R/bcontSurvGunivL_ExcessHazard.R

In GJRM: Generalised Joint Regression Modelling

bcontSurvGunivL_ExcessHazard <- function(params, respvec, VC, ps, AT = FALSE){
  p1 <- p2 <- pdf1 <- pdf2 <- c.copula.be2 <- c.copula.be1 <- c.copula2.be1be2 <- NA

  n <- VC$n
  
  # Only c1 and c2 needed in LEFT censoring case 
  c1 <- VC$hrate
  c2 <- exp(-VC$d.lchrate)

  
  
  # C.i <- VC$indvU*(-VC$d.lchrate) + VC$indvR*(-VC$d.lchrate)

  
  #################################################################################   
  
  
  
  
  
  monP <- monP1 <- monP2 <- k <- 0; V <- list()
  
  etad <- etas1 <- etas2 <- l.ln <- NULL 
  
  params1 <- params[1:VC$X1.d2]
  params1[VC$mono.sm.pos] <- exp( params1[VC$mono.sm.pos] )
  
  eta1 <- VC$X1%*%params1
  Xd1P <- VC$Xd1%*%params1  
  
  
  indN <- as.numeric(Xd1P < 0) 
  
  #if(!is.null(VC$indexT)) print(table(indN))
  
  Xd1P <- ifelse(Xd1P < VC$min.dn, VC$min.dn, Xd1P ) 
  
  if( any(indN == TRUE) && !is.null(VC$indexT) ){
    
    monP22 <- matrix(0, length(params),length(params))
    
    for(i in 1:length(VC$pos.pb)){
      
      V[[i]] <- as.numeric(diff(params1[ VC$pos.pb[[i]] ]) < 0)
      monP22[ VC$pos.pb[[i]], VC$pos.pb[[i]] ] <- t(VC$D[[i]]*V[[i]])%*%VC$D[[i]]
      
    } 
    
    
    k <- VC$my.env$k
    
    monP2 <- k*monP22
    monP  <- k/2*crossprod(params, monP22)%*%params 
    monP1 <- k*(monP22%*%params)   
    
    VC$my.env$k <- k*2
    
    
  }
  
  
  
  ##################
  
  pd1  <- probmS(eta1, VC$margins[1], min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr) 
  
  p1       <- pd1$pr
  dS1eta1  <- pd1$dS
  d2S1eta1 <- pd1$d2S
  d3S1eta1 <- pd1$d3S
  
  ##################
  
  
  l.par <- VC$weights*( 
    
    VC$cens*log(c1*p1 - dS1eta1*Xd1P) + 
      
    (1 - VC$cens)*log( 1 - p1*c2 ) #+ 
    
    #C.i
    
  )   
  
  res   <- -sum(l.par)
  
  ##################
  
  der.par1 <- der2.par1 <- params1
  
  der.par1[-c( VC$mono.sm.pos )] <- 1
  der2.par1[-c( VC$mono.sm.pos )] <- 0
  
  der2eta1dery1b1 <- t(t(VC$Xd1)*der.par1)
  dereta1derb1    <- t(t(VC$X1)*der.par1)
  
  ##################
  
  dl.dbe1 <- -VC$weights*(   
    
    
    VC$cens*( c((c1*p1 - dS1eta1*Xd1P)^-1)*( c(c1*dS1eta1)*dereta1derb1 - c(d2S1eta1*Xd1P)*dereta1derb1 - c(dS1eta1)*der2eta1dery1b1 ) ) + 
      
    (1 - VC$cens)*-c( ( 1 - p1*c2 )^-1*dS1eta1*c2 )*dereta1derb1 # minus here in front from L censoring
      

  )
  
  
  
  
  G <- colSums(dl.dbe1)
  
  ########################
  ########################                                                                                                 
  
  
  H <-  -(   
    
      crossprod(c(VC$weights*VC$cens*( ( c1*p1 - dS1eta1*Xd1P )^-1*(c1*d2S1eta1) ))*dereta1derb1, dereta1derb1 ) +      
      
      crossprod(c(VC$weights*VC$cens*(-( c1*p1 - dS1eta1*Xd1P )^-1*(d3S1eta1*Xd1P)  ))*dereta1derb1, dereta1derb1 ) +   
      
      crossprod(c(VC$weights*VC$cens*(-( c1*p1 - dS1eta1*Xd1P )^-1*d2S1eta1 ))*dereta1derb1, der2eta1dery1b1 ) +   
      
      crossprod(c(VC$weights*VC$cens*(-( c1*p1 - dS1eta1*Xd1P )^-1*d2S1eta1 ))*der2eta1dery1b1, dereta1derb1 ) +   
      
      
      
      diag( colSums( t( t(c(VC$weights*VC$cens*( c1*p1 - dS1eta1*Xd1P )^-1*(c1*dS1eta1) )*VC$X1)*der2.par1 ) ) ) +  
      
      diag( colSums( t( t(c(VC$weights*VC$cens*-( c1*p1 - dS1eta1*Xd1P )^-1*(d2S1eta1*Xd1P) )*VC$X1)*der2.par1 ) ) ) + 
      
      diag( colSums( t( t(c(VC$weights*VC$cens*-( c1*p1 - dS1eta1*Xd1P )^-1*dS1eta1 )*VC$Xd1)*der2.par1 ) ) ) +        
      
      
      crossprod(c(VC$weights*VC$cens*(-( c1*p1 - dS1eta1*Xd1P )^-2*(c1*dS1eta1)^2 ))*dereta1derb1, dereta1derb1) +   
      
      crossprod(c(VC$weights*VC$cens*(-( c1*p1 - dS1eta1*Xd1P )^-2*(d2S1eta1*Xd1P)^2 ))*dereta1derb1, dereta1derb1) +   
      
      crossprod(c(VC$weights*VC$cens*(-( c1*p1 - dS1eta1*Xd1P )^-2*dS1eta1^2 ))*der2eta1dery1b1, der2eta1dery1b1) +     
      
      
      crossprod(c(VC$weights*VC$cens*(2*( c1*p1 - dS1eta1*Xd1P )^-2*( (c1*dS1eta1)*(d2S1eta1*Xd1P) ) ))*dereta1derb1, dereta1derb1) +    
      
      crossprod(c(VC$weights*VC$cens*( ( c1*p1 - dS1eta1*Xd1P )^-2*(c1*dS1eta1^2) ))*dereta1derb1, der2eta1dery1b1) + 
      
      crossprod(c(VC$weights*VC$cens*( ( c1*p1 - dS1eta1*Xd1P )^-2*(c1*dS1eta1^2) ))*der2eta1dery1b1, dereta1derb1 ) + 
      
      crossprod(c(VC$weights*VC$cens*(-( c1*p1 - dS1eta1*Xd1P )^-2*( (d2S1eta1*Xd1P)*dS1eta1 ) ))*dereta1derb1, der2eta1dery1b1) + 
      
      crossprod(c(VC$weights*VC$cens*(-( c1*p1 - dS1eta1*Xd1P )^-2*( (d2S1eta1*Xd1P)*dS1eta1 ) ))*der2eta1dery1b1, dereta1derb1) - # minus here! 
      
      
      
      crossprod(c(VC$weights*(1 - VC$cens)*(( 1 - p1*c2 )^-2*(dS1eta1*c2)^2 +
                                         ( 1 - p1*c2 )^-1*(d2S1eta1*c2) ))*dereta1derb1, dereta1derb1) -
      
      diag( colSums( t( t(c(VC$weights*(1 - VC$cens)*( 1 - p1*c2 )^-1*(dS1eta1*c2) )*VC$X1)*der2.par1 ) ) ) 
      
    
  )
  
  
  
  ########################################################################
  
  if(VC$extra.regI == "pC") H <- regH(H, type = 1)
  
  S.h  <- ps$S.h + monP2                                # hess
  S.h1 <- 0.5*crossprod(params, ps$S.h)%*%params + monP # lik
  S.h2 <- S.h%*%params + monP1                          # grad   
  
  
  S.res <- res
  res   <- S.res + S.h1
  G     <- G + S.h2
  H     <- H + S.h  
  
  if(VC$extra.regI == "sED") H <- regH(H, type = 2)   
  
  
  list(value=res, gradient=G, hessian=H, S.h=S.h, S.h1=S.h1, S.h2=S.h2, indN = indN, V = V, 
       l=S.res, l.ln = l.ln, l.par=l.par, ps = ps, k = VC$my.env$k, monP2 = monP2, params1 = params1,
       eta1=eta1, 
                                          p1 = p1, p2 = p2, pdf1 = -dS1eta1, pdf2 = pdf2,          
       	      	                           c.copula.be2 = c.copula.be2,
	      	                           c.copula.be1 = c.copula.be1,
       dl.dbe1          = NULL,       
       dl.dbe2          = NULL,       
       dl.dteta.st      = NULL) 
  
}