9.6.2. Second-level fMRI model: true positive proportion in clusters

This script showcases the so-called “All resolution inference” procedure, in which the proportion of true discoveries in arbitrary clusters is estimated. The clusters can be defined from the input image, i.e. in a circular way, as the error control accounts for arbitrary cluster selection.

Rosenblatt JD, Finos L, Weeda WD, Solari A, Goeman JJ. All-Resolutions Inference for brain imaging. Neuroimage. 2018 Nov 1;181:786-796. doi: 10.1016/j.neuroimage.2018.07.060

9.6.2.1. Fetch dataset

We download a list of left vs right button press contrasts from a localizer dataset. Note that we fetch individual t-maps that represent the BOLD activity estimate divided by the uncertainty about this estimate.

from nilearn.datasets import fetch_localizer_contrasts
n_subjects = 16
data = fetch_localizer_contrasts(
    ["left vs right button press"], n_subjects,
    get_tmaps=True, legacy_format=False
)
from nilearn import plotting

9.6.2.2. Estimate second level model

We define the input maps and the design matrix for the second level model and fit it.

import pandas as pd
second_level_input = data['cmaps']
design_matrix = pd.DataFrame([1] * len(second_level_input),
                             columns=['intercept'])

Model specification and fit

from nilearn.glm.second_level import SecondLevelModel
second_level_model = SecondLevelModel(smoothing_fwhm=8.0)
second_level_model = second_level_model.fit(second_level_input,
                                            design_matrix=design_matrix)

To estimate the contrast is very simple. We can just provide the column name of the design matrix.

z_map = second_level_model.compute_contrast(output_type='z_score')

We threshold the second level contrast at uncorrected p < 0.001 and plot

from scipy.stats import norm
p_val = 0.001
p001_uncorrected = norm.isf(p_val)

from nilearn.glm import cluster_level_inference
proportion_true_discoveries_img = cluster_level_inference(
    z_map, threshold=[3, 4, 5], alpha=.05)

plotting.plot_stat_map(
    proportion_true_discoveries_img, threshold=0.,
    display_mode='z', vmax=1, colorbar=True,
    title='group left-right button press, proportion true positives')

plotting.plot_stat_map(
    z_map, threshold=p001_uncorrected, colorbar=True, display_mode='z',
    title='group left-right button press (uncorrected p < 0.001)')


plotting.show()

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Estimated memory usage: 9 MB