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

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,
)

Downloading data from https://osf.io/download/5d27cb281c5b4a001aa07e29/ ...
 ...done. (2 seconds, 0 min)
Downloading data from https://osf.io/download/5d27ca3d1c5b4a001b9eeddb/ ...
 ...done. (1 seconds, 0 min)
Downloading data from https://osf.io/download/5d27e787114a420016059c22/ ...
 ...done. (2 seconds, 0 min)
Downloading data from https://osf.io/download/5d27eba2114a420016059fbf/ ...
 ...done. (1 seconds, 0 min)
Downloading data from https://osf.io/download/5d27efab1c5b4a001aa0a0c2/ ...
 ...done. (1 seconds, 0 min)
Downloading data from https://osf.io/download/5d27f296114a42001704a5d9/ ...
 ...done. (1 seconds, 0 min)
Downloading data from https://osf.io/download/5d28095545253a001c3e59a2/ ...
 ...done. (1 seconds, 0 min)
Downloading data from https://osf.io/download/5d280608a26b3400180868d1/ ...
 ...done. (1 seconds, 0 min)
Downloading data from https://osf.io/download/5d28144c114a42001804739e/ ...
 ...done. (1 seconds, 0 min)
Downloading data from https://osf.io/download/5d2811d0114a42001704b988/ ...
 ...done. (1 seconds, 0 min)
Downloading data from https://osf.io/download/5d281e3d114a42001605cb02/ ...
 ...done. (2 seconds, 0 min)
Downloading data from https://osf.io/download/5d281f851c5b4a001b9f2315/ ...
 ...done. (2 seconds, 0 min)
Downloading data from https://osf.io/download/5d28375345253a001c3e90a2/ ...
 ...done. (2 seconds, 0 min)
Downloading data from https://osf.io/download/5d282d9045253a001c3e80a1/ ...
 ...done. (1 seconds, 0 min)
Downloading data from https://osf.io/download/5d283f021c5b4a001aa100cb/ ...
 ...done. (2 seconds, 0 min)
Downloading data from https://osf.io/download/5d283ee0a26b34001609f58e/ ...
 ...done. (1 seconds, 0 min)
Downloading data from https://osf.io/download/5d2852caa26b340018089ae5/ ...
 ...done. (1 seconds, 0 min)
Downloading data from https://osf.io/download/5d285263114a4200160602c6/ ...
 ...done. (2 seconds, 0 min)
Downloading data from https://osf.io/download/5d28660b1c5b4a001aa122c7/ ...
 ...done. (1 seconds, 0 min)
Downloading data from https://osf.io/download/5d285d61114a42001904a343/ ...
 ...done. (1 seconds, 0 min)
Downloading data from https://osf.io/download/5d2868f9114a42001704f6a5/ ...
 ...done. (1 seconds, 0 min)
Downloading data from https://osf.io/download/5d28709e114a420016061aa1/ ...
 ...done. (1 seconds, 0 min)
Downloading data from https://osf.io/download/5d28847d114a42001904b87b/ ...
 ...done. (2 seconds, 0 min)
Downloading data from https://osf.io/download/5d287b3a45253a00193d145e/ ...
 ...done. (2 seconds, 0 min)
Downloading data from https://osf.io/download/5d289736114a4200170518d7/ ...
 ...done. (1 seconds, 0 min)
Downloading data from https://osf.io/download/5d28966345253a00193d2e27/ ...
 ...done. (2 seconds, 0 min)
Downloading data from https://osf.io/download/5d28b135a26b3400160a648e/ ...
 ...done. (1 seconds, 0 min)
Downloading data from https://osf.io/download/5d28a431a26b340019090fa2/ ...
 ...done. (2 seconds, 0 min)
Downloading data from https://osf.io/download/5d28c0a81c5b4a001b9fb89a/ ...
 ...done. (1 seconds, 0 min)
Downloading data from https://osf.io/download/5d28b761a26b3400160a6ba8/ ...
 ...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)
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()

• 
• 

Estimated memory usage: 8 MB