[R] Survival Analysis with an Historical Control

Paul Miller pjmiller_57 at yahoo.com
Thu Jul 10 18:11:40 CEST 2014

Hi Dr. Therneau,

Thanks for your response. This is very helpful.

My historical control value is 16 weeks. I've been having some trouble though determining how this value was obtained. Are you able to indicate how people normally go about determining a value for the historical control? Or do you have an view on how it ought to be done? 

It does seem like selecting an appropriate value is extremely important. Otherwise the results obtained from the analysis are likely to be nonsense. 



On Thu, 7/10/14, Therneau, Terry M., Ph.D. <therneau at mayo.edu> wrote:

 Subject: Re: Survival Analysis with an Historical Control
 To: r-help at r-project.org, "Andrews, Chris" <chrisaa at med.umich.edu>, pjmill
 Received: Thursday, July 10, 2014, 8:52 AM

 You are asking for a one sample
 test.  Using your own data:

 connection <- textConnection("
 GD2  1   8 12  GD2  3 -12
 10  GD2  6 -52  7
 GD2  7  28 10  GD2  8  44 
 6  GD2 10  14  8
 GD2 12   3  8  GD2 14 -52 
 9  GD2 15  35 11
 GD2 18   6 13  GD2 20  12 
 7  GD2 23  -7 13
 GD2 24 -52  9  GD2 26 -52 12  GD2 28  36
 GD2 31 -52  8  GD2 33   9 10 
 GD2 34 -11 16
 GD2 36 -52  6  GD2 39  15 14  GD2
 40  13 13
 GD2 42  21 13  GD2 44 -24 16  GD2 46 -52 13
 GD2 48  28  9  GD2  2  15 
 9  GD2  4 -44 10
 GD2  5  -2 12  GD2 
 9   8  7  GD2 11  12  7
 GD2 13 -52  7  GD2 16  21  7  GD2
 17  19 11
 GD2 19   6 16  GD2 21  10 16 
 GD2 22 -15  6
 GD2 25   4 15  GD2 27  -9 
 9  GD2 29  27 10
 GD2 30   1 17  GD2 32  12 
 8  GD2 35  20  8
 GD2 37 -32  8  GD2 38  15  8  GD2
 41   5 14
 GD2 43  35 13  GD2 45  28  9  GD2
 47   6 15

 hsv <- data.frame(scan(connection, list(vac="", pat=0,
 wks=0, x=0)))
 hsv <- transform(hsv, status= (wks >0), wks =

 fit1 <- survreg(Surv(wks, status) ~ 1, data=hsv,
 temp <- predict(fit1, type='quantile', p=.5, se=TRUE)

 c(median= temp$fit[1], std= temp$se[1])
    median    std
 24.32723  4.36930

 The predict function gives the predicted median survival and
 standard deviation for each 
 observation in the data set.  Since this was a mean
 only model all n of them are the same 
 and I printed only the first.
 For prediction they make the assumption that the std error
 for my future study will be the 
 same as the std from this one, you want the future 95% CI to
 not include the value of 16, 
 so the future mean will need to be at least 16 + 1.96*

 A nonparmetric version of the argument would be

 > fit2 <- survfit(Surv(wks, status) ~ 1, data=hsv)
 > print(fit2)
 records   n.max n.start  events 
 median 0.95LCL 0.95UCL
       48      48   
   48      31     
 21      15      35

 Then make the argument that in our future study, the 95% CI
 will stretch 6 units to the 
 left of the median, just like it did here.  This
 argument is a bit more tenuous though. 
 The exponential CI width depends on the total number of
 events and total follow-up time, 
 and we can guess that the new study will be similar. 
 The Kaplan-Meier CI also depends on 
 the spacing of the deaths, which is less likely to

   1. Use summary(fit2)$table to extract the CI
 values.  In R the print functions don't 
 allow you to "grab" what was printed, summary normally
   2. For the exponential we could work out the formula
 in closed form -- a good homework 
 exercise for grad students perhaps but not an exciting way
 to spend my own afternoon.  An 
 advantage of the above approach is that we can easily use a
 more realistic model like the 
   3. I've never liked extracting out the "Surv(t,s)"
 part of a formula as a separate 
 statement on another line.  If I ever need to read this
 code again, or even just the 
 printout from the run, keeping it all together gives much
 better documentation.
   4. Future calculations for survival data, of any
 form, are always tenuous since they 
 depend critically on the total number of events that will be
 in the future study.  We can 
 legislate the total enrollment and follow-up time for that
 future study, but the number of 
 events is never better than a guess.  Paraphrasing a
 motto found on the door of a well 
 respected investigator I worked with 30 years ago (because I
 don't remember it exaclty):

    "The incidence of the condition under
 consideration and its subsequent death rate will 
 both drop by 1/2 at the commencement of a study, and will
 not return to their former 
 values until the study finishes or the PI retires."

 Terry T.


 On 07/10/2014 05:00 AM, r-help-request at r-project.org
 > Hello All,
 > I'm trying to figure out how to perform a survival
 analysis with an historical control. I've spent some time
 looking online and in my boooks but haven't found much
 showing how to do this. Was wondering if there is a R
 package that can do it, or if there are resources somewhere
 that show the actual steps one takes, or if some
 knowledgeable person might be willing to share some code.
 > Here is a statement that describes the sort of analyis
 I'm being asked to do.
 > A one-sample parametric test assuming an exponential
 form of survival was used to test the hypothesis that the
 treatment produces a median PFS no greater than the
 historical control PFS of 16 weeks.  A sample median
 PFS greater than 20.57 weeks would fall beyond the critical
 value associated with the null hypothesis, and would be
 considered statistically significant at alpha = .05, 1
 > My understanding is that the cutoff of 20.57 weeks was
 obtained using an online calculator that can be found at:
 > http://www.swogstat.org/stat/public/one_survival.htm
 > Thus far, I've been unable to determine what values
 were plugged into the calculator to get the cutoff.
 > There's another calculator for a nonparamertric test
 that can be found at:
 > http://www.swogstat.org/stat/public/one_nonparametric_survival.htm
 > It would be nice to try doing this using both a
 parameteric and a non-parametric model.
 > So my first question would be whether the approach
 outlined above is valid or if the analysis should be done
 some other way. If the basic idea is correct, is it
 relatively easy (for a Terry Therneau type genius) to
 implement the whole thing using R? The calculator is a great
 tool, but, if reasonable, it would be nice to be able to
 look at some code to see how the numbers actually get

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