Simulate data for coordinate based meta-analysis

Simulating data before you run your meta-analysis is a great way to test your assumptions and see how the meta-analysis would perform with simplified data

import matplotlib.pyplot as plt
from nilearn.plotting import plot_stat_map

from nimare.correct import FDRCorrector
from nimare.generate import create_coordinate_dataset
from nimare.meta import ALE

Create function to perform a meta-analysis and plot results

def analyze_and_plot(dset, ground_truth_foci=None, correct=True, return_cres=False):
    meta = ALE(kernel__fwhm=10)
    results = meta.fit(dset)
    if correct:
        corr = FDRCorrector()
        cres = corr.transform(results)
    else:
        cres = results

    # get the z coordinates
    if ground_truth_foci:
        stat_map_kwargs = {"cut_coords": [c[2] for c in ground_truth_foci]}
    else:
        stat_map_kwargs = {}

    fig, ax = plt.subplots()
    display = plot_stat_map(
        cres.get_map("z"),
        display_mode="z",
        draw_cross=False,
        cmap="Purples",
        threshold=2.3,
        symmetric_cbar=False,
        figure=fig,
        axes=ax,
        **stat_map_kwargs,
    )

    if ground_truth_foci:
        # place red dots indicating the ground truth foci
        display.add_markers(ground_truth_foci)

    if return_cres:
        return fig, cres

    return fig

Create Dataset

In this example, each of the 30 generated fake studies select 4 coordinates from a probability map representing the probability that particular coordinate will be chosen. There are 4 “hot” spots centered on 3D gaussian distributions, meaning each study will likely select 4 foci that are close to those hot spots, but there is still random jittering. Each study has a sample_size sampled from a uniform distribution from 20 to 40. so some studies may have fewer than 30 participants and some more.

ground_truth_foci, dset = create_coordinate_dataset(foci=4, sample_size=(20, 40), n_studies=30)

Analyze and plot simple dataset

The red dots in this plot and subsequent plots represent the simulated ground truth foci, and the clouds represent the statistical maps of the simulated data.

analyze_and_plot(dset, ground_truth_foci)

<Figure size 640x480 with 6 Axes>

Fine-tune dataset creation

Perhaps you want more control over the studies being generated. you can set:

• the specific peak coordinates (i.e., foci)

• the percentage of studies that contain the foci of interest (foci_percentage)

• how tightly the study specific foci are selected around the ground truth (i.e., fwhm)

• the sample size for each study (i.e., sample_size)

• the number of noise foci in each study (i.e., n_noise_foci)

• the number of studies (i.e., n_studies)

foci = [(0, 0, 0)]
foci_percentage = 1.0
fwhm = 10.0
n_studies = 30
sample_sizes = [30] * n_studies
sample_sizes[0] = 300
n_noise_foci = 10

_, manual_dset = create_coordinate_dataset(
    foci=foci, fwhm=fwhm, sample_size=sample_sizes, n_studies=n_studies, n_noise_foci=n_noise_foci
)

Analyze and plot manual dataset

fig = analyze_and_plot(manual_dset, ground_truth_foci)
fig.show()

Control percentage of studies with the foci of interest

Often times a converging peak is not found in all studies within the meta-analysis, but only a portion. We can select a percentage of studies where a coordinate is selected around the ground truth foci.

_, perc_foci_dset = create_coordinate_dataset(
    foci=ground_truth_foci[0:2], foci_percentage="50%", fwhm=10.0, sample_size=30, n_studies=30
)

Analyze and plot the 50% foci dataset

fig = analyze_and_plot(perc_foci_dset, ground_truth_foci[0:2])
fig.show()

Create a null dataset

Perhaps you are interested in the number of false positives your favorite meta-analysis algorithm typically gives. At an alpha of 0.05 we would expect no more than 5% of results to be false positives. To test this, we can create a dataset with no foci that converge, but have many distributed foci.

_, no_foci_dset = create_coordinate_dataset(
    foci=0, sample_size=(20, 30), n_studies=30, n_noise_foci=100
)

Analyze and plot no foci dataset

When not performing a multiple comparisons correction, there is a false positive rate of approximately 5%.

fig, cres = analyze_and_plot(no_foci_dset, correct=False, return_cres=True)
fig.show()

p_values = cres.get_map("p", return_type="array")
# what percentage of voxels are not significant?
non_significant_percent = ((p_values > 0.05).sum() / p_values.size) * 100
print(f"{non_significant_percent}% of voxels are not significant")

93.88532188390384% of voxels are not significant