def CombinePValues(covar_matrix, p_values, extra_info = False):
m = int(covar_matrix.shape[0])
#print "m", m
df_fisher = 2.0*m
Expected = 2.0*m
cov_sum = 0
for i in range(m):
for j in range(i+1, m):
cov_sum += covar_matrix[i, j]
#print "cov sum", cov_sum
Var = 4.0*m+2*cov_sum
c = Var/(2.0*Expected)
df_brown = 2.0*Expected**2/Var
if df_brown > df_fisher:
df_brown = df_fisher
c = 1.0
x = 2.0*sum([-np.log(p) for p in p_values])
#print "x", x
p_brown = chi2_cdf(df_brown, 1.0*x/c)
p_fisher = chi2_cdf(df_fisher, 1.0*x)
if extra_info:
return p_brown, p_fisher, c, df_brown
else:
return p_brown
def CombinePValues(covar_matrix, p_values, extra_info=False):
'''
Input: A m x m numpy array of covariances between transformed data vectors and a vector of m p-values to combine.
Output: A combined P-value.
If extra_info == True: also returns the p-value from Fisher's method, the scale factor c, and the new degrees of freedom from Brown's Method
'''
m = int(covar_matrix.shape[0])
#print "m", m
df_fisher = 2.0 * m
Expected = 2.0 * m
cov_sum = 0
for i in range(m):
for j in range(i + 1, m):
cov_sum += covar_matrix[i, j]
#print "cov sum", cov_sum
Var = 4.0 * m + 2 * cov_sum
c = Var / (2.0 * Expected)
df_brown = 2.0 * Expected**2 / Var
if df_brown > df_fisher:
df_brown = df_fisher
c = 1.0
x = 2.0 * sum([-np.log(p) for p in p_values])
#print "x", x
p_brown = chi2_cdf(df_brown, 1.0 * x / c)
p_fisher = chi2_cdf(df_fisher, 1.0 * x)
if extra_info:
return p_brown, p_fisher, c, df_brown
else:
return p_brown
def CombinePValues(covar_matrix, p_values, extra_info=False):
m = int(covar_matrix.shape[0])
df_fisher = 2.0 * m
Expected = 2.0 * m
cov_sum = 0
for i in range(m):
for j in range(i + 1, m):
cov_sum += covar_matrix[i, j]
print("covar_sum", cov_sum)
Var = 4.0 * m + 2 * cov_sum
c = Var / (2.0 * Expected)
df_brown = 2.0 * Expected**2 / Var
if df_brown > df_fisher:
df_brown = df_fisher
c = 1.0
print("c", c)
x = 2.0 * sum([-np.log(p) for p in p_values])
print("x", x)
p_brown = chi2_cdf(df_brown, 1.0 * x / c)
p_fisher = chi2_cdf(df_fisher, 1.0 * x)
if extra_info:
return p_brown, p_fisher, c, df_brown
else:
return p_brown
def self_contained(pvals, pmat=None, weights=None):
'''
Parameters:
pvals: a list of p-values to be combined
pmat: a list of lists of p-values randomly obtained from the data
weights: a list of weights for p-values in pvals
'''
pvals = np.array(pvals, dtype=np.float64)
if np.isnan(pvals).any():
raise Error('List pvals contains None value!')
if pvals.min() < 0:
raise Error('List pvals contains negative value!')
if pvals.max() > 1:
raise Error('List pvals contains > 1 value!')
pvals = __handle(pvals)
if pmat is not None:
pmat = np.matrix(pmat, dtype=np.float64)
if len(pvals) != len(pmat):
raise Error('Dimensions of p-values and p-matrix don\'t match!')
if np.isnan(pmat).any():
raise Error('List pmat contains None value!')
if pmat.min() < 0:
raise Error('List pmat contains negative value!')
if pmat.max() > 1:
raise Error('List pmat contains > 1 value!')
pmat = __handle(pmat)
if weights is None:
weights = np.repeat(2, pvals.size)
else:
if pvals.size != len(weights):
raise Error('Dimensions of p-values and weights don\'t match!')
weights = np.array(weights, dtype=np.float64)
if np.isnan(weights).any():
raise Error('List pvals contains None value!')
if weights.min() < 0:
raise Error('List weights contains negative value!')
# e: E(T)
e = weights.sum()
# var: Var(T)
if pmat is None:
var = 2 * weights.sum()
else:
var = np.cov(
np.apply_along_axis(
lambda q: chi2.ppf(1 - q, weights),
0,
pmat)).sum()
# v: new degrees of freedom based on Satterthwaite's approximation
v = 2 * (e**2 / var)
# T: Lancaster test statistic
T = chi2.ppf(1 - pvals, weights).sum()
c = var / 2 / e
pval = chi2_cdf(v, T / c)
if pmat is None:
cor = np.diag(np.repeat(1, pvals.size))
else:
cor = np.corrcoef(pmat)
return {
'pval': pval,
'cor': cor
}