loss function of cox model

[EQUIWDH]

Hello, I am wondering if fit$loss returned by ncvsurv represents only the cox -2*logL calculating by estImated $\beta$ or the -2logL + penalty form ，thanks!

[EQUIWDH]

Sorry for disturbing, I am using the loss function structure provided by loss.R which is

loss<- function(x,beta,y ,total=TRUE) {
  eta = x%*%beta
  ind <- order(y[,1])
  d <- as.double(y[ind,2])
  if (is.matrix(eta)) {
    eta <- eta[ind, , drop=FALSE]
    r <- apply(eta, 2, function(x) rev(cumsum(rev(exp(x)))))
  } else {
    eta <- eta[ind]
    r <- rev(cumsum(rev(exp(eta))))
  }
  if (total) {
    return(-2*(crossprod(d, eta) - crossprod(d, log(r))))
  } else { 
    return(-2*(eta[d==1,] - log(r)[d==1,]))
  }
}

compareloss(fit$X,fit$beta,train$y) and fit$loss, I find they don't correspond as the picture showing

[EQUIWDH]

[pbreheny]

fit$loss returns the loss only (negative of cox partial likelihood), not the penalty.

The internal function ncvreg:::loss.ncvsurv(), as well as the modified version of it that you show above, assumes that the data has been ordered by survival time. In addition, loss.ncvsurv() returns the deviance (2*loss).

So:

library(ncvreg)
data(Lung)
X <- Lung$X
y <- Lung$y
fit <- ncvsurv(X, y)
l1 <- 2*fit$loss
l2 <- ncvreg:::loss.ncvsurv(cbind(fit$time, fit$fail), fit$linear.predictors)
cbind(l1, drop(l2)) |> head()
#>                l1          
#> 0.44806 1010.6732 1010.6732
#> 0.41786 1000.5671 1000.5555
#> 0.38970  992.8519  992.8484
#> 0.36344  986.8651  986.8599
#> 0.33894  982.1560  982.1534
#> 0.31610  978.4471  978.4455

[EQUIWDH]

ok，understand，but if I use AIC function provided in stats package. The IC form will be -2log(partial likelihood) + 2(parameter number) right?

[pbreheny]

Correct