# This file from www.richardsconsulting.co.uk/lectures

# First load in the survival library
library(survival)

# Now create a list of (i) survival times and (ii) censoring/event status.
#
# Note that '1' = death and '0' = censored in the status variable.
example5<-list(v = c(1.0, 0.50, 0.50, 0.25, 0.25, 0.25),
               d = c(  0,    1,    0,    1,    1,    0))

# First, the direct MLE approach:
sum(example5$d) / sum(example5$v)
1.090909

# Now try the exponential survival model:
expfit<-survreg(Surv(v, d) ~ 1, dist="exponential", example5)
summary(expfit)

             Value Std. Error      z    p
(Intercept) -0.087      0.577 -0.151 0.88


# Note that the exponential distribution is parameterised here with lambda,
# where mu = 1 / lambda.  Also, the parameter estimates are on a log scale,
# so we need the following to recover mu as we want it:
1/exp(expfit$coef[1])
(Intercept) 
   1.090909 

# Now try the Poisson approach:
poissonfit<-glm(example5$d ~ 1, family="poisson", offset=log(example5$v))
summary(poissonfit)

Coefficients:
            Estimate Std. Error z value Pr(>|z|)
(Intercept)  0.08701    0.57735   0.151     0.88


# Again note that the parameters are given on a log scale,
# so we need the following to recover mu as we want it:
exp(poissonfit$coef[1])
(Intercept) 
   1.090909
   
# It seems silly to use the survreg() and glm() functions to accomplish what
# we can evaluate directly.  However, the advantage lies in the ability to
# easily regress on multiple variables -- say gender, drug treatment etc --
# and to consider more complicated forms for mu than a simple constant value.