R/parallel_line_st.R

In ailizhe/BioassayAnalyse: for the statistical analysis of bioassay data based on the methods recorded in Chinese Pharmacopeia 2020 Edition (1431)

parallel_line_st<-function(AT,sdose,tdose,ns,nt,ys,yt,ratio,method=c("random","block"),select=c("2.2","3.3","4.4","3.2","4.3")){
  #verifaction
  if(sum(ns)!=length(ys)|sum(nt)!=length(yt)|length(sdose)!=length(ns)|length(tdose)!=length(nt))
    return("error input");
  if(min(ns)!=max(ns))
    {local_interim<-c(which((rep(max(ns),length(ns))-ns)>0));
    miss_interim<-max(ns)-ns[local_interim];
    m_interim<-max(ns);
    for(i in 1:length(local_interim))
    {
     if(i==length(local_interim))
       {y_interim<-c(ys[1:((local_interim[i]-1)*m_interim+ns[local_interim[i]])],rep(NA,miss_interim[i]));
       ys<-y_interim;}
     if(i!=length(local_interim))
        {y_interim<-c(ys[1:((local_interim[i]-1)*m_interim+ns[local_interim[i]])],rep(NA,miss_interim[i]),ys[((local_interim[i]-1)*m_interim+ns[local_interim[i]]+1):length(ys)]);
        ys<-y_interim;}
     i<-i+1;
     }
     ns<-rep(max(ns),length(ns));
    }
  if(min(nt)!=max(nt))
    {local_interim<-c(which((rep(max(nt),length(nt))-nt)>0));
  miss_interim<-max(nt)-nt[local_interim];
  m_interim<-max(nt);
  for(i in 1:length(local_interim))
  {
    if(i==length(local_interim))
    {y_interim<-c(yt[1:((local_interim[i]-1)*m_interim+nt[local_interim[i]])],rep(NA,miss_interim[i]));
    yt<-y_interim;}
    if(i!=length(local_interim))
    {y_interim<-c(yt[1:((local_interim[i]-1)*m_interim+nt[local_interim[i]])],rep(NA,miss_interim[i]),yt[((local_interim[i]-1)*m_interim+nt[local_interim[i]]+1):length(yt)]);
    yt<-y_interim;}
    i<-i+1;
  }
  nt<-rep(max(nt),length(nt));
  }
  if(mean(ns)<mean(nt))
    {local_interim<-c(which((rep(max(nt),length(ns))-ns)>0));
  miss_interim<-max(nt)-ns[local_interim];
  m_interim<-max(nt);
  for(i in 1:length(local_interim))
  {
    if(i==length(local_interim))
    {y_interim<-c(ys[1:((local_interim[i]-1)*m_interim+ns[local_interim[i]])],rep(NA,miss_interim[i]));
    ys<-y_interim;}
    if(i!=length(local_interim))
    {y_interim<-c(ys[1:((local_interim[i]-1)*m_interim+ns[local_interim[i]])],rep(NA,miss_interim[i]),ys[((local_interim[i]-1)*m_interim+ns[local_interim[i]]+1):length(ys)]);
    ys<-y_interim;}
    i<-i+1;
  }
  ns<-rep(max(nt),length(ns));
  }
  if(mean(nt)<mean(ns))
    {local_interim<-c(which((rep(max(ns),length(nt))-nt)>0));
  miss_interim<-max(ns)-nt[local_interim];
  m_interim<-max(ns);
  for(i in 1:length(local_interim))
  {
    if(i==length(local_interim))
    {y_interim<-c(yt[1:((local_interim[i]-1)*m_interim+nt[local_interim[i]])],rep(NA,miss_interim[i]));
    yt<-y_interim;}
    if(i!=length(local_interim))
    {y_interim<-c(yt[1:((local_interim[i]-1)*m_interim+nt[local_interim[i]])],rep(NA,miss_interim[i]),yt[((local_interim[i]-1)*m_interim+nt[local_interim[i]]+1):length(yt)]);
    yt<-y_interim;}
    i<-i+1;
  }
  nt<-rep(max(ns),length(nt));
  }

  #summary as matrix
  data_matrix<-matrix(c(ys,yt),nrow=mean(ns));
  sname<-c("S1","S2","S3","S4");
  tname<-c("T1","T2","T3","T4");
  colnames(data_matrix)<-c(sname[1:length(ns)],tname[1:length(nt)]);
  rownames(data_matrix)<-c(1:mean(ns));

  #outlier Dixon Grubbs
  m<-length(data_matrix[,1]);
  k<-length(sdose)+length(tdose);
  Jstandrd<-c(0,0,0.988,0.889,0.780,0.698,0.637,0.683,0.635,0.597,0.679,0.642,0.615);
   if(m>=3&m<=7){
    for(i in 1:length(data_matrix[1,])){
      y_interim<-sort(data_matrix[,i]);
      Jmin1<-(y_interim[2]-y_interim[1])/(y_interim[m]-y_interim[1]);
      Jmax1<-(y_interim[m]-y_interim[m-1])/(y_interim[m]-y_interim[1]);
      if(Jmin1>Jstandrd[m]){data_matrix[which.min(data_matrix[,i]),i]<-NA}
      if(Jmax1>Jstandrd[m]){data_matrix[which.max(data_matrix[,i]),i]<-NA}
      i<-i+1;
    }
  }
   if(m>=8&m<=10){
    for(i in 1:length(data_matrix[1,])){
      y_interim<-sort(data_matrix[,i]);
      Jmin2<-(y_interim[2]-y_interim[1])/(y_interim[m-1]-y_interim[1]);
      Jmax2<-(y_interim[m]-y_interim[m-1])/(y_interim[m]-y_interim[2]);
      if(Jmin2>Jstandrd[m]){data_matrix[which.min(data_matrix[,i]),i]<-NA}
      if(Jmax2>Jstandrd[m]){data_matrix[which.max(data_matrix[,i]),i]<-NA}
      i<-i+1;
    }
  }
   if(m>=11&m<=13){
     for(i in 1:length(data_matrix[1,])){
       y_interim<-sort(data_matrix[,i]);
       Jmin3<-(y_interim[3]-y_interim[1])/(y_interim[m-1]-y_interim[1]);
       Jmax3<-(y_interim[m]-y_interim[m-3])/(y_interim[m]-y_interim[2]);
       if(Jmin3>Jstandrd[m]){data_matrix[which.min(data_matrix[,i]),i]<-NA}
       if(Jmax3>Jstandrd[m]){data_matrix[which.max(data_matrix[,i]),i]<-NA}
       i<-i+1;
     }
   }
   if(m>13){
     p<-1-0.01/(2*m);
     G<-(m-1)*qt(p,m-2)/(m*(m-2+qt(p,m-2)^2))^0.5;
     for(i in 1:length(data_matrix[1,])){
       y_interim<-data_matrix[,i];
       data_matrix[((y_interim-mean(y_interim))/sd(y_interim)>G),i]<-NA;
       i<-i+1;
     }
   }

  #missing fill
  f_correct<-sum(is.na(data_matrix[is.na(data_matrix)]));
   if(method=="random"&f_correct>0){
  for(i in 1:length(data_matrix[1,])){
    y_interim<-data_matrix[,i][!is.na(data_matrix[,i])];
    data_matrix[is.na(data_matrix[,i]),i]<-mean(y_interim);
    i<i+1;
   }
  }
   if(method=="block"&f_correct>0){
    if(f_correct==1){
      if(which(is.na(data_matrix))%%m==0){nrow<-m; ncol<-which(is.na(data_matrix))%/%m;}
      if(which(is.na(data_matrix))%%m!=0){nrow<-which(is.na(data_matrix))%%m;ncol<-which(is.na(data_matrix))%/%m+1;}
      c<-sum(data_matrix[-nrow,ncol]);
      r<-sum(data_matrix[nrow,-ncol]);
      k<-length(sdose)+length(tdose);
      g<-sum(data_matrix[!is.na(data_matrix)]);
      data_matrix[is.na(data_matrix)]<-(k*c+m*r-g)/((k-1)*(m-1));
    }
    if(f_correct>1){
      n_interim<-which(is.na(data_matrix));
      data_matrix[n_interim]<-100;
      for(ii in 1:100){
        i<-1;
      for(i in 1:length(n_interim)){
        if(n_interim[i] %% m==0){nrow<-m;ncol<-n_interim[i]%/%m;}
        if(n_interim[i] %% m!=0){nrow<-n_interim[i]%%m;ncol<-n_interim[i]%/%m+1;}
        c<-sum(data_matrix[-nrow,ncol]);
        r<-sum(data_matrix[nrow,-ncol]);
        k<-length(sdose)+length(tdose);
        g<-sum(data_matrix)-data_matrix[nrow,ncol];
        data_matrix[n_interim[i]]<-(k*c+m*r-g)/((k-1)*(m-1));
        i<-i+1;
      }
        ii<-ii+1;
      }
    }
   }

  #ANOVA
   if(method=="random"){
    ss_total<-sum(data_matrix^2)-sum(data_matrix)^2/(m*k);f_total<-m*k-1;ms_total<-ss_total/f_total;
    ss_dose<-sum(colSums(data_matrix)^2)/m-sum(data_matrix)^2/(m*k);f_dose<-k-1;ms_dose<-ss_dose/f_dose;
    ss_error<-ss_total-ss_dose;f_error<-(m-1)*k-f_correct;ms_error<-ss_error/f_error;
    ss1<-c(ss_dose,ss_error,ss_total);
    df1<-c(f_dose,f_error,f_total);
    ms1<-c(ms_dose,ms_error,ms_total);
    F1<-c(ms_dose/ms_error,NA,NA);
    p1<-c(1-pf(F1[1],f_dose,f_error),NA,NA);
    ANOVA_data1<-data.frame(Variation=c("Dose","Error","Total"),SS=ss1,Df=df1,MS=ms1,F=F1,P=p1);
   }
   if(method=="block"){
    ss_total<-sum(data_matrix^2)-sum(data_matrix)^2/(m*k);f_total<-m*k-1;ms_total<-ss_total/f_total;
    ss_dose<-sum(colSums(data_matrix)^2)/m-sum(data_matrix)^2/(m*k);f_dose<-k-1;ms_dose<-ss_dose/f_dose;
    ss_block<-sum(rowSums(data_matrix)^2)/k-sum(data_matrix)^2/(m*k);f_block<-m-1;ms_block<-ss_block/f_block;
    ss_error<-ss_total-ss_dose-ss_block;f_error<-(k-1)*(m-1)-f_correct;ms_error<-ss_error/f_error;
    ss1<-c(ss_dose,ss_block,ss_error,ss_total);
    df1<-c(f_dose,f_block,f_error,f_total);
    ms1<-c(ms_dose,ms_block,ms_error,ms_total);
    F1<-c(ms_dose/ms_error,ms_block/ms_error,NA,NA);
    p1<-c(1-pf(F1[1],f_dose,f_error),1-pf(F1[2],f_block,f_error),NA,NA);
    ANOVA_data1<-data.frame(Variation=c("Dose","Block","Error","Total"),SS=ss1,Df=df1,MS=ms1,F=F1,P=p1);
    }

  #Reliability
  c_correct2.2<-matrix(c(-1,-1,1,1,-1,1,-1,1,1,-1,-1,1),nrow=3,byrow=T);
  c_correct3.3<-matrix(c(-1,-1,-1,1,1,1,-1,0,1,-1,0,1,1,0,-1,-1,0,1,1,-2,1,1,-2,1,-1,2,-1,1,-2,1),nrow=5,byrow=T);
  c_correct4.4<-matrix(c(rep(-1,4),rep(1,4),-3,-1,1,3,-3,-1,1,3,3,1,-1,-3,-3,-1,1,3,1,-1,-1,1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1),nrow=5,byrow=T);
  c_correct3.2<-matrix(c(-2,-2,-2,3,3,-2,0,2,-1,1,1,0,-1,-2,2,1,-2,1,0,0),nrow=4,byrow=T);
  c_correct4.3<-matrix(c(rep(-3,4),rep(4,3),-3,-1,1,3,-2,0,2,3,1,-1,-3,-5,0,5,3,-3,-3,3,2,-4,2,-1,1,1,-1,1,-2,1),nrow=5,byrow=T);
   if(select=="2.2"){
    ms_preparation<-sum(colSums(data_matrix)*c_correct2.2[1,])^2/(m*sum(c_correct2.2[1,]^2));
    ms_regression<-sum(colSums(data_matrix)*c_correct2.2[2,])^2/(m*sum(c_correct2.2[2,]^2));
    ms_line<-sum(colSums(data_matrix)*c_correct2.2[3,])^2/(m*sum(c_correct2.2[3,]^2));
    F_preparation<-ms_preparation/ms_error;
    F_regression<-ms_regression/ms_error;
    F_line<-ms_line/ms_error;
    p_preparation<-1-pf(F_preparation,1,f_error);
    p_regression<-1-pf(F_regression,1,f_error);
    p_line<-1-pf(F_line,1,f_error);
    ss2<-c(ms_preparation,ms_regression,ms_line);
    df2<-c(1,1,1);
    ms2<-ss2;
    F2<-c(ms_preparation/ms_error,ms_regression/ms_error,ms_line/ms_error);
    p2<-c(1-pf(F2[1],1,f_error),1-pf(F2[2],1,f_error),1-pf(F2[3],1,f_error));
    ANOVA_data2<-data.frame(Variation=c("Preparation","Regression","Line"),SS=ss2,Df=df2,MS=ms2,F=F2,P=p2);
   }
   if(select=="3.3"){
    ms_preparation<-sum(colSums(data_matrix)*c_correct3.3[1,])^2/(m*sum(c_correct3.3[1,]^2));
    ms_regression<-sum(colSums(data_matrix)*c_correct3.3[2,])^2/(m*sum(c_correct3.3[2,]^2));
    ms_line<-sum(colSums(data_matrix)*c_correct3.3[3,])^2/(m*sum(c_correct3.3[3,]^2));
    ms_conic<-sum(colSums(data_matrix)*c_correct3.3[4,])^2/(m*sum(c_correct3.3[4,]^2));
    ms_inverseconic<-sum(colSums(data_matrix)*c_correct3.3[5,])^2/(m*sum(c_correct3.3[5,]^2));
    F_preparation<-ms_preparation/ms_error;
    F_regression<-ms_regression/ms_error;
    F_line<-ms_line/ms_error;
    F_conic<-ms_conic/ms_error;
    F_inverseconic<-ms_inverseconic/ms_error;
    p_preparation<-1-pf(F_preparation,1,f_error);
    p_regression<-1-pf(F_regression,1,f_error);
    p_line<-1-pf(F_line,1,f_error);
    p_conic<-1-pf(F_conic,1,f_error);
    p_inverseconic<-1-pf(F_inverseconic,1,f_error);
    ss2<-c(ms_preparation,ms_regression,ms_line,ms_conic,ms_inverseconic);
    df2<-c(1,1,1,1,1);
    ms2<-ss2;
    F2<-c(ms_preparation/ms_error,ms_regression/ms_error,ms_line/ms_error,ms_conic/ms_error,ms_inverseconic/ms_error);
    p2<-c(1-pf(F2[1],1,f_error),1-pf(F2[2],1,f_error),1-pf(F2[3],1,f_error),1-pf(F2[4],1,f_error),1-pf(F2[5],1,f_error));
    ANOVA_data2<-data.frame(Variation=c("Preparation","Regression","Line","Conic","InverseConic"),SS=ss2,Df=df2,MS=ms2,F=F2,P=p2);
   }
   if(select=="4.4"){
     ms_preparation<-sum(colSums(data_matrix)*c_correct4.4[1,])^2/(m*sum(c_correct4.4[1,]^2));
     ms_regression<-sum(colSums(data_matrix)*c_correct4.4[2,])^2/(m*sum(c_correct4.4[2,]^2));
     ms_line<-sum(colSums(data_matrix)*c_correct4.4[3,])^2/(m*sum(c_correct4.4[3,]^2));
     ms_conic<-sum(colSums(data_matrix)*c_correct4.4[4,])^2/(m*sum(c_correct4.4[4,]^2));
     ms_inverseconic<-sum(colSums(data_matrix)*c_correct4.4[5,])^2/(m*sum(c_correct4.4[5,]^2));
     F_preparation<-ms_preparation/ms_error;
     F_regression<-ms_regression/ms_error;
     F_line<-ms_line/ms_error;
     F_conic<-ms_conic/ms_error;
     F_inverseconic<-ms_inverseconic/ms_error;
     p_preparation<-1-pf(F_preparation,1,f_error);
     p_regression<-1-pf(F_regression,1,f_error);
     p_line<-1-pf(F_line,1,f_error);
     p_conic<-1-pf(F_conic,1,f_error);
     p_inverseconic<-1-pf(F_inverseconic,1,f_error);
     ss2<-c(ms_preparation,ms_regression,ms_line,ms_conic,ms_inverseconic);
     df2<-c(1,1,1,1,1);
     ms2<-ss2;
     F2<-c(ms_preparation/ms_error,ms_regression/ms_error,ms_line/ms_error,ms_conic/ms_error,ms_inverseconic/ms_error);
     p2<-c(1-pf(F2[1],1,f_error),1-pf(F2[2],1,f_error),1-pf(F2[3],1,f_error),1-pf(F2[4],1,f_error),1-pf(F2[5],1,f_error));
     ANOVA_data2<-data.frame(Variation=c("Preparation","Regression","Line","Conic","InverseConic"),SS=ss2,Df=df2,MS=ms2,F=F2,P=p2);
   }
   if(select=="3.2"){
    ms_preparation<-sum(colSums(data_matrix)*c_correct3.2[1,])^2/(m*sum(c_correct3.2[1,]^2));
    ms_regression<-sum(colSums(data_matrix)*c_correct3.2[2,])^2/(m*sum(c_correct3.2[2,]^2));
    ms_line<-sum(colSums(data_matrix)*c_correct3.2[3,])^2/(m*sum(c_correct3.2[3,]^2));
    ms_conic<-sum(colSums(data_matrix)*c_correct3.2[4,])^2/(m*sum(c_correct3.2[4,]^2));
    F_preparation<-ms_preparation/ms_error;
    F_regression<-ms_regression/ms_error;
    F_line<-ms_line/ms_error;
    F_conic<-ms_conic/ms_error;
    p_preparation<-1-pf(F_preparation,1,f_error);
    p_regression<-1-pf(F_regression,1,f_error);
    p_line<-1-pf(F_line,1,f_error);
    p_conic<-1-pf(F_conic,1,f_error);
    ss2<-c(ms_preparation,ms_regression,ms_line,ms_conic);
    df2<-c(1,1,1,1);
    ms2<-ss2;
    F2<-c(ms_preparation/ms_error,ms_regression/ms_error,ms_line/ms_error,ms_conic/ms_error);
    p2<-c(1-pf(F2[1],1,f_error),1-pf(F2[2],1,f_error),1-pf(F2[3],1,f_error),1-pf(F2[4],1,f_error));
    ANOVA_data2<-data.frame(Variation=c("Preparation","Regression","Line","Conic"),SS=ss2,Df=df2,MS=ms2,F=F2,P=p2);
   }
   if(select=="4.3"){
    ms_preparation<-sum(colSums(data_matrix)*c_correct4.3[1,])^2/(m*sum(c_correct4.3[1,]^2));
    ms_regression<-sum(colSums(data_matrix)*c_correct4.3[2,])^2/(m*sum(c_correct4.3[2,]^2));
    ms_line<-sum(colSums(data_matrix)*c_correct4.3[3,])^2/(m*sum(c_correct4.3[3,]^2));
    ms_conic<-sum(colSums(data_matrix)*c_correct4.3[4,])^2/(m*sum(c_correct4.3[4,]^2));
    ms_inverseconic<-sum(colSums(data_matrix)*c_correct4.3[5,])^2/(m*sum(c_correct4.3[5,]^2));
    F_preparation<-ms_preparation/ms_error;
    F_regression<-ms_regression/ms_error;
    F_line<-ms_line/ms_error;
    F_conic<-ms_conic/ms_error;
    F_inverseconic<-ms_inverseconic/ms_error;
    p_preparation<-1-pf(F_preparation,1,f_error);
    p_regression<-1-pf(F_regression,1,f_error);
    p_line<-1-pf(F_line,1,f_error);
    p_conic<-1-pf(F_conic,1,f_error);
    p_inverseconic<-1-pf(F_inverseconic,1,f_error);
    ss2<-c(ms_preparation,ms_regression,ms_line,ms_conic,ms_inverseconic);
    df2<-c(1,1,1,1,1);
    ms2<-ss2;
    F2<-c(ms_preparation/ms_error,ms_regression/ms_error,ms_line/ms_error,ms_conic/ms_error,ms_inverseconic/ms_error);
    p2<-c(1-pf(F2[1],1,f_error),1-pf(F2[2],1,f_error),1-pf(F2[3],1,f_error),1-pf(F2[4],1,f_error),1-pf(F2[5],1,f_error));
    ANOVA_data2<-data.frame(Variation=c("Preparation","Regression","Line","Conic","InverseConic"),SS=ss2,Df=df2,MS=ms2,F=F2,P=p2);
  }

  #potency
  v_correct2.2<-c(rep(-1/2,2),rep(1/2,2));
  v_correct3.3<-c(rep(-1/3,3),rep(1/3,3));
  v_correct4.4<-c(rep(-1/4,4),rep(1/4,4));
  v_correct3.2<-c(rep(-1/3,3),rep(1/2,2));
  v_correct4.3<-c(rep(-1/4,4),rep(1/3,3));
  sum_data<-colSums(data_matrix);
  names(sum_data)<-NULL;
   if(select=="2.2"){
     v<-sum(sum_data*v_correct2.2);
     w<-1/2*(sum_data[4]-sum_data[3]+sum_data[2]-sum_data[1]);
     D<-sdose[2]/tdose[2];
     A<-1;B<-1;g<-(qt(0.975,f_error)^2)*ms_error*m/w^2;
     I<-log10(ratio);
     sm<-I/(w^2*(1-g))*(m*ms_error*((1-g)*A*w^2+B*v^2))^0.5;
     potency<-AT*D*10^(I*v/w);
     potency_low<-AT*10^(log10(D*10^(I*v/w))/(1-g)-qt(0.975,f_error)*sm);
     potency_up<-AT*10^(log10(D*10^(I*v/w))/(1-g)+qt(0.975,f_error)*sm);
   }
   if(select=="3.3"){
    v<-sum(sum_data*v_correct3.3);
    w<-1/4*(sum_data[6]-sum_data[4]+sum_data[3]-sum_data[1]);
    D<-sdose[3]/tdose[3];
    A<-2/3;B<-1/4;g<-(qt(0.975,f_error)^2)*ms_error*m/(4*w^2);
    I<-log10(ratio);
    sm<-I/(w^2*(1-g))*(m*ms_error*((1-g)*A*w^2+B*v^2))^0.5;
    potency<-AT*D*10^(I*v/w);
    potency_low<-AT*10^(log10(D*10^(I*v/w))/(1-g)-qt(0.975,f_error)*sm);
    potency_up<-AT*10^(log10(D*10^(I*v/w))/(1-g)+qt(0.975,f_error)*sm);
  }
   if(select=="4.4"){
    v<-sum(sum_data*v_correct4.4);
    w<-1/20*((sum_data[7]-sum_data[6]+sum_data[3]-sum_data[2])+3*(sum_data[8]-sum_data[5]+sum_data[4]-sum_data[1]));
    D<-sdose[4]/tdose[4];
    A<-1/2;B<-1/10;g<-(qt(0.975,f_error)^2)*ms_error*m/(10*w^2);
    I<-log10(ratio);
    sm<-I/(w^2*(1-g))*(m*ms_error*((1-g)*A*w^2+B*v^2))^0.5;
    potency<-AT*D*10^(I*v/w);
    potency_low<-AT*10^(log10(D*10^(I*v/w))/(1-g)-qt(0.975,f_error)*sm);
    potency_up<-AT*10^(log10(D*10^(I*v/w))/(1-g)+qt(0.975,f_error)*sm);
   }
   if(select=="3.2"){
    v<-sum(sum_data*v_correct3.2);
    w<-1/5*((sum_data[5]-sum_data[4])+2*(sum_data[3]-sum_data[1]));
    D<-sdose[3]/tdose[2]*(1/ratio^0.5);
    A<-5/6;B<-2/5;g<-2*(qt(0.975,f_error)^2)*ms_error*m/(5*w^2);
    I<-log10(ratio);
    sm<-I/(w^2*(1-g))*(m*ms_error*((1-g)*A*w^2+B*v^2))^0.5;
    potency<-AT*D*10^(I*v/w);
    potency_low<-AT*10^(log10(D*10^(I*v/w))/(1-g)-qt(0.975,f_error)*sm);
    potency_up<-AT*10^(log10(D*10^(I*v/w))/(1-g)+qt(0.975,f_error)*sm);
  }
   if(select=="4.3"){
    v<-sum(sum_data*v_correct4.3);
    w<-1/14*(2*(sum_data[7]-sum_data[5])+(sum_data[3]-sum_data[2])+3*(sum_data[4]-sum_data[1]));
    D<-sdose[4]/tdose[3]*(1/ratio^0.5);
    A<-7/12;B<-1/7;g<-(qt(0.975,f_error)^2)*ms_error*m/(7*w^2);
    I<-log10(ratio);
    sm<-I/(w^2*(1-g))*(m*ms_error*((1-g)*A*w^2+B*v^2))^0.5;
    potency<-AT*D*10^(I*v/w);
    potency_low<-AT*10^(log10(D*10^(I*v/w))/(1-g)-qt(0.975,f_error)*sm);
    potency_up<-AT*10^(log10(D*10^(I*v/w))/(1-g)+qt(0.975,f_error)*sm);
  }

  #return outcome
  outcome<-list(Data=data_matrix,ANOVA=ANOVA_data1,Reliability=ANOVA_data2,Potency=potency,Potency_95low=potency_low,Potency_95up=potency_up);
  return(outcome);
}