# [R] Survival analysis extrapolation

TReason timothy.reason at heronhealth.com
Wed May 26 16:24:44 CEST 2010

```Dear all,

I'm trying to fit a curve to some 1 year failure-time data, so that I can
extrapolate and predict failure rates up to 3 years. The data is in the
general form:

Treatment	       Time	                      Status
Treatment A	       28	                          0
Treatment B	       28	                          0
Treatment B	       28	                          0
Treatment A	       28	                          1
Treatment B	       56	                          0
Treatment A	       56	                          0
Treatment B	       84	                          0
Treatment A	       84	                          0
Treatment A	       84	                          0

etc etc

Where time is in days and goes up to 360, 0 represents a withdrawal and 1
represents a failure. The code I've tried is as follows:

WeiModel<-survreg(Surv(survdata\$Time,survdata\$Status)~survdata\$Treatment)

summary(WeiModel)

n<-seq(0, 1080, 30 )

##Compute Weibull CDF

A<-pweibull(n, scale=exp(WeiModel\$coef[1]), shape=1/WeiModel\$scale)

B<-pweibull(n,
scale=exp(WeiModel\$coef[1]+WeiModel\$coef[2]),shape=1/WeiModel\$scale)

##Transform into survivor function

ACurv<-1-A

BCurv<-1-B

The problem is, that the Weibull curve is predicting a survival probability
for treatment B of around 11% at the end of year 3 (day 1080), and past
analyses have shown that this value should be somewhere in the region of
~40%. I'm finding a similar problem for treatment A also. I've also tried
fitting an exponential distribution but encountered the same problems. My
questions are:

1)      Have I computed the survivor function correctly, in terms of moving
from the survreg output to the    pweibull parameters?

2)      If the above seems correct, then is there an obvious methodological
reason why I'm getting survival probabilities far less than expected? (for
example, is the general method I'm using not the best approach? If so can
you suggest a better one?)

3)      Is it worth trying to do the same thing with the other distributions
that R uses for survival analysis (lognormal, gaussian etc). If so, how do
you extrapolate the model out to 3 years? Are there functions that are
equivalent to the 'pweibull' function for all these distributions?

Kind regards,

Tim.

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