def test_fdr(self):
pvals = np.array([.005, .1, .2, .5])
fdr_p = stats.fdr(pvals)
self.assertEqual(fdr_p, pvals[0])
def __init__(self, dataset, ids, ids2=None, q=0.01, prior=0.5,
min_studies=1):
""" Initialize a new MetaAnalysis instance and run an analysis.
Args:
dataset: A Dataset instance.
ids: A list of Mappable IDs to include in the meta-analysis.
ids2: Optional second list of Mappable IDs. If passed, the set of
studies will be restricted to the union of ids and ids2 before
performing the meta-analysis. This is useful for meta-analytic
contrasts, as the resulting images will in effect identify
regions that are reported/activated more frequently in one
list than in the other.
q: The FDR threshold to use when correcting for multiple
comparisons. Set to .01 by default.
prior: The prior to use when calculating conditional probabilities.
This is the prior probability of a feature being used in a
study (i.e., p(F)). For example, if set to 0.25, the analysis
will assume that 1/4 of studies load on the target feature, as
opposed to the empirically estimated p(F), which is len(ids) /
total number of studies in the dataset. If prior is not passed,
defaults to 0.5, reflecting an effort to put all terms on level
footing and avoid undue influence of base rates (because some
terms are much more common than others). Note that modifying
the prior will only affect the effect size/probability maps,
and not the statistical inference (z-score) maps.
min_studies: Integer or float indicating which voxels to mask out
from results due to lack of stability. If an integer is passed,
all voxels that activate in fewer than this number of studies
will be ignored (i.e., a value of 0 will be assigned in all
output images). If a float in the range of 0 - 1 is passed,
this will be interpreted as a proportion to use as the cut-off
(e.g., passing 0.03 will exclude all voxels active in fewer
than 3% of the entire dataset). Defaults to 1, meaning all
voxels that activate at least one study will be kept.
"""
self.dataset = dataset
mt = dataset.image_table
self.selected_ids = list(set(mt.ids) & set(ids))
self.selected_id_indices = np.in1d(mt.ids, ids)
# If ids2 is provided, we only use mappables explicitly in either ids or ids2.
# Otherwise, all mappables not in the ids list are used as the control
# condition.
unselected_id_indices = ~self.selected_id_indices if ids2 is None \
else np.in1d(mt.ids, ids2)
mappable_id_indices = self.selected_id_indices | unselected_id_indices
# Calculate different count variables
logger.debug("Calculating counts...")
n_selected = len(self.selected_ids)
n_unselected = np.sum(unselected_id_indices)
n_mappables = n_selected + n_unselected
n_selected_active_voxels = mt.data.dot(self.selected_id_indices)
n_unselected_active_voxels = mt.data.dot(unselected_id_indices)
# Nomenclature for variables below: p = probability, F = feature present, g = given,
# U = unselected, A = activation. So, e.g., pAgF = p(A|F) = probability of activation
# in a voxel if we know that the feature is present in a study.
pF = (n_selected * 1.0) / n_mappables
mappable_data = mt.data if ids2 is None else mt.data[:, mappable_id_indices]
pA = np.array((mappable_data.sum(axis=1) * 1.0) / n_mappables).squeeze()
# Conditional probabilities
logger.debug("Calculating conditional probabilities...")
pAgF = n_selected_active_voxels * 1.0 / n_selected
pAgU = n_unselected_active_voxels * 1.0 / n_unselected
pFgA = pAgF * pF / pA
# Recompute conditionals with uniform prior
logger.debug("Recomputing with uniform priors...")
pA_prior = prior * pAgF + (1 - prior) * pAgU
pFgA_prior = pAgF * prior / pA_prior
def p_to_z(p, sign):
p = p / 2 # convert to two-tailed
# prevent underflow
p[p < 1e-240] = 1e-240
# Convert to z and assign tail
z = np.abs(norm.ppf(p)) * sign
# Set very large z's to max precision
z[np.isinf(z)] = norm.ppf(1e-240) * -1
return z
# One-way chi-square test for consistency of activation
p_vals = stats.one_way(
np.squeeze(n_selected_active_voxels), n_selected)
p_vals[p_vals < 1e-240] = 1e-240
z_sign = np.sign(
n_selected_active_voxels - np.mean(
n_selected_active_voxels)).ravel()
pAgF_z = p_to_z(p_vals, z_sign)
fdr_thresh = stats.fdr(p_vals, q)
pAgF_z_FDR = imageutils.threshold_img(
pAgF_z, fdr_thresh, p_vals, mask_out='above')
# Two-way chi-square for specificity of activation
cells = np.squeeze(
np.array([[n_selected_active_voxels, n_unselected_active_voxels],
[n_selected - n_selected_active_voxels, n_unselected -
n_unselected_active_voxels]]).T)
p_vals = stats.two_way(cells)
p_vals[p_vals < 1e-240] = 1e-240
z_sign = np.sign(pAgF - pAgU).ravel()
pFgA_z = p_to_z(p_vals, z_sign)
fdr_thresh = stats.fdr(p_vals, q)
pFgA_z_FDR = imageutils.threshold_img(
pFgA_z, fdr_thresh, p_vals, mask_out='above')
# Retain any images we may want to save or access later
self.images = {
'pA': pA,
'pAgF': pAgF,
'pFgA': pFgA,
('pA_given_pF=%0.2f' % prior): pA_prior,
('pFgA_given_pF=%0.2f' % prior): pFgA_prior,
'uniformity-test_z': pAgF_z,
'association-test_z': pFgA_z,
('uniformity-test_z_FDR_%s' % q): pAgF_z_FDR,
('association-test_z_FDR_%s' % q): pFgA_z_FDR
}
# Mask out all voxels below num_studies threshold
if min_studies > 0:
if isinstance(min_studies, int):
min_studies = float(
min_studies) / n_mappables # Recalculate as proportion
vox_to_exclude = np.where(pA < min_studies)[0] # Create mask
# Mask each image
for k in self.images:
self.images[k][vox_to_exclude] = 0
def __init__(self,
dataset,
ids,
ids2=None,
q=0.01,
prior=0.5,
min_studies=1):
""" Initialize a new MetaAnalysis instance and run an analysis.
Args:
dataset: A Dataset instance.
ids: A list of Mappable IDs to include in the meta-analysis.
ids2: Optional second list of Mappable IDs. If passed, the set of
studies will be restricted to the union of ids and ids2 before
performing the meta-analysis. This is useful for meta-analytic
contrasts, as the resulting images will in effect identify
regions that are reported/activated more frequently in one
list than in the other.
q: The FDR threshold to use when correcting for multiple
comparisons. Set to .01 by default.
prior: The prior to use when calculating conditional probabilities.
This is the prior probability of a feature being used in a
study (i.e., p(F)). For example, if set to 0.25, the analysis
will assume that 1/4 of studies load on the target feature, as
opposed to the empirically estimated p(F), which is len(ids) /
total number of studies in the dataset. If prior is not passed,
defaults to 0.5, reflecting an effort to put all terms on level
footing and avoid undue influence of base rates (because some
terms are much more common than others). Note that modifying
the prior will only affect the effect size/probability maps,
and not the statistical inference (z-score) maps.
min_studies: Integer or float indicating which voxels to mask out
from results due to lack of stability. If an integer is passed,
all voxels that activate in fewer than this number of studies
will be ignored (i.e., a value of 0 will be assigned in all
output images). If a float in the range of 0 - 1 is passed,
this will be interpreted as a proportion to use as the cut-off
(e.g., passing 0.03 will exclude all voxels active in fewer
than 3% of the entire dataset). Defaults to 1, meaning all
voxels that activate at least one study will be kept.
"""
self.dataset = dataset
mt = dataset.image_table
self.selected_ids = list(set(mt.ids) & set(ids))
self.selected_id_indices = np.in1d(mt.ids, ids)
# If ids2 is provided, we only use mappables explicitly in either ids or ids2.
# Otherwise, all mappables not in the ids list are used as the control
# condition.
unselected_id_indices = ~self.selected_id_indices if ids2 == None \
else np.in1d(mt.ids, ids2)
# Calculate different count variables
logger.debug("Calculating counts...")
n_selected = len(self.selected_ids)
n_unselected = np.sum(unselected_id_indices)
n_mappables = n_selected + n_unselected
n_selected_active_voxels = mt.data.dot(self.selected_id_indices)
n_unselected_active_voxels = mt.data.dot(unselected_id_indices)
# Nomenclature for variables below: p = probability, F = feature present, g = given,
# U = unselected, A = activation. So, e.g., pAgF = p(A|F) = probability of activation
# in a voxel if we know that the feature is present in a study.
pF = (n_selected * 1.0) / n_mappables
pA = np.array((mt.data.sum(axis=1) * 1.0) / n_mappables).squeeze()
# Conditional probabilities
logger.debug("Calculating conditional probabilities...")
pAgF = n_selected_active_voxels * 1.0 / n_selected
pAgU = n_unselected_active_voxels * 1.0 / n_unselected
pFgA = pAgF * pF / pA
# Recompute conditionals with uniform prior
logger.debug("Recomputing with uniform priors...")
pAgF_prior = prior * pAgF + (1 - prior) * pAgU
pFgA_prior = pAgF * prior / pAgF_prior
def p_to_z(p, sign):
p = p / 2 # convert to two-tailed
# prevent underflow
p[p < 1e-240] = 1e-240
# Convert to z and assign tail
z = np.abs(norm.ppf(p)) * sign
# Set very large z's to max precision
z[np.isinf(z)] = norm.ppf(1e-240) * -1
return z
# One-way chi-square test for consistency of activation
p_vals = stats.one_way(np.squeeze(n_selected_active_voxels),
n_selected)
p_vals[p_vals < 1e-240] = 1e-240
z_sign = np.sign(n_selected_active_voxels -
np.mean(n_selected_active_voxels)).ravel()
pAgF_z = p_to_z(p_vals, z_sign)
fdr_thresh = stats.fdr(p_vals, q)
pAgF_z_FDR = imageutils.threshold_img(pAgF_z,
fdr_thresh,
p_vals,
mask_out='above')
# Two-way chi-square for specificity of activation
cells = np.squeeze(
np.array([[n_selected_active_voxels, n_unselected_active_voxels],
[
n_selected - n_selected_active_voxels,
n_unselected - n_unselected_active_voxels
]]).T)
p_vals = stats.two_way(cells)
p_vals[p_vals < 1e-240] = 1e-240
z_sign = np.sign(pAgF - pAgU).ravel()
pFgA_z = p_to_z(p_vals, z_sign)
fdr_thresh = stats.fdr(p_vals, q)
pFgA_z_FDR = imageutils.threshold_img(pFgA_z,
fdr_thresh,
p_vals,
mask_out='above')
# Retain any images we may want to save or access later
self.images = {
'pA': pA,
'pAgF': pAgF,
'pFgA': pFgA,
('pAgF_given_pF=%0.2f' % prior): pAgF_prior,
('pFgA_given_pF=%0.2f' % prior): pFgA_prior,
'consistency_z': pAgF_z,
'specificity_z': pFgA_z,
('pAgF_z_FDR_%s' % q): pAgF_z_FDR,
('pFgA_z_FDR_%s' % q): pFgA_z_FDR
}
# Mask out all voxels below num_studies threshold
if min_studies > 0:
if isinstance(min_studies, int):
min_studies = float(
min_studies) / n_mappables # Recalculate as proportion
vox_to_exclude = np.where(pA < min_studies)[0] # Create mask
# Mask each image
for k in self.images:
self.images[k][vox_to_exclude] = 0
def test_fdr(self):
pvals = np.array([.005, .1, .2, .5])
fdr_p = stats.fdr(pvals)
self.assertEqual(fdr_p, pvals[0])