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MATS_LRT.py
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MATS_LRT.py
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#This script generates the WinBug input files by Simulated RNA-Seq data
import re,os,sys,warnings,numpy,scipy,math,itertools;
from scipy import stats;
from numpy import *;
from multiprocessing import Pool;
from scipy.optimize import fmin_cobyla
from scipy.optimize import fmin_l_bfgs_b
from math import log;
numpy.random.seed(1231);
warnings.filterwarnings('ignore');
#ReadLength
#Dummy length here. Adapt to the new rMATS structure
read_length=50;
#JunctionLength
#Dummy length here. Adapt to the new rMATS structure
junction_length=84;
#Output folder
if len(sys.argv)<3:
print("Error: Less than two input parameters.");
else:
output_folder=sys.argv[2];
#MultiProcessor
MultiProcessor=1;
if len(sys.argv)>=4:
MultiProcessor=int(sys.argv[3]);
#splicing difference cutoff
cutoff=0.1;
if len(sys.argv)>=5:
cutoff=float(sys.argv[4]);
rho=0.9
#binomial MLE optimization functions
def logit(x):
if x<0.01:
x=0.01;
if x>0.99:
x=0.99;
return(log(x/(1-x)));
def logit_list(x_list):
res=[];
for x in x_list:
if x<0.01:
x=0.01;
if x>0.99:
x=0.99;
res.append(log(x/(1-x)));
return(res);
#Not use multivar in the MATS LRT
def myfunc_multivar(x,*args):
psi1=args[0];psi2=args[1];var1=args[2];var2=args[3];
sum1=0;sum2=0;
for i in range(len(psi1)):
sum1+=pow(logit((psi1[i]-psi2[i])/2+0.5)-logit((x[0]-x[1])/2+0.5),2)
sum1=sum1/var2/2;
return(sum1+0.1*0.5*(pow(rho,2))/(1-pow(rho,2))*(pow(stats.norm.ppf(x[0]),2)+pow(stats.norm.ppf(x[1]),2)-2*rho*stats.norm.ppf(x[0])*stats.norm.ppf(x[1])));
#return(sum1);
#Not use multivar in the MATS LRT
def myfunc_multivar_der(x,*args):
psi1=args[0];psi2=args[1];var1=args[2];var2=args[3];
sum1=0;sum2=0;
for i in range(len(psi1)):
sum1+=-2*(logit((psi1[i]-psi2[i])/2+0.5)-logit((x[0]-x[1])/2+0.5))/((x[0]-x[1])/2+0.5)/(0.5-(x[0]-x[1])/2)*0.5;
sum1=sum1/var1/2;
res1=sum1+0.1*0.5*(pow(rho,2))/(1-pow(rho,2))*(2*stats.norm.ppf(x[0])-2*rho*stats.norm.ppf(x[1]))/stats.norm.pdf(stats.norm.ppf(x[0]));
for i in range(len(psi2)):
sum2+=-2*(logit((psi1[i]-psi2[i])/2+0.5)-logit((x[0]-x[1])/2+0.5))/((x[0]-x[1])/2+0.5)/(0.5-(x[0]-x[1])/2)*(-0.5);
sum2=sum2/var2/2;
res2=sum2+0.1*0.5*(pow(rho,2))/(1-pow(rho,2))*(2*stats.norm.ppf(x[1])-2*rho*stats.norm.ppf(x[0]))/stats.norm.pdf(stats.norm.ppf(x[1]));
return(numpy.array([res1,res2]));
#note to me: change this in unpaired rMATS
def myfunc_1(x,*args):
I1=args[0][0];I2=args[0][1];S1=args[1][0];S2=args[1][1];beta1=args[2][0];beta2=args[2][1];var=args[3];effective_inclusion_length=args[4];effective_skipping_length=args[5];
inclusion_length=effective_inclusion_length;
skipping_length=effective_skipping_length;
new_psi1=inclusion_length*(x+cutoff)/(inclusion_length*(x+cutoff)+skipping_length*(1-(x+cutoff)));new_psi2=inclusion_length*x/(inclusion_length*x+skipping_length*(1-x));
binomial_sum=-1*(I1*log(new_psi1)+S1*log(1-new_psi1)+I2*log(new_psi2)+S2*log(1-new_psi2));
multivar_sum=0.1*0.5*(pow(rho,2))/(1-pow(rho,2))*(pow(stats.norm.ppf(x+cutoff),2)+pow(stats.norm.ppf(x),2)-2*rho*stats.norm.ppf(x+cutoff)*stats.norm.ppf(x))
return(binomial_sum+multivar_sum);
def myfunc_der_1(x,*args):
I1=args[0][0];I2=args[0][1];S1=args[1][0];S2=args[1][1];beta1=args[2][0];beta2=args[2][1];var=args[3];effective_inclusion_length=args[4];effective_skipping_length=args[5];
inclusion_length=effective_inclusion_length;
skipping_length=effective_skipping_length;
new_psi1=inclusion_length*(x+cutoff)/(inclusion_length*(x+cutoff)+skipping_length*(1-(x+cutoff)));new_psi2=inclusion_length*x/(inclusion_length*x+skipping_length*(1-x));
new_psi1_der=inclusion_length*skipping_length/pow(inclusion_length*(x+cutoff)+skipping_length*(1-(x+cutoff)),2);
new_psi2_der=inclusion_length*skipping_length/pow(inclusion_length*x+skipping_length*(1-x),2);
res1=-1*(I1/new_psi1-S1/(1-new_psi1))*new_psi1_der;
res1+=0.1*0.5*(pow(rho,2))/(1-pow(rho,2))*(2*stats.norm.ppf(x+cutoff)-2*rho*stats.norm.ppf(x))/stats.norm.pdf(stats.norm.ppf(x+cutoff))
res2=-1*(I2/new_psi2-S2/(1-new_psi2))*new_psi2_der;
res2+=0.1*0.5*(pow(rho,2))/(1-pow(rho,2))*(2*stats.norm.ppf(x)-2*rho*stats.norm.ppf(x+cutoff))/stats.norm.pdf(stats.norm.ppf(x));
return(numpy.array(res1+res2));
def myfunc_2(x, *args):
I1=args[0][0];I2=args[0][1];S1=args[1][0];S2=args[1][1];beta1=args[2][0];beta2=args[2][1];var=args[3];effective_inclusion_length=args[4];effective_skipping_length=args[5];
inclusion_length=effective_inclusion_length;
skipping_length=effective_skipping_length;
new_psi1=inclusion_length*(x)/(inclusion_length*(x)+skipping_length*(1-(x)));new_psi2=inclusion_length*(x+cutoff)/(inclusion_length*(x+cutoff)+skipping_length*(1-(x+cutoff)));
binomial_sum=-1*(I1*log(new_psi1)+S1*log(1-new_psi1)+I2*log(new_psi2)+S2*log(1-new_psi2));
multivar_sum=0.1*0.5*(pow(rho,2))/(1-pow(rho,2))*(pow(stats.norm.ppf(x),2)+pow(stats.norm.ppf(x+cutoff),2)-2*rho*stats.norm.ppf(x)*stats.norm.ppf(x+cutoff))
return(binomial_sum+multivar_sum);
def myfunc_der_2(x,*args):
I1=args[0][0];I2=args[0][1];S1=args[1][0];S2=args[1][1];beta1=args[2][0];beta2=args[2][1];var=args[3];effective_inclusion_length=args[4];effective_skipping_length=args[5];
inclusion_length=effective_inclusion_length;
skipping_length=effective_skipping_length;
new_psi1=inclusion_length*x/(inclusion_length*x+skipping_length*(1-x));new_psi2=inclusion_length*(x+cutoff)/(inclusion_length*(x+cutoff)+skipping_length*(1-(x+cutoff)));
new_psi1_der=inclusion_length*skipping_length/pow(inclusion_length*x+skipping_length*(1-x),2);
new_psi2_der=inclusion_length*skipping_length/pow(inclusion_length*(x+cutoff)+skipping_length*(1-(x+cutoff)),2);
res1=-1*(I1/new_psi1-S1/(1-new_psi1))*new_psi1_der;
res1+=0.1*0.5*(pow(rho,2))/(1-pow(rho,2))*(2*stats.norm.ppf(x)-2*rho*stats.norm.ppf((x+cutoff)))/stats.norm.pdf(stats.norm.ppf(x))
res2=-1*(I2/new_psi2-S2/(1-new_psi2))*new_psi2_der;
res2+=0.1*0.5*(pow(rho,2))/(1-pow(rho,2))*(2*stats.norm.ppf((x+cutoff))-2*rho*stats.norm.ppf(x))/stats.norm.pdf(stats.norm.ppf((x+cutoff)));
return(numpy.array(res1+res2));
def myfunc_individual(x,*args):
I1=args[0][0];I2=args[0][1];S1=args[1][0];S2=args[1][1];beta1=args[2][0];beta2=args[2][1];var=args[3];effective_inclusion_length=args[4];effective_skipping_length=args[5];
inclusion_length=effective_inclusion_length;
skipping_length=effective_skipping_length;
new_psi1=inclusion_length*x[0]/(inclusion_length*x[0]+skipping_length*(1-x[0]));new_psi2=inclusion_length*x[1]/(inclusion_length*x[1]+skipping_length*(1-x[1]));
binomial_sum=-1*(I1*log(new_psi1)+S1*log(1-new_psi1)+I2*log(new_psi2)+S2*log(1-new_psi2));
multivar_sum=0.1*0.5*(pow(rho,2))/(1-pow(rho,2))*(pow(stats.norm.ppf(x[0]),2)+pow(stats.norm.ppf(x[1]),2)-2*rho*stats.norm.ppf(x[0])*stats.norm.ppf(x[1]))
return(binomial_sum+multivar_sum);
def myfunc_individual_der(x,*args):
I1=args[0][0];I2=args[0][1];S1=args[1][0];S2=args[1][1];beta1=args[2][0];beta2=args[2][1];var=args[3];effective_inclusion_length=args[4];effective_skipping_length=args[5];
inclusion_length=effective_inclusion_length;
skipping_length=effective_skipping_length;
new_psi1=inclusion_length*x[0]/(inclusion_length*x[0]+skipping_length*(1-x[0]));new_psi2=inclusion_length*x[1]/(inclusion_length*x[1]+skipping_length*(1-x[1]));
new_psi1_der=inclusion_length*skipping_length/pow(inclusion_length*x[0]+skipping_length*(1-x[0]),2);
new_psi2_der=inclusion_length*skipping_length/pow(inclusion_length*x[1]+skipping_length*(1-x[1]),2);
res1=-1*(I1/new_psi1-S1/(1-new_psi1))*new_psi1_der;
res1+=0.1*0.5*(pow(rho,2))/(1-pow(rho,2))*(2*stats.norm.ppf(x[0])-2*rho*stats.norm.ppf(x[1]))/stats.norm.pdf(stats.norm.ppf(x[0]))
res2=-1*(I2/new_psi2-S2/(1-new_psi2))*new_psi2_der;
res2+=0.1*0.5*(pow(rho,2))/(1-pow(rho,2))*(2*stats.norm.ppf(x[1])-2*rho*stats.norm.ppf(x[0]))/stats.norm.pdf(stats.norm.ppf(x[1]));
return(numpy.array([res1,res2]));
def myfunc_likelihood(x, args):
I1=args[0][0];I2=args[0][1];S1=args[1][0];S2=args[1][1];beta1=args[2][0];beta2=args[2][1];var=args[3];
sum=0;N1=I1+S1;N2=I2+S2;
if (N1+N2)==0:
return(0);
sum+=-0.5*((I1-N1*x[0])*(I1-N1*x[0])/(N1*x[0])+(S1-N1*(1-x[0]))*(S1-N1*(1-x[0]))/(N1*(1-x[0])));
sum+=-0.5*((I2-N2*x[1])*(I2-N2*x[1])/(N2*x[1])+(S2-N2*(1-x[1]))*(S2-N2*(1-x[1]))/(N2*(1-x[1])));
sum+=pow(logit(beta1)-logit(beta2)-logit(x[0])+logit(x[1]),2);
return(sum);
def MLE_iteration_constrain(i1,i2,s1,s2,effective_inclusion_length,effective_skipping_length):
psi1=vec2psi(i1,s1,effective_inclusion_length,effective_skipping_length);psi2=vec2psi(i2,s2,effective_inclusion_length,effective_skipping_length);
iter_cutoff=1;iter_maxrun=100;count=0;previous_sum=0;
while((iter_cutoff>0.01)&(count<=iter_maxrun)):
count+=1;
#iteration of beta
beta_0=sum(psi1)/len(psi1);
beta_1=sum(psi2)/len(psi2);
var1=0;var2=0;
current_sum=0;likelihood_sum=0;
new_psi1=[];new_psi2=[];
if (sum(psi1)/len(psi1))>(sum(psi2)/len(psi2)):#minize psi2 if this is the case
xopt = fmin_l_bfgs_b(myfunc_1,[sum(psi2)/len(psi2)],myfunc_der_1,args=[[i1[0],i2[0]],[s1[0],s2[0]],[beta_0,beta_1],var1,effective_inclusion_length,effective_skipping_length],bounds=[[0.001,0.999-cutoff]],iprint=-1)
theta2 = max(min(float(xopt[0]),1-cutoff),0);theta1=theta2+cutoff;
else:#minize psi1 if this is the case
xopt = fmin_l_bfgs_b(myfunc_2,[sum(psi1)/len(psi1)],myfunc_der_2,args=[[i1[0],i2[0]],[s1[0],s2[0]],[beta_0,beta_1],var1,effective_inclusion_length,effective_skipping_length],bounds=[[0.001,0.999-cutoff]],iprint=-1)
theta1 = max(min(float(xopt[0]),1-cutoff),0);theta2=theta1+cutoff;
#Debug;print('constrain_1xopt');print('theta');print(theta1);print(theta2);print(xopt);
current_sum+=float(xopt[1]);
new_psi1.append(theta1);new_psi2.append(theta2);
psi1=new_psi1;psi2=new_psi2;
if count>1:
iter_cutoff=abs(previous_sum-current_sum)/abs(previous_sum);
previous_sum=current_sum;
#Debug;print('constrain');print(theta1);print(theta2);print(psi1);print(psi2);print(current_sum);print(likelihood_sum);
#print('constrain');print(xopt);print(theta1);print(theta2);
return([current_sum,[psi1,psi2,beta_0,beta_1,var1,var2]]);
def MLE_iteration(i1,i2,s1,s2,effective_inclusion_length,effective_skipping_length):
psi1=vec2psi(i1,s1,effective_inclusion_length,effective_skipping_length);psi2=vec2psi(i2,s2,effective_inclusion_length,effective_skipping_length);
iter_cutoff=1;iter_maxrun=100;count=0;previous_sum=0;
while((iter_cutoff>0.01)&(count<=iter_maxrun)):
count+=1;
#iteration of beta
beta_0=sum(psi1)/len(psi1);
beta_1=sum(psi2)/len(psi2);
var1=0;var2=0;
current_sum=0;likelihood_sum=0;
new_psi1=[];new_psi2=[];
#Debug;print('unconstrain_1xopt');
for i in range(len(psi1)):
xopt = fmin_l_bfgs_b(myfunc_individual,[psi1[i],psi2[i]],myfunc_individual_der,args=[[i1[i],i2[i]],[s1[i],s2[i]],[beta_0,beta_1],var1,effective_inclusion_length,effective_skipping_length],bounds=[[0.01,0.99],[0.01,0.99]],iprint=-1);
new_psi1.append(float(xopt[0][0]));current_sum+=float(xopt[1]);
new_psi2.append(float(xopt[0][1]));
#Debug;print(xopt);
likelihood_sum+=myfunc_likelihood([new_psi1[i],new_psi2[i]],[[i1[i],i2[i]],[s1[i],s2[i]],[beta_0,beta_1],var1]);
psi1=new_psi1;psi2=new_psi2;
#Debug;print('count');print(count);print('previous_sum');print(previous_sum);print('current_sum');print(current_sum);
if count>1:
iter_cutoff=abs(previous_sum-current_sum)/abs(previous_sum);
previous_sum=current_sum;
if count>iter_maxrun:
return([current_sum,[psi1,psi2,0,0,var1,var2]]);
#print('unconstrain');print(xopt);
return([current_sum,[psi1,psi2,beta_0,beta_1,var1,var2]]);
#Random Sampling Function
def likelihood_test(i1,i2,s1,s2,effective_inclusion_length,effective_skipping_length,flag):
if flag==0:
return(1);
else:
res=MLE_iteration(i1,i2,s1,s2,effective_inclusion_length,effective_skipping_length);
if abs(res[1][2]-res[1][3])<=cutoff:
#Debug;print('1<=cutoff');print(res);print((res[1][2]-res[1][3]));
return(1);
else:
res_constrain=MLE_iteration_constrain(i1,i2,s1,s2,effective_inclusion_length,effective_skipping_length);
#Debug;print('2>cutoff');print('res');print(res);print('res_constrain');print(res_constrain);
#Debug;print(abs(res_constrain[0]-res[0]));print('2end');
return(1-scipy.stats.chi2.cdf(2*(abs(res_constrain[0]-res[0])),1));
#MultiProcessorFunction
def MultiProcessorPool(n_original_diff):
i1=n_original_diff[0];i2=n_original_diff[1];s1=n_original_diff[2];s2=n_original_diff[3];effective_inclusion_length=n_original_diff[4];effective_skipping_length=n_original_diff[5];flag=n_original_diff[6];
P=likelihood_test(i1,i2,s1,s2,effective_inclusion_length,effective_skipping_length,flag);
return(P);
#Function for vector handling
def vec2float(vec):
res=[];
for i in vec:
res.append(float(i));
return(res);
def vec2sum(vec):
res=0;
for i in vec:
res+=float(i);
return([res]);
def vecprod(vec):
res=1;
for i in vec:
res=res*i;
return(res);
def vec2remove0psi(inc,skp):
res1=[];res2=[];
for i in range(len(inc)):
if (inc[i]!=0) | (skp[i]!=0):
res1.append(inc[i]);res2.append(skp[i]);
return([res1,res2]);
def vec2psi(inc,skp,effective_inclusion_length,effective_skipping_length):
psi=[];
inclusion_length=effective_inclusion_length;
skipping_length=effective_skipping_length;
for i in range(len(inc)):
if (float(inc[i])+float(skp[i]))==0:
psi.append(0.5);
else:
psi.append(float(inc[i])/inclusion_length/(float(inc[i])/inclusion_length+float(skp[i])/skipping_length));
return(psi);
def vec210(vec):
res=[];
for i in vec:
if i>0:
res.append(1);
else:
res.append(-1);
return(res);
def myttest(vec1,vec2):
if (len(vec1)==1) & (len(vec2)==1):
res=stats.ttest_ind([vec1[0],vec1[0]],[vec2[0],vec2[0]]);
else:
res=stats.ttest_ind(vec1,vec2);
return(res);
ifile=open(sys.argv[1]);
title=ifile.readline();
#analyze the title of the inputed data file to find the information of how much simulation are involved
#the min simulated round is 10, each time it increases by 10 times
element=re.findall('[^ \t\n]+',title);
ofile=open(output_folder+'/rMATS_Result_P.txt','w');
ofile.write(title[:-1]+'\tPValue'+'\n');
list_n_original_diff=[];probability=[];psi_list_1=[];psi_list_2=[];rho_list=[];psi1_for_rho_list=[];psi2_for_rho_list=[];
ilines=ifile.readlines();
for i in range(len(ilines)):
element=re.findall('[^ \t\n]+',ilines[i]);
inc1=re.findall('[^,]+',element[1]);skp1=re.findall('[^,]+',element[2]);inc2=re.findall('[^,]+',element[3]);skp2=re.findall('[^,]+',element[4]);
#Dummy effective_inclusion_length and flanking exon length here. Adapt to the new rMATS structure
effective_inclusion_length=int(element[5]);
effective_skipping_length=int(element[6]);
#inc1=vec2float(inc1);skp1=vec2float(skp1);inc2=vec2float(inc2);skp2=vec2float(skp2);
inc1=vec2sum(inc1);skp1=vec2sum(skp1);inc2=vec2sum(inc2);skp2=vec2sum(skp2);
if ((vecprod(inc1)+vecprod(skp1))==0) | ((vecprod(inc2)+vecprod(skp2))==0):
list_n_original_diff.append([inc1,inc2,skp1,skp2,effective_inclusion_length,effective_skipping_length,0]);
else:
psi1=vec2psi(inc1,skp1,effective_inclusion_length,effective_skipping_length);psi2=vec2psi(inc2,skp2,effective_inclusion_length,effective_skipping_length);
for i in range(len(psi1)):
if len(psi1_for_rho_list)<=i:
psi1_for_rho_list.append([]);
psi1_for_rho_list[i].append(psi1[i]);
for i in range(len(psi2)):
if len(psi2_for_rho_list)<=i:
psi2_for_rho_list.append([]);
psi2_for_rho_list[i].append(psi2[i]);
psi_list_1.append(sum(inc1)/(sum(inc1)+sum(skp1)));
psi_list_2.append(sum(inc2)/(sum(inc2)+sum(skp2)));
#temp1=vec2remove0psi(inc1,skp1);temp2=vec2remove0psi(inc2,skp2);
#inc1=temp1[0];skp1=temp1[1];inc2=temp2[0];skp2=temp2[1];
list_n_original_diff.append([inc1,inc2,skp1,skp2,effective_inclusion_length,effective_skipping_length,1]);
#if i>2:
# break;
#rho_list for paired data
for i in range(len(psi1_for_rho_list)):
this_rho=stats.pearsonr(numpy.array(psi1_for_rho_list[i]),numpy.array(psi2_for_rho_list[i]));this_rho=this_rho[0];
if this_rho>0.9:
this_rho=0.9;
rho_list.append(this_rho);
rho=stats.pearsonr(numpy.array(psi_list_1),numpy.array(psi_list_2));rho=rho[0];
if rho>0.9:
rho=0.9;
#rho_list=[0.95,0.95,0.95,0.95];
#rho_list=[0,0,0,0];
rho=0.9;
#print('rho');print(rho);
if MultiProcessor>1:
pool=Pool(processes=MultiProcessor);
probability=pool.map(MultiProcessorPool,list_n_original_diff);
else:
for i in range(len(list_n_original_diff)):
#print(list_n_original_diff[i]);
probability.append(MultiProcessorPool(list_n_original_diff[i]));
#print(probability);
index=0;
for i in range(len(ilines)):
element=re.findall('[^ \t\n]+',ilines[i]);
ofile.write(ilines[i][:-1]+'\t'+str(probability[i])+'\n');
ofile.close();