‘crfx’, ‘cmfx’ or ‘cffx’

inference method under study

swap = False: if True, a random sign swap of the data is performed

This is used to simulate a null hypothesis on the data.

verbose=0 : verbosity mode

Returns

score (float): the desired cluster-level reproducibility index

nipy.labs.utils.reproducibility_measures.cluster_threshold(stat_map, domain, th, csize)

Perform a thresholding of a map at the cluster-level

Parameters

stat_map: array of shape(nbvox)

the input data

domain: Nifti1Image instance,

referential- and domain-defining image

th (float): cluster-forming threshold

csize (int>0): cluster size threshold

Returns

binary array of shape (nvox): the binarized thresholded map

Notes

Should be replaced by a more standard function in the future

nipy.labs.utils.reproducibility_measures.conjunction(x, vx, k)

Returns a conjunction statistic as the sum of the k lowest t-values

Parameters

x: array of shape(nrows, ncols),

effect matrix

vx: array of shape(nrows, ncols),

variance matrix

k: int,

number of subjects in the conjunction

Returns

t array of shape(nrows): conjunction statistic

nipy.labs.utils.reproducibility_measures.coord_bsa(domain, betas, theta=3.0, dmax=5.0, ths=0, thq=0.5, smin=0, afname=None)

main function for performing bsa on a dataset where bsa = nipy.labs.spatial_models.bayesian_structural_analysis

Parameters

domain: image instance,

referential- and domain-defining image

betas: array of shape (nbnodes, subjects),

the multi-subject statistical maps

theta: float, optional

first level threshold

dmax: float>0, optional

expected cluster std in the common space in units of coord

ths: int, >=0), optional

representatitivity threshold

thq: float, optional,

posterior significance threshold should be in [0,1]

smin: int, optional,

minimal size of the regions to validate them

afname: string, optional

path where intermediate results cam be pickled

Returns

afcoord array of shape(number_of_regions,3):

coordinate of the found landmark regions

nipy.labs.utils.reproducibility_measures.draw_samples(nsubj, ngroups, split_method='default')

Draw randomly ngroups sets of samples from [0..nsubj-1]

Parameters

nsubj, int, the total number of items

ngroups, int, the number of desired groups

split_method: string, optional,

to be chosen among ‘default’, ‘bootstrap’, ‘jacknife’ if ‘bootstrap’, then each group will be nsubj

drawn with repetitions among nsubj

if ‘jacknife’ the population is divided into

ngroups disjoint equally-sized subgroups

if ‘default’, ‘bootstrap’ is used when nsubj < 10 * ngroups

otherwise jacknife is used

Returns

samples, a list of ngroups array that represent the subsets.

fixme : this should allow variable bootstrap,

i.e. draw ngroups of groupsize among nsubj

nipy.labs.utils.reproducibility_measures.fttest(x, vx)

Assuming that x and vx represent a effect and variance estimates, returns a cumulated (‘fixed effects’) t-test of the data over each row

Parameters

x: array of shape(nrows, ncols): effect matrix

vx: array of shape(nrows, ncols): variance matrix

Returns

t array of shape(nrows): fixed effect statistics array

nipy.labs.utils.reproducibility_measures.get_cluster_position_from_thresholded_map(stat_map, domain, thr=3.0, csize=10)

the clusters above thr of size greater than csize in 18-connectivity are computed

Parameters

stat_map : array of shape (nbvox),

map to threshold

mask: Nifti1Image instance,

referential- and domain-defining image

thr: float, optional,

cluster-forming threshold

cisze=10: int

cluster size threshold

Returns

positions array of shape(k,anat_dim):

the cluster positions in physical coordinates where k= number of clusters if no such cluster exists, None is returned

nipy.labs.utils.reproducibility_measures.get_peak_position_from_thresholded_map(stat_map, domain, threshold)

The peaks above thr in 18-connectivity are computed

Parameters

stat_map: array of shape (nbvox): map to threshold

deomain: referential- and domain-defining image

thr, float: cluster-forming threshold

Returns

positions array of shape(k,anat_dim):

the cluster positions in physical coordinates where k= number of clusters if no such cluster exists, None is returned

nipy.labs.utils.reproducibility_measures.group_reproducibility_metrics(mask_images, contrast_images, variance_images, thresholds, ngroups, method, cluster_threshold=10, number_of_samples=10, sigma=6.0, do_clusters=True, do_voxels=True, do_peaks=True, swap=False)

Main function to perform reproducibility analysis, including nifti1 io

Parameters

threshold: list or 1-d array,

the thresholds to be tested

Returns

cluster_rep_results: dictionary,

results of cluster-level reproducibility analysis

voxel_rep_results: dictionary,

results of voxel-level reproducibility analysis

peak_rep_results: dictionary,

results of peak-level reproducibility analysis

nipy.labs.utils.reproducibility_measures.histo_repro(h)

Given the histogram h, compute a standardized reproducibility measure

Parameters

h array of shape(xmax+1), the histogram values

Returns

hr, float: the measure

nipy.labs.utils.reproducibility_measures.map_reproducibility(data, vardata, domain, ngroups, method='crfx', swap=False, verbose=0, **kwargs)

Return a reproducibility map for the given method

Parameters

data: array of shape (nvox,nsubj)

the input data from which everything is computed

vardata: array of the same size

the corresponding variance information

domain: referential- and domain-defining image

ngroups (int): the size of each subrgoup to be studied

threshold (float): binarization threshold

(makes sense only if method==rfx)

method=’crfx’, string to be chosen among ‘crfx’, ‘cmfx’, ‘cffx’

inference method under study

verbose=0 : verbosity mode

Returns

rmap: array of shape(nvox)

the reproducibility map

nipy.labs.utils.reproducibility_measures.mfx_ttest(x, vx)

Idem fttest, but returns a mixed-effects statistic

Parameters

x: array of shape(nrows, ncols): effect matrix

vx: array of shape(nrows, ncols): variance matrix

Returns

t array of shape(nrows): mixed effect statistics array

nipy.labs.utils.reproducibility_measures.peak_reproducibility(data, vardata, domain, ngroups, sigma, method='crfx', swap=False, verbose=0, **kwargs)

Return a measure of cluster-level reproducibility of activation patterns (i.e. how far clusters are from each other)

Parameters

data: array of shape (nvox,nsubj)

the input data from which everything is computed

vardata: array of shape (nvox,nsubj)

the variance of the data that is also available

domain: referential- and domain-defining image

ngroups (int),

Number of subbgroups to be drawn

sigma: float, parameter that encodes how far far is

threshold: float, binarization threshold

method: string to be chosen among ‘crfx’, ‘cmfx’ or ‘cffx’,

inference method under study

swap = False: if True, a random sign swap of the data is performed

This is used to simulate a null hypothesis on the data.

verbose=0 : verbosity mode

Returns

score (float): the desired cluster-level reproducibility index

nipy.labs.utils.reproducibility_measures.split_group(nsubj, ngroups)

Split the proposed group into random disjoint subgroups

Parameters

nsubj (int) the number of subjects to be split

ngroups(int) Number of subbgroups to be drawn

Returns

samples: a list of ngroups arrays containing

the indexes of the subjects in each subgroup

nipy.labs.utils.reproducibility_measures.statistics_from_position(target, data, sigma=1.0)

Return a number characterizing how close data is from target using a kernel-based statistic

Parameters

target: array of shape(nt,anat_dim) or None

the target positions

data: array of shape(nd,anat_dim) or None

the data position

sigma=1.0 (float), kernel parameter

or a distance that say how good good is

Returns

sensitivity (float): how well the targets are fitted

by the data in [0,1] interval 1 is good 0 is bad

nipy.labs.utils.reproducibility_measures.ttest(x)

Returns the t-test for each row of the data x

nipy.labs.utils.reproducibility_measures.voxel_reproducibility(data, vardata, domain, ngroups, method='crfx', swap=False, verbose=0, **kwargs)

return a measure of voxel-level reproducibility of activation patterns

Parameters

data: array of shape (nvox,nsubj)

the input data from which everything is computed

vardata: array of shape (nvox,nsubj)

the corresponding variance information ngroups (int): Number of subbgroups to be drawn

domain: referential- and domain-defining image

ngourps: int,

number of groups to be used in the resampling procedure

method: string, to be chosen among ‘crfx’, ‘cmfx’, ‘cffx’

inference method under study

verbose: bool, verbosity mode

Returns

kappa (float): the desired reproducibility index

nipy.labs.utils.reproducibility_measures.voxel_thresholded_ttest(x, threshold)

Returns a binary map of the ttest>threshold