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Association analysis of complex diseases using triads, parent-child dyads and singleton monads

Multiplicative

FT.MULT = function(triad, dyad, monad)
{ Nsnp = nrow(triad)
     #3.Multiplicative ft
     ft.M <- function(x,c1,c2,c3,c4,k1,k2,k3,k4,t1,t2,t3,t4,N,M,S)
     {
          f1 <- (c1+k1+t1)/x[1]-(c2+k2+t2)/(1-x[1])-2*(N+M+S)*(x[2]-1)/(x[1]*x[2]+1-x[1])
          f2 <- (c3+k3+t3+2*c4+2*k4+2*t4)/x[2]-2*(N+M+S)*x[1]/(x[1]*x[2]+1-x[1])
          (f <- rbind(f1, f2))
     }

     #3.Multiplicative Jacobian
     Jac.M <- function(x,c1,c2,c3,c4,k1,k2,k3,k4,t1,t2,t3,t4,N,M,S)
     {
          J <- matrix(0,ncol=2,nrow=2)
          J[1,1]<- -(c1+k1+t1)/(x[1]^2)-(c2+k2+t2)/((1-x[1])^2)+2*(N+M+S)*(x[2]-1)^2/((x[1]*x[2]+1-x[1])^2)
          J[1,2]<- -2*(N+M+S)/((x[1]*x[2]+1-x[1])^2)
          J[2,1]<- J[1,2]
          J[2,2]<- -(c3+k3+t3+2*c4+2*k4+2*t4)/(x[2]^2)+2*(N+M+S)*x[1]^2/((x[1]*x[2]+1-x[1])^2)
          J
     }

     #3.Multiplicative Newton
     newton.M <- function(x,c1,c2,c3,c4,k1,k2,k3,k4,t1,t2,t3,t4,N,M,S)
     {
          max <- 1000
          eps <- 1e-10
          xx <- x
          for (ii in 1:max)
          {
               JJ <- Jac.M(xx,c1,c2,c3,c4,k1,k2,k3,k4,t1,t2,t3,t4,N,M,S)
               if (kappa(JJ)>1e+10)
               {
                    break
               }
               xx <- xx-solve(JJ)%*%ft.M(xx,c1,c2,c3,c4,k1,k2,k3,k4,t1,t2,t3,t4,N,M,S)
          }
          return(list(JJ,xx))
     }

     #3.Multiplicative Solve function
     Solve.M <- function(triad, dyad, monad, model)
     {
          p0 <- matrix(0,Nsnp,1)
          p1 <- matrix(0,Nsnp,1)
          psi1 <- matrix(0,Nsnp,1)
          LR.M <- matrix(0,Nsnp,1)
          LRT.M <- matrix(0,Nsnp,1)
          pvalue.M <- matrix(0,Nsnp,1)

          for (i in 1:Nsnp)
          {
               n <- array(0)
               m <- array(0)
               s <- array(0)

               #1st: Full Triad + Parent Child + Case only
               if (model==1)
               {
                    for (j in 1:10)
                    {
                         n[j] <- triad[i,j]
                    }
                    N <- triad[i,11]
                    for (j in 1:7)
                    {
                         m[j] <- dyad[i,j]
                    }
                    M <- dyad[i,8]
                    for (j in 1:3)
                    {
                         s[j] <- monad[i,j]
                    }
                    S <- monad[i,4]
               }

               #2nd: Full Triad + Parent Child
               if (model==2)
               {
                    for (j in 1:10)
                    {
                         n[j] <- triad[i,j]
                    }
                    N <- triad[i,11]
                    for (j in 1:7)
                    {
                         m[j] <- dyad[i,j]
                    }
                    M <- dyad[i,8]
                    for (j in 1:3)
                    {
                         s[j] <- 0
                    }
                    S <- 0
               }

               #3rd: Full Triad Only
               if (model==3)
               {
                    for (j in 1:10)
                    {
                         n[j] <- triad[i,j]
                    }
                    N <- triad[i,11]
                    for (j in 1:7)
                    {
                         m[j] <- 0
                    }
                    M <- 0
                    for (j in 1:3)
                    {
                         s[j] <- 0
                    }
                    S <- 0
               }

               c1 <- 4*n[1] + 3*n[2] + 3*n[3] + 2*n[4] + 2*n[5] + 2*n[6] + 2*n[7] + n[8] + n[9]
               c2 <- n[2] + n[3] + 2*n[4] + 2*n[5] + 2*n[6] + 2*n[7] + 3*n[8] + 3*n[9] + 4*n[10]
               c3 <- n[3] + n[4] + n[6] + n[8]
               c4 <- n[1] + n[2] + n[5]
               k1 <- 3*m[1] + 2*m[2] + 2*m[3] + m[4] + m[5] + m[6]
               k2 <- m[2] + m[3] + m[4] + 2*m[5] + 2*m[6] + 3*m[7]
               k3 <- m[2] + m[4] + m[6]
               k4 <- m[1] + m[3]
               t1 <- 2*s[3] + s[2]
               t2 <- s[2] + 2*s[1]
               t3 <- s[2]
               t4 <- s[3]


               #Multiplicative sol
               p0[i] <- (c1+k1+t1)/(c1+c2+k1+k2+t1+t2)
               x0 <- matrix(c(p0[i],0.5),nrow=2)
               rtn <- newton.M(x0,c1,c2,c3,c4,k1,k2,k3,k4,t1,t2,t3,t4,N,M,S)
               JJ <- do.call(rbind, rtn[1])
               sol <- do.call(rbind, rtn[2])
               if (norm(ft.M(sol,c1,c2,c3,c4,k1,k2,k3,k4,t1,t2,t3,t4,N,M,S))> 1e-10 | norm(sol) >1e+10 | sol[1] > 1 | sol[2] < 0)
               {
                    sol <- 0
                    p0[i] <- (c1+k1+t1)/(c1+c2+k1+k2+t1+t2)
                    p1[i] <- NA
                    psi1[i] <- NA
               }
               else
               {
                    p0[i] <- (c1+k1+t1)/(c1+c2+k1+k2+t1+t2)
                    p1[i] <- sol[1]
                    psi1[i] <- sol[2]
               }
               LR.M[i] <- (p0[i]/p1[i])^(c1+k1+t1)*((1-p0[i])/(1-p1[i]))^(c2+k2+t2)*(1/psi1[i])^(c3+k3+t3+2*c4+2*k4+2*t4)*(p1[i]*psi1[i]+1-p1[i])^(2*(N+M+S))
               LRT.M[i] <- round(-2*log(LR.M[i]),digits=3)
               pvalue.M[i] <- round(1 - pchisq(LRT.M[i], df = 1),digits=3)
          }

          result.M <- cbind(round(p0,digits=3), round(p1,digits=3), round(psi1,digits=3), LRT.M, pvalue.M)
          if (model==1) colnames(result.M) <- c('p0', 'p', 'psi1', 'FT+PC+CO LRT', 'p-value')
          if (model==2) colnames(result.M) <- c('p0', 'p', 'psi1', 'FT+PC LRT', 'p-value')
          if (model==3) colnames(result.M) <- c('p0', 'p', 'psi1', 'FT LRT', 'p-value')
          rownames(result.M) <- row.names(triad)
          return(result.M)
     }

     esult.M1 = Solve.M(triad, dyad, monad, model=1)
     result.M2 = Solve.M(triad, dyad, monad, model=2)
     result.M3 = Solve.M(triad, dyad, monad, model=3)
     return(cbind(result.M1, result.M2, result.M3))
}
Last Updated Date: 09/03/2013
Last Reviewed Date: 09/03/2013

Contact Information

Name: Dr Paul Albert
Chief and Senior Investigator
Biostatistics and Bioinformatics Branch
Phone: 301-496-5582
E-mail: albertp@mail.nih.gov

Staff Directory
Vision National Institutes of Health Home BOND National Institues of Health Home Home Storz Lab: Section on Environmental Gene Regulation Home Machner Lab: Unit on Microbial Pathogenesis Home Division of Intramural Population Health Research Home Bonifacino Lab: Section on Intracellular Protein Trafficking Home Lilly Lab: Section on Gamete Development Home Lippincott-Schwartz Lab: Section on Organelle Biology