def RealVar(self,y,X):
lmmg=LMM()
m=np.shape(X)[1];
n=len(y);
lmmg.setG(X/math.sqrt(m))
lmmg.sety(y);
lmmg.setX(np.ones([n,1]))
try:
dct=lmmg.findH2();
except:
dct={};
dct['h2']=.5;
mn=sum(y)/float(n);
dct['sigma2']=sum([(i-mn)**2 for i in y])/float(n);
h2=dct['h2'];
s2=dct['sigma2'];
sg2=h2*s2;
se2=s2-sg2;
return [se2,sg2];
def RealVar(self, y, X):
lmmg = LMM()
m = np.shape(X)[1]
n = len(y)
lmmg.setG(X / math.sqrt(m))
lmmg.sety(y)
lmmg.setX(np.ones([n, 1]))
try:
dct = lmmg.findH2()
except:
dct = {}
dct['h2'] = .5
mn = sum(y) / float(n)
dct['sigma2'] = sum([(i - mn)**2 for i in y]) / float(n)
h2 = dct['h2']
s2 = dct['sigma2']
sg2 = h2 * s2
se2 = s2 - sg2
return [se2, sg2]
class GwasPrototype(object):
"""
class to perform genome-wide scan
"""
def __init__(self, train_snps, test_snps, phen, delta=None, cov=None, REML=False, train_pcs=None, mixing=0.0):
"""
set up GWAS object
"""
self.REML = REML
self.train_snps = train_snps
self.test_snps = test_snps
self.phen = phen
if delta is None:
self.delta=None
else:
self.delta = delta * train_snps.shape[1]
self.n_test = test_snps.shape[1]
self.n_ind = len(self.phen)
self.train_pcs = train_pcs
self.mixing = mixing
# add bias if no covariates are used
if cov is None:
self.cov = np.ones((self.n_ind, 1))
else:
self.cov = cov
self.n_cov = self.cov.shape[1]
self.lmm = None
self.res_null = None
self.res_alt = []
self.ll_null = None
self.ll_alt = np.zeros(self.n_test)
self.p_values = np.zeros(self.n_test)
self.sorted_p_values = np.zeros(self.n_test)
# merge covariates and test snps
self.X = np.hstack((self.cov, self.test_snps))
def precompute_UX(self, X):
'''
precompute UX for all snps to be tested
--------------------------------------------------------------------------
Input:
X : [N*D] 2-dimensional array of covariates
--------------------------------------------------------------------------
'''
logging.info("precomputing UX")
self.UX = self.lmm.U.T.dot(X)
self.k = self.lmm.S.shape[0]
self.N = self.lmm.X.shape[0]
if (self.k<self.N):
self.UUX = X - self.lmm.U.dot(self.UX)
logging.info("done.")
def train_null(self):
"""
train model under null hypothesis
"""
logging.info("training null model")
# use LMM
self.lmm = LMM()
self.lmm.setG(self.train_snps, self.train_pcs, a2=self.mixing)
self.lmm.setX(self.cov)
self.lmm.sety(self.phen)
logging.info("finding delta")
if self.delta is None:
result = self.lmm.findH2(REML=self.REML, minH2=0.00001 )
self.delta = 1.0/result['h2']-1.0
# UX = lmm_null.U.dot(test_snps)
self.res_null = self.lmm.nLLeval(delta=self.delta, REML=self.REML)
self.ll_null = -self.res_null["nLL"]
def set_current_UX(self, idx):
"""
set the current UX to pre-trained LMM
"""
si = idx + self.n_cov
self.lmm.X = np.hstack((self.X[:,0:self.n_cov], self.X[:,si:si+1]))
self.lmm.UX = np.hstack((self.UX[:,0:self.n_cov], self.UX[:,si:si+1]))
if (self.k<self.N):
self.lmm.UUX = np.hstack((self.UUX[:,0:self.n_cov], self.UUX[:,si:si+1]))
def train_alt(self):
"""
train alternative model
"""
assert self.lmm != None
self.precompute_UX(self.X)
for idx in xrange(self.n_test):
self.set_current_UX(idx)
res = self.lmm.nLLeval(delta=self.delta, REML=self.REML)
self.res_alt.append(res)
self.ll_alt[idx] = -res["nLL"]
if idx % 1000 == 0:
logging.info("processing snp {0}".format(idx))
def compute_p_values(self):
"""
given trained null and alt models, compute p-values
"""
# from C++ (?)
#real df = rank_beta[ snp ] - ((real)1.0 * rank_beta_0[ snp ]) ;
#pvals[ snp ] = PvalFromLikelihoodRatioTest( LL[ snp ] - LL_0[ snp ], ((real)0.5 * df) );
degrees_of_freedom = 1
assert len(self.res_alt) == self.n_test
for idx in xrange(self.n_test):
test_statistic = self.ll_alt[idx] - self.ll_null
self.p_values[idx] = stats.chi2.sf(2.0 * test_statistic, degrees_of_freedom)
self.p_idx = np.argsort(self.p_values)
self.sorted_p_values = self.p_values[self.p_idx]
def plot_result(self):
"""
plot results
"""
import pylab
pylab.semilogy(self.p_values)
pylab.show()
dummy = [self.res_alt[idx]["nLL"] for idx in xrange(self.n_test)]
pylab.hist(dummy, bins=100)
pylab.title("neg likelihood")
pylab.show()
pylab.hist(self.p_values, bins=100)
pylab.title("p-values")
pylab.show()
def run_gwas(self):
"""
invoke all steps in the right order
"""
self.train_null()
self.train_alt()
self.compute_p_values()
class GwasPrototype(object):
"""
class to perform genome-wide scan
"""
def __init__(self, train_snps, test_snps, phen, delta=None, cov=None, REML=False, train_pcs=None, mixing=0.0):
"""
set up GWAS object
"""
self.REML = REML
self.train_snps = train_snps
self.test_snps = test_snps
self.phen = phen
if delta is None:
self.delta=None
else:
self.delta = delta * train_snps.shape[1]
self.n_test = test_snps.shape[1]
self.n_ind = len(self.phen)
self.train_pcs = train_pcs
self.mixing = mixing
# add bias if no covariates are used
if cov is None:
self.cov = np.ones((self.n_ind, 1))
else:
self.cov = cov
self.n_cov = self.cov.shape[1]
self.lmm = None
self.res_null = None
self.res_alt = []
self.ll_null = None
self.ll_alt = np.zeros(self.n_test)
self.p_values = np.zeros(self.n_test)
self.sorted_p_values = np.zeros(self.n_test)
# merge covariates and test snps
self.X = np.hstack((self.cov, self.test_snps))
def precompute_UX(self, X):
'''
precompute UX for all snps to be tested
--------------------------------------------------------------------------
Input:
X : [N*D] 2-dimensional array of covariates
--------------------------------------------------------------------------
'''
logging.info("precomputing UX")
self.UX = self.lmm.U.T.dot(X)
self.k = self.lmm.S.shape[0]
self.N = self.lmm.X.shape[0]
if (self.k<self.N):
self.UUX = X - self.lmm.U.dot(self.UX)
logging.info("done.")
def train_null(self):
"""
train model under null hypothesis
"""
logging.info("training null model")
# use LMM
self.lmm = LMM()
self.lmm.setG(self.train_snps, self.train_pcs, a2=self.mixing)
self.lmm.setX(self.cov)
self.lmm.sety(self.phen)
logging.info("finding delta")
if self.delta is None:
result = self.lmm.findH2(REML=self.REML, minH2=0.00001 )
self.delta = 1.0/result['h2']-1.0
# UX = lmm_null.U.dot(test_snps)
self.res_null = self.lmm.nLLeval(delta=self.delta, REML=self.REML)
self.ll_null = -self.res_null["nLL"]
def set_current_UX(self, idx):
"""
set the current UX to pre-trained LMM
"""
si = idx + self.n_cov
self.lmm.X = np.hstack((self.X[:,0:self.n_cov], self.X[:,si:si+1]))
self.lmm.UX = np.hstack((self.UX[:,0:self.n_cov], self.UX[:,si:si+1]))
if (self.k<self.N):
self.lmm.UUX = np.hstack((self.UUX[:,0:self.n_cov], self.UUX[:,si:si+1]))
def train_alt(self):
"""
train alternative model
"""
assert self.lmm != None
self.precompute_UX(self.X)
for idx in xrange(self.n_test):
self.set_current_UX(idx)
res = self.lmm.nLLeval(delta=self.delta, REML=self.REML)
self.res_alt.append(res)
self.ll_alt[idx] = -res["nLL"]
if idx % 1000 == 0:
logging.info("processing snp {0}".format(idx))
def compute_p_values(self):
"""
given trained null and alt models, compute p-values
"""
# from C++ (?)
#real df = rank_beta[ snp ] - ((real)1.0 * rank_beta_0[ snp ]) ;
#pvals[ snp ] = PvalFromLikelihoodRatioTest( LL[ snp ] - LL_0[ snp ], ((real)0.5 * df) );
degrees_of_freedom = 1
assert len(self.res_alt) == self.n_test
for idx in xrange(self.n_test):
test_statistic = self.ll_alt[idx] - self.ll_null
self.p_values[idx] = stats.chi2.sf(2.0 * test_statistic, degrees_of_freedom)
self.p_idx = np.argsort(self.p_values)
self.sorted_p_values = self.p_values[self.p_idx]
def plot_result(self):
"""
plot results
"""
import pylab
pylab.semilogy(self.p_values)
pylab.show()
dummy = [self.res_alt[idx]["nLL"] for idx in xrange(self.n_test)]
pylab.hist(dummy, bins=100)
pylab.title("neg likelihood")
pylab.show()
pylab.hist(self.p_values, bins=100)
pylab.title("p-values")
pylab.show()
def run_gwas(self):
"""
invoke all steps in the right order
"""
self.train_null()
self.train_alt()
self.compute_p_values()