# 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) 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])
   1.090909 


# We can calculate an approximate confidence interval as follows:
# Approximate 95% lower bound:
1/exp(expfit$coef[1] + 2*sqrt(expfit$var[1]))
  0.3438021 


# Approximate 95% upper bound:
1/exp(expfit$coef[1] - 2*sqrt(expfit$var[1]))
   3.461534