R help - Jan 2007 - Error in basehaz function ?

Hello R-users.

I believe that the way basehaz (in the survival package) compute  the
baseline hazard function is false.

I come to question this function when it gives me hazard probabilities
greater than 1.

Looking at the code I think I've localised the error :

hazard probability is computed as :

H <- -log(surv)

but it seems to me that hazard probabilities is rather an instantaneous
survival rate that could be computed this way :

H[i] <- 1 - surv[i] / surv[i-1]

Using this rule I achieve satisfiable results with the two following
functions :

surv2haz <- function(surv) {

  haz <- surv

  haz[1] <- 1 - surv[1]
  
  for(i in c(2:length(surv)))
    {
      haz[i] <- 1 - surv[i] / surv[i - 1]
    }

  return(haz)
}

haz2surv <- function(haz) {

  surv <- haz

  surv[1] <- 1 - haz[1]
  
  for(i in c(2:length(haz)))
    {
      surv[i] <- (1 - haz[i]) * surv[i-1]
    }

  return(surv)
}

If I'm right, wouldn't it be a good idea to change the basehaz
function, to avoid misleading the overconfident user (as I happen to be)
?

I hope this will help contributing to a wonderful tool that speed up my
understanding of statistical analysis and my research.

David

-- 
David Mas
ERMES-FRE 2887-CNRS
Universit? Pantheon-Assas Paris II
12, place du Pantheon
F-75230 Paris Cedex 05
Tel: +33 (0)1 44 41 89 91
Mob: +33 (0)6 84 15 77 67 
Fax: +33 (0)1 40 51 81 30
http://www.u-paris2.fr/ermes/

Hi,

David Mas wrote:
> I believe that the way basehaz (in the survival package) compute  the
> baseline hazard function is false.
>
> I come to question this function when it gives me hazard probabilities
> greater than 1.
>
> Looking at the code I think I've localised the error :
>
> hazard probability is computed as :
>
> H <- -log(surv)
Maybe the documentation is not clear enough about that, but what you obtain
in the previous code line is not the "hazard probability" but the
"Cumulative Hazard Rate".
The hazard rate is typically defined h(t)=f(t)/S(t) where f(t) is the
density at time t and S(t) is the value of the survival function at time t.
And please note that this is not a probability. The hazard can take on
values larger than 1.

Besides the literature given in ?basehaz, I can recommend
Klein, JP Moeschberger, ML. Survival Analysis: Techniques for Censored and
Truncated Data. Springer 2003

Starting at page 27, the hazard function and the cumulative hazard are
introduced.

Hope this helps,
Roland

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