Second-level fMRI model: true positive proportion in clusters

This script showcases the so-called “All resolution inference” procedure (Rosenblatt et al.[1]), 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.

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,
    legacy_format=False,
)

[get_dataset_dir] Dataset found in
/home/runner/nilearn_data/brainomics_localizer
[fetch_single_file] Downloading data from
https://osf.io/download/5d27cb281c5b4a001aa07e29/ ...
[fetch_single_file]  ...done. (2 seconds, 0 min)

[fetch_single_file] Downloading data from
https://osf.io/download/5d27e787114a420016059c22/ ...
[fetch_single_file]  ...done. (2 seconds, 0 min)

[fetch_single_file] Downloading data from
https://osf.io/download/5d27efab1c5b4a001aa0a0c2/ ...
[fetch_single_file]  ...done. (2 seconds, 0 min)

[fetch_single_file] Downloading data from
https://osf.io/download/5d28095545253a001c3e59a2/ ...
[fetch_single_file]  ...done. (2 seconds, 0 min)

[fetch_single_file] Downloading data from
https://osf.io/download/5d28144c114a42001804739e/ ...
[fetch_single_file]  ...done. (2 seconds, 0 min)

[fetch_single_file] Downloading data from
https://osf.io/download/5d281e3d114a42001605cb02/ ...
[fetch_single_file]  ...done. (2 seconds, 0 min)

[fetch_single_file] Downloading data from
https://osf.io/download/5d28375345253a001c3e90a2/ ...
[fetch_single_file]  ...done. (1 seconds, 0 min)

[fetch_single_file] Downloading data from
https://osf.io/download/5d283f021c5b4a001aa100cb/ ...
[fetch_single_file]  ...done. (1 seconds, 0 min)

[fetch_single_file] Downloading data from
https://osf.io/download/5d2852caa26b340018089ae5/ ...
[fetch_single_file]  ...done. (1 seconds, 0 min)

[fetch_single_file] Downloading data from
https://osf.io/download/5d28660b1c5b4a001aa122c7/ ...
[fetch_single_file]  ...done. (2 seconds, 0 min)

[fetch_single_file] Downloading data from
https://osf.io/download/5d2868f9114a42001704f6a5/ ...
[fetch_single_file]  ...done. (1 seconds, 0 min)

[fetch_single_file] Downloading data from
https://osf.io/download/5d28847d114a42001904b87b/ ...
[fetch_single_file]  ...done. (2 seconds, 0 min)

[fetch_single_file] Downloading data from
https://osf.io/download/5d289736114a4200170518d7/ ...
[fetch_single_file]  ...done. (3 seconds, 0 min)

[fetch_single_file] Downloading data from
https://osf.io/download/5d28b135a26b3400160a648e/ ...
[fetch_single_file]  ...done. (4 seconds, 0 min)

[fetch_single_file] Downloading data from
https://osf.io/download/5d28c0a81c5b4a001b9fb89a/ ...
[fetch_single_file]  ...done. (2 seconds, 0 min)

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, n_jobs=2)
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=0.05
)

from nilearn import plotting

plotting.plot_stat_map(
    proportion_true_discoveries_img,
    threshold=0.0,
    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()

• 
• 

References

[1]

Jonathan D. Rosenblatt, Livio Finos, Wouter D. Weeda, Aldo Solari, and Jelle J. Goeman. All-resolutions inference for brain imaging. NeuroImage, 181:786–796, November 2018. doi:10.1016/j.neuroimage.2018.07.060.

Estimated memory usage: 175 MB