LogRank1 <- function(z1,d1,Hz1)

# This function compute the one sample logrank test.
# z1 are the observed (possibly censored) times, 
# d1 are the censoring indicators, 1--uncensored, 0--censored;
# Hz1 should be a vector of null cumulative hazard at the observed times
# i.e. H_0(z1).  Please note this is different from the Splus convention.
# There you input the Survival at times, i.e. S(z1). [now use glm()]
{
   if( (length(z1)!=length(d1)) | (length(d1)!=length(Hz1)) ) 
       stop("input must have same length")
   if(any((d1!=0)&(d1!=1)) ) stop("d1 must be 0/1's for censor/not-censor") 
   if(any(Hz1 < 0)) stop("Hz1 must be nonnegative")

   EE <- sum(Hz1) 
   diff <- sum(d1) - EE  

   temp2 <- diff/sqrt(EE)
   pval <- 1-pchisq((temp2)^2, df=1)

   list(Logrank=temp2, ApproxPvalue2side=pval)
} 

# An example of the test in action is   LogRank1(z, d, 0.3*z)
# this tests if the lifetime distribution of (z,d) is exp(0.3), since
# the cumulative hazard function of exp(0.3) is  H(t)= 0.3 * t 
#
# In fact we even do not need the z1 in the input!  only the length.
# For reference see Klein and Moeschberger book

### Wilcoxon-Gehan test: 
##  S1 <- exp(-Hz1)
##  EE <- length(z1) - sum(S1)
##  diff <- sum(S1*d1) - EE 
##  FF <- 0.5*( length(z1) - sum(S1*S1))

##  temp2 <- diff/sqrt(FF)
##  pval <- 1-pchisq( (temp2)^2, df=1)
##