R/TMLjac22.W.R

In RobustAFT: Truncated Maximum Likelihood Fit and Robust Accelerated Failure Time Regression for Gaussian and Log-Weibull Case

TMLjac22.W <-
function(d.Beta,d.sigma,rs0,delta,X,cl,cu) {
# Jacobian of sigma TML equation wrt sigma.hat
n     <- length(rs0)
D1    <- D2 <- D3 <- D <- rep(0,n); p <- ncol(X); zero <- 1e-6
rsd   <- (rs0-X%*%d.Beta)/d.sigma
Fo    <- plweibul(rsd)
fo    <- dlweibul(rsd)
ok    <- (1-Fo) > zero
ai    <- (pmax(rs0,cl)-X%*%d.Beta)/d.sigma
bi    <- (cu  -        X%*%d.Beta)/d.sigma
foai  <- dlweibul(ai)
fobi  <- dlweibul(bi)
Foai  <- plweibul(ai)
Fobi  <- plweibul(bi)
fopai <- foai*(-ps0W(ai))
fopbi <- fobi*(-ps0W(bi))
D1    <- - delta*ww(rs0,cl,cu)*psp1W(rsd)*rsd
D2[ok]    <- -(  (1-delta)*fo/(1-Fo)^2*(foai*ai - fobi*bi + Fobi - Foai)*rsd  )[ok]
D3[ok]    <- -(  (1-delta)/(1-Fo)*( fopai*ai^2 - fopbi*bi^2 )                 )[ok]
D     <- D1 + D2 + D3
Jac   <- sum(D)/d.sigma/(n-p)
Jac}