def calculate_pseudo_heritability(phen_vals,K):
"""
Retrieve pseudo heritability for phenotype
"""
lmm = LinearMixedModel(phen_vals)
lmm.add_random_effect(K)
reml_dict = lmm.get_REML()
return reml_dict['pseudo_heritability']
def emmax_step_wise(phenotypes, K, sd=None, num_steps=10, file_prefix=None, forward_backwards=True,
local=False, cand_gene_list=None, plot_xaxis=True, with_qq_plots=True, sign_threshold=None,
log_qq_max_val=5, highlight_loci=None, save_pvals=False, pval_file_prefix=None, snp_priors=None,
K2=None, snp_choose_criteria='pval', emma_num=0, markersize=3, chrom_col_map=None, **kwargs):
"""
Run step-wise EMMAX forward-backward.
"""
import gwaResults as gr
if local:
with_qq_plots = False
if sd:
kwargs['snps'] = sd.getSnps()
kwargs['positions'] = sd.getPositions()
kwargs['chromosomes'] = sd.get_chr_list()
d = sd.get_mafs()
kwargs['macs'] = d['mafs']
kwargs['mafs'] = d['marfs']
if snp_priors:
print 'Using provided SNP priors'
kwargs['snp_priors'] = snp_priors[:]
snps = kwargs['snps'][:]
positions = kwargs['positions'][:]
chromosomes = kwargs['chromosomes'][:]
mafs = kwargs['mafs'][:]
macs = kwargs['macs'][:]
chr_pos_list = zip(chromosomes, positions)
lmm = LinearMixedModel(phenotypes)
lmm.add_random_effect(K)
if K2 != None:
lmm.add_random_effect(K2)
num_snps = len(snps)
if snp_priors == None:
print "Using default SNP priors"
snp_priors = [1.0 / num_snps] * num_snps
if not sign_threshold: # Then use Bonferroni threshold
sign_threshold = 1.0 / (num_snps * 20.0)
print "Running EMMAX stepwise"
s1 = time.time()
step_info_list = []
cofactors = [] # A list of the loci found, together with their statistics.
cofactor_snps = []
step_i = 0
num_par = 2 # mean and variance scalar
num_pher_0 = 0
if K2 != None: # Then first estimate K
res = lmm.get_estimates_3()
pherit = res['perc_var1']
print res['perc_var1'], res['perc_var2']
K = res['opt_k']
eig_L = lmm._get_eigen_L_(K=K)
eig_R = lmm._get_eigen_R_(K=K)
reml_res = lmm.get_REML(eig_L=eig_L, eig_R=eig_R)
ml_res = lmm.get_ML(eig_L=eig_L, eig_R=eig_R)
H_sqrt_inv = reml_res['H_sqrt_inv']
ll = ml_res['max_ll']
rss = float(reml_res['rss'])
reml_mahalanobis_rss = float(reml_res['mahalanobis_rss'])
criterias = {'ebics':[], 'mbics':[], 'bonf':[], 'mbonf':[]}
(bic, extended_bic, modified_bic) = _calc_bic_(ll, num_snps, num_par, lmm.n) # Calculate the BICs
criterias['ebics'].append(extended_bic)
criterias['mbics'].append(modified_bic)
max_cofactor_pval = 0 # 5e-324 #min float, a hack to fix an annoying bug
criterias['mbonf'].append(max_cofactor_pval)
criterias['bonf'].append(0)
criterias['min_cof_ppa'] = [1] # Posterior probability of association
cof_snp_priors = []
ppa_cofactors = []
action = 'None'
if K2 == None:
pherit = reml_res['pseudo_heritability']
print '\nStep %d: action=%s, num_par=%d, p_her=%0.4f, ll=%0.2f, rss=%0.2f, reml_m_rss=%0.2f, bic=%0.2f, extended_bic=%0.2f, modified_bic=%0.2f, num_snps=%d' % \
(step_i, action, num_par, pherit, ll, rss, reml_mahalanobis_rss, \
bic, extended_bic, modified_bic, num_snps)
print 'Cofactors:', _cofactors_to_string_(cofactors)
quantiles_dict = {'log':[], 'norm':[], 'labels':[]}
for step_i in range(1, num_steps + 1):
emmax_res = lmm._emmax_f_test_(snps, H_sqrt_inv, snp_priors=snp_priors, emma_num=emma_num)
if step_i == 1:
first_emmax_res = emmax_res
min_pval_i = sp.argmin(emmax_res['ps'])
min_pval = emmax_res['ps'][min_pval_i]
mahalnobis_rss = emmax_res['rss'][min_pval_i]
min_pval_chr_pos = chr_pos_list[min_pval_i]
max_ppa_i = sp.argmax(emmax_res['ppas'])
max_ppa = emmax_res['ppas'][max_ppa_i]
print 'Min p-value:', min_pval
criterias['bonf'].append(min_pval)
print 'Min Mahalanobis RSS:', mahalnobis_rss
step_info = {'pseudo_heritability':pherit, 'rss':rss, \
'reml_mahalanobis_rss': reml_res['mahalanobis_rss'], 'mahalanobis_rss':mahalnobis_rss,
'll':ll, 'bic':bic, 'e_bic':extended_bic, 'm_bic':modified_bic, 'mbonf':max_cofactor_pval,
'cofactors':map(tuple, cofactors[:]), 'cofactor_snps':cofactor_snps[:],
'min_pval':min_pval, 'min_pval_chr_pos': min_pval_chr_pos,
'max_ppa':max_ppa, 'max_ppa_pval':emmax_res['ps'][max_ppa_i],
'max_ppa_chr_pos':chr_pos_list[max_ppa_i], 'ppa_cofactors':map(tuple, ppa_cofactors[:])}
ppas = emmax_res['ppas'].tolist()
if snp_choose_criteria == 'pval':
snp_i = min_pval_i
elif snp_choose_criteria == 'ppas':
snp_i = max_ppa_i
ex_pvals = emmax_res['ps'].tolist()
ex_perc_var_expl = emmax_res['var_perc'].tolist()
# Plot gwas results per step
if file_prefix:
_plot_manhattan_and_qq_(file_prefix, step_i - 1, ex_pvals, quantiles_dict, positions=positions,
chromosomes=chromosomes, mafs=mafs, macs=macs, perc_var_expl=ex_perc_var_expl,
plot_bonferroni=True,
highlight_markers=cofactors, cand_genes=cand_gene_list, plot_xaxis=plot_xaxis,
log_qq_max_val=log_qq_max_val, with_qq_plots=with_qq_plots,
highlight_loci=highlight_loci, write_pvals=save_pvals, ppas=ppas,
highlight_ppa_markers=ppa_cofactors, markersize=markersize,
chrom_col_map=chrom_col_map)
if save_pvals or pval_file_prefix:
res = gr.Result(scores=ex_pvals, perc_var_expl=ex_perc_var_expl, **kwargs)
res.filter_percentile(0.02, reversed=True)
if save_pvals:
step_info['res'] = res
if pval_file_prefix:
pval_file_name = '%s_step%d.pvals' % (pval_file_prefix, step_i)
res.write_to_file(pval_file_name, only_pickled=True, additional_columns='perc_var_expl')
step_info['kolmogorov_smirnov'] = agr.calc_ks_stats(ex_pvals)
step_info['pval_median'] = agr.calc_median(ex_pvals)
print step_info['kolmogorov_smirnov'], step_info['pval_median']
step_info_list.append(step_info)
# Adding the new SNP as a cofactor
lmm.add_factor(snps[snp_i])
cofactor_snps.append(snps[snp_i])
if K2 != None: # Again first estimate K
res = lmm.get_estimates_3()
pherit = res['perc_var1']
K = res['opt_k']
eig_L = lmm._get_eigen_L_(K=K)
eig_R = lmm._get_eigen_R_(X=lmm.X, K=K)
reml_res = lmm.get_REML(eig_L=eig_L, eig_R=eig_R)
ml_res = lmm.get_ML(eig_L=eig_L, eig_R=eig_R)
H_sqrt_inv = reml_res['H_sqrt_inv']
ll = ml_res['max_ll']
rss = float(reml_res['rss'])
reml_mahalanobis_rss = float(reml_res['mahalanobis_rss'])
num_par += 1
action = '+'
cof_snp_priors.append(snp_priors[snp_i])
ppa_cofactors.append([chromosomes[snp_i], positions[snp_i], max_ppa])
cofactors.append([chromosomes[snp_i], positions[snp_i], min_pval])
# Re-estimate the p-value of the cofactors... with the smallest in the list.
cofactor_pvals = []
if snp_priors != None:
cofactor_ppas = [] # Posterior probabilities of association
for i, snp in enumerate(cofactor_snps):
t_cofactors = cofactor_snps[:]
del t_cofactors[i]
lmm.set_factors(t_cofactors)
res = lmm._emmax_f_test_([snp], H_sqrt_inv, snp_priors=[cof_snp_priors[i]], emma_num=0)
cofactor_ppas.append(res['ppas'][0])
ppa_cofactors[i][2] = res['ppas'][0]
pval = res['ps'][0]
cofactor_pvals.append(pval)
cofactors[i][2] = -math.log10(pval)
lmm.set_factors(cofactor_snps)
max_cofactor_pval = max(cofactor_pvals)
criterias['mbonf'].append(max_cofactor_pval)
if snp_priors != None:
criterias['min_cof_ppa'].append(min(cofactor_ppas))
# Remove the found SNP from considered SNPs
del snps[snp_i]
del snp_priors[snp_i]
del positions[snp_i]
del chromosomes[snp_i]
del chr_pos_list[snp_i]
del mafs[snp_i]
del macs[snp_i]
num_snps -= 1
(bic, extended_bic, modified_bic) = _calc_bic_(ll, num_snps, num_par, lmm.n) # Calculate the BICs
criterias['ebics'].append(extended_bic)
criterias['mbics'].append(modified_bic)
if K2 == None:
pherit = reml_res['pseudo_heritability']
print '\nStep %d: action=%s, num_par=%d, p_her=%0.4f, ll=%0.2f, rss=%0.2f, reml_m_rss=%0.2f, bic=%0.2f, extended_bic=%0.2f, modified_bic=%0.2f, num_snps=%d' % \
(step_i, action, num_par, pherit, ll, rss, reml_mahalanobis_rss, \
bic, extended_bic, modified_bic, num_snps)
print 'Cofactors:', _cofactors_to_string_(cofactors)
print ppa_cofactors
# if reml_res['pseudo_heritability'] < 0.01 and num_pher_0 < 1:
# num_pher_0 += 1
# elif reml_res['pseudo_heritability'] < 0.01:
# if reml_res['pseudo_heritability'] < 0.01:
if pherit < 0.001:
if num_pher_0 < 1:
num_pher_0 += 1
else:
print 'Breaking early, since pseudoheritability is close to 0.'
break
emmax_res = lmm._emmax_f_test_(snps, H_sqrt_inv, snp_priors=snp_priors, emma_num=emma_num) #FINISH!!!
min_pval_i = sp.argmin(emmax_res['ps'])
min_pval = emmax_res['ps'][min_pval_i]
mahalnobis_rss = emmax_res['rss'][min_pval_i]
min_pval_chr_pos = chr_pos_list[min_pval_i]
max_ppa_i = sp.argmax(emmax_res['ppas'])
ppas = emmax_res['ppas'].tolist()
print 'Min p-value:', min_pval
print 'Min Mahalanobis RSS:', mahalnobis_rss
step_info = {'pseudo_heritability':pherit, 'rss':rss, 'reml_mahalanobis_rss': reml_res['mahalanobis_rss'],
'mahalanobis_rss':mahalnobis_rss, 'll':ll, 'bic':bic, 'e_bic':extended_bic, 'm_bic':modified_bic,
'mbonf':max_cofactor_pval, 'cofactors':map(tuple, cofactors[:]), 'cofactor_snps':cofactor_snps[:],
'min_pval':min_pval, 'min_pval_chr_pos': min_pval_chr_pos,
'max_ppa':emmax_res['ppas'][max_ppa_i], 'max_ppa_pval':emmax_res['ps'][max_ppa_i],
'max_ppa_chr_pos':chr_pos_list[max_ppa_i], 'ppa_cofactors':map(tuple, ppa_cofactors[:])}
ex_pvals = emmax_res['ps'].tolist()
ex_perc_var_expl = emmax_res['var_perc'].tolist()
if save_pvals:
step_info['ps'] = ex_pvals
print "Generating plots"
# Now plotting!
if file_prefix:
_plot_manhattan_and_qq_(file_prefix, step_i, ex_pvals, quantiles_dict, positions=positions,
chromosomes=chromosomes, mafs=mafs, macs=macs, perc_var_expl=ex_perc_var_expl,
plot_bonferroni=True,
highlight_markers=cofactors, cand_genes=cand_gene_list, plot_xaxis=plot_xaxis,
log_qq_max_val=log_qq_max_val, with_qq_plots=with_qq_plots,
highlight_loci=highlight_loci, write_pvals=save_pvals, ppas=ppas,
highlight_ppa_markers=ppa_cofactors, markersize=markersize,
chrom_col_map=chrom_col_map)
# Plot posterior probabilities of association
if save_pvals or pval_file_prefix:
res = gr.Result(scores=ex_pvals, perc_var_expl=ex_perc_var_expl, **kwargs)
res.filter_percentile(0.02, reversed=True)
if save_pvals:
step_info['res'] = res
if pval_file_prefix:
pval_file_name = '%s_step%d.pvals' % (pval_file_prefix, step_i)
res.write_to_file(pval_file_name, only_pickled=True, additional_columns='perc_var_expl')
step_info['kolmogorov_smirnov'] = agr.calc_ks_stats(ex_pvals)
step_info['pval_median'] = agr.calc_median(ex_pvals)
print step_info['kolmogorov_smirnov'], step_info['pval_median']
step_info_list.append(step_info)
if pval_file_prefix != None or save_pvals:
res = gr.Result(scores=ex_pvals, perc_var_expl=ex_perc_var_expl, **kwargs)
res.filter_percentile(0.02, reversed=True)
if pval_file_prefix != None:
pval_file_name = '%s_step%d.pvals' % (pval_file_prefix, step_i)
res.write_to_file(pval_file_name, only_pickled=True, additional_columns='perc_var_expl')
if save_pvals:
step_info['res'] = res
max_num_cofactors = len(cofactors)
# Now backward stepwise.
if forward_backwards:
print 'Starting backwards..'
while len(cofactor_snps) > 1:
step_i += 1
f_stats = sp.zeros(len(cofactor_snps))
ppas = sp.zeros(len(cofactor_snps))
for i, snp in enumerate(cofactor_snps):
t_cofactors = cofactor_snps[:]
del t_cofactors[i]
lmm.set_factors(t_cofactors)
res = lmm._emmax_f_test_([snp], H_sqrt_inv, snp_priors=[cof_snp_priors[i]], emma_num=0)
ppas[i] = res['ppas'][0]
cofactors[i][2] = -math.log10(res['ps'][0])
f_stats[i] = res['f_stats'][0]
if snp_choose_criteria == 'pval':
i_to_remove = f_stats.argmin()
elif snp_choose_criteria == 'ppas':
i_to_remove = ppas.argmin()
del ppa_cofactors[i_to_remove]
del cofactor_snps[i_to_remove]
del cofactors[i_to_remove]
lmm.set_factors(cofactor_snps)
num_snps += 1
# Re-estimating the REML and ML.
if K2 != None: # Again first estimate K
res = lmm.get_estimates_3()
pherit = res['perc_var1']
K = res['opt_k']
eig_L = lmm._get_eigen_L_(K=K)
eig_R = lmm._get_eigen_R_(X=lmm.X, K=K)
reml_res = lmm.get_REML(eig_L=eig_L, eig_R=eig_R)
ml_res = lmm.get_ML(eig_L=eig_L, eig_R=eig_R)
ll = ml_res['max_ll']
H_sqrt_inv = reml_res['H_sqrt_inv']
rss = float(reml_res['rss'])
reml_mahalanobis_rss = float(reml_res['mahalanobis_rss'])
num_par -= 1
action = '-'
# Update the p-values
cofactor_pvals = []
if snp_priors != None:
cofactor_ppas = [] # Posterior probabilities of association
for i, snp in enumerate(cofactor_snps):
t_cofactors = cofactor_snps[:]
del t_cofactors[i]
lmm.set_factors(t_cofactors)
res = lmm._emmax_f_test_([snp], H_sqrt_inv, snp_priors=[cof_snp_priors[i]], emma_num=0)
cofactor_ppas.append(res['ppas'][0])
ppa_cofactors[i][2] = res['ppas'][0]
pval = res['ps'][0]
cofactor_pvals.append(pval)
cofactors[i][2] = -math.log10(pval)
max_cofactor_pval = max(cofactor_pvals)
criterias['mbonf'].append(max_cofactor_pval)
criterias['min_cof_ppa'].append(min(cofactor_ppas))
# Calculate the BICs
(bic, extended_bic, modified_bic) = _calc_bic_(ll, num_snps, num_par, lmm.n)
criterias['ebics'].append(extended_bic)
criterias['mbics'].append(modified_bic)
if K2 == None:
pherit = reml_res['pseudo_heritability']
print '\nStep %d: action=%s, num_par=%d, p_her=%0.4f, ll=%0.2f, rss=%0.2f, reml_m_rss=%0.2f, bic=%0.2f, extended_bic=%0.2f, modified_bic=%0.2f, num_snps=%d' % \
(step_i, action, num_par, pherit, ll, rss,
reml_mahalanobis_rss, bic, extended_bic, modified_bic, num_snps)
print 'Cofactors:', _cofactors_to_string_(cofactors)
print ppa_cofactors
step_info = {'pseudo_heritability':pherit, 'rss':rss, \
'reml_mahalanobis_rss': reml_res['mahalanobis_rss'], 'll':ll, 'bic':bic,
'e_bic':extended_bic, 'm_bic':modified_bic, 'mbonf':max_cofactor_pval,
'cofactors':map(tuple, cofactors[:]), 'cofactor_snps':cofactor_snps[:],
'mahalanobis_rss':None, 'min_pval':None, 'min_pval_chr_pos':None,
'kolmogorov_smirnov':None, 'pval_median':None,
'ppa_cofactors': map(tuple, ppa_cofactors[:])}
step_info_list.append(step_info)
print step_info['kolmogorov_smirnov'], step_info['pval_median']
opt_dict, opt_indices = _analyze_opt_criterias_(criterias, sign_threshold, max_num_cofactors, file_prefix,
with_qq_plots, lmm, step_info_list, quantiles_dict,
plot_bonferroni=True, cand_genes=cand_gene_list, plot_xaxis=plot_xaxis,
log_qq_max_val=log_qq_max_val, eig_L=eig_L, type='emmax',
highlight_loci=highlight_loci, write_pvals=save_pvals,
markersize=markersize, chrom_col_map=chrom_col_map, emma_num=emma_num,
**kwargs)
for step_i in opt_indices:
for h in ['mahalanobis_rss', 'min_pval', 'min_pval_chr_pos', 'kolmogorov_smirnov', 'pval_median', 'res']:
step_info_list[step_i][h] = opt_indices[step_i][h]
if save_pvals:
step_info_list[step_i]['res'] = opt_indices[step_i]['res']
secs = time.time() - s1
if secs > 60:
mins = int(secs) / 60
secs = secs - mins * 60
print 'Took %d mins and %f seconds.' % (mins, secs)
else:
print 'Took %f seconds.' % (secs)
if file_prefix:
_plot_stepwise_stats_(file_prefix, step_info_list, sign_threshold, type='emmax')
res_dict = {'step_info_list':step_info_list, 'first_emmax_res':first_emmax_res, 'opt_dict':opt_dict}
return res_dict
def emmax_step(phen_vals, genotype, K, cof_chr_pos_list, eig_L=None, eig_R=None, progress_file_writer=None, plot_prefix=None,
emma_num=100):
"""
EMMAX single SNPs
Returns various stats useful for stepwise regression.
"""
import bisect
t = Timer()
lmm = LinearMixedModel(phen_vals)
lmm.add_random_effect(K)
if not eig_L:
log.debug('Calculating the eigenvalues of K')
eig_L = lmm._get_eigen_L_()
log.debug('Done.')
reml_dict = lmm.get_REML(eig_L=eig_L)
h0_rss = float(reml_dict['rss'])
cof_indices = []
"""
chrom_pos_list = sd.get_chr_pos_list()
log.debug('Looking up cofactors')
for chrom_pos in cof_chr_pos_list:
i = bisect.bisect(chrom_pos_list, chrom_pos) - 1
assert chrom_pos_list[i] == chrom_pos, 'Cofactor missing??'
cof_indices.append(i)"""
num_snps = genotype.num_snps
cof_snps_ix,cof_snps = genotype.get_snps_from_pos(cof_chr_pos_list)
lmm.set_factors(cof_snps)
if not eig_R:
log.debug("Calculating the eigenvalues of S(K+I)S where S = I-X(X'X)^-1X'")
eig_R = lmm._get_eigen_R_()
log.debug('Done')
log.debug('Getting variance components estimates')
reml_dict = lmm.get_REML(eig_L=eig_L, eig_R=eig_R)
ml_dict = lmm.get_ML(eig_L=eig_L, eig_R=eig_R)
log.debug('Done.')
log.info('pseudo_heritability: %s' % reml_dict['pseudo_heritability'])
H_sqrt_inv = reml_dict['H_sqrt_inv']
if not progress_file_writer == None:
progress_file_writer.update_progress_bar(progress=0.20, task_status='Performing AMM')
progress_file_writer.set_step(0.05)
r = lmm._emmax_f_test_(genotype, num_snps,H_sqrt_inv, progress_file_writer=progress_file_writer, emma_num=emma_num)
min_pval_i = sp.argmin(r['ps'])
step_dict = {}
step_dict['min_pval_i'] = min_pval_i
step_dict['min_pval'] = r['ps'][min_pval_i]
step_dict['mahalanobis_rss'] = r['rss'][min_pval_i]
step_dict['min_pval_chr_pos'] = genotype.get_chr_pos_from_index(min_pval_i)
step_dict['h0_rss'] = h0_rss
ll = ml_dict['max_ll']
step_dict['max_ll'] = ll
num_par = lmm.X.shape[1] + 1
step_dict['num_snps'] = num_snps
step_dict['num_par'] = num_par
(bic, extended_bic, modified_bic) = _calc_bic_(ll, num_snps, num_par, lmm.n) # Calculate the BICs
step_dict['ebic'] = extended_bic
step_dict['mbic'] = modified_bic
step_dict['bic'] = bic
step_dict['ve'] = reml_dict['ve']
step_dict['vg'] = reml_dict['vg']
p_her = reml_dict['pseudo_heritability']
step_dict['pseudo_heritability'] = p_her
step_dict['rss'] = float(reml_dict['rss'])
step_dict['reml_mahalanobis_rss'] = reml_dict['mahalanobis_rss']
perc_var_expl = 1.0 - (step_dict['rss'] / h0_rss)
step_dict['perc_var_expl'] = perc_var_expl
step_dict['remain_perc_gen_var'] = (1 - perc_var_expl) * p_her
step_dict['remain_perc_err_var'] = (1 - perc_var_expl) * (1 - p_her)
# Calculate maximum cofactor p-value\
log.debug('Updating the cofactor p-values')
cof_pvals = []
cof_chrom_pos_pval_list = []
for i, snp in enumerate(cof_snps):
t_cofactors = cof_snps[:]
del t_cofactors[i]
lmm.set_factors(t_cofactors)
res = lmm._emmax_f_test_([snp], H_sqrt_inv, emma_num=0)
cof_pval = res['ps'][0]
cof_pvals.append(cof_pval)
cof_chrom_pos_pval_list.append((cof_chr_pos_list[i][0], cof_chr_pos_list[i][1], -math.log10(cof_pval)))
for i, pval in zip(cof_indices, cof_pvals):
r['ps'][i] = pval
if len(cof_pvals):
step_dict['max_cof_pval'] = max(cof_pvals)
else:
step_dict['max_cof_pval'] = 0.0
# step_dict['cofactor_snps'] = cof_snps
log.info('Took %s' % t.stop(True))
return {'stats':step_dict, 'res':r, 'upd_H_sqrt_inv':H_sqrt_inv,'cof_chrom_pos_pval_list':cof_chrom_pos_pval_list}