Simulation-Survival-Data-in-R

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F R E Q U E N T I S T I C

S I M U L A T I O N

SIMULATE SURVIVAL DATA

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The example is a comparison of three different methods for

estimating the hazard ratio in a randomised trial with a survival outcome.

Consider the proportional hazards model,

where we have the hazard rate

(event rate at time t conditional on survival until at least time t)

for the ith patient

hi(t) = h0(t) exp(Xi𝜃),

In our simulation study true β = - 0.5.

So the hazard ratio is exp(β) = 0.6065307.

The interpretation of the hazard ratio of 0.607 is that

patients with Treatment (x=1) die at about 0.607 times than

the patients with Treatment (x=0).Another way of expressing

the hazard ratio that can be more meaningful to subject matter

scientists is to describe it as a percentage increase/decrease

over the null value of 1.In our simulation study one would say

that the death rate among patients with Treatment 1 (x=1)

is (1-0.607)100% = 39.3% smaller than among patients with

Treatment 0 (x=0) throughout the study

We generate random numbers from Weibull distribution with scale

parameter gamma = 1 which is the same as exponential distribution

and random numbers from weibull with gamma =1.5.We regress them to

three different proportional hazard models:

1)Exponential

2)Weibull

3)Cox

Then we check the bias,coverage,model standard error,relative standard error,replative precision

and other performance measures in R.