# RE: st: Survival analysis question

 From "Feiveson, Alan H. (JSC-SK311)" To "statalist@hsphsun2.harvard.edu" Subject RE: st: Survival analysis question Date Thu, 4 Nov 2010 12:23:51 -0500

```Hi Steve - OK - So I tried what was suggested in the link. To make this really simple I just did -stset- for the first two id's (with all failures):

. gen time0=0
. list id treat post fail t ttrxt time0 if id<=2 ,sepby(id)

+------------------------------------------------+
| id   treat   post   fail     t   ttrxt   time0 |
|------------------------------------------------|
1. |  1     pre      0      1   169     169       0 |
2. |  1    post      1      1   141     310       0 |
|------------------------------------------------|
3. |  2     pre      0      1   114     114       0 |
4. |  2    post      1      1    84     198       0 |
+------------------------------------------------+

. stset t, id(id) failure(fail) exit(time .) enter(time0) if(id<=2)

id:  id
failure event:  fail != 0 & fail < .
obs. time interval:  (t[_n-1], t]
enter on or after:  time time0
exit on or before:  time .
if:  id<=2

------------------------------------------------------------------------------
16  total obs.
12  ignored per request (if(), etc.)
------------------------------------------------------------------------------
4  obs. remaining, representing
2  subjects
4  failures in multiple failure-per-subject data
283  total analysis time at risk, at risk from t =         0
earliest observed entry t =         0
last observed exit t =       169

But the total time at risk should be 169 + 141 + 114 + 84 = 508 (not 283). Note 283 = 169 + 114 is the sum of the "pre" failure times.

Now, I redefine my "time0" variable to be where the previous test left off and use the cumulated time as the time variable:

. replace time0=ttrxt[_n-1] if post==1

. stset ttrxt, id(id) failure(fail) exit(time .) enter(time0) if(id<=2)

id:  id
failure event:  fail != 0 & fail < .
obs. time interval:  (ttrxt[_n-1], ttrxt]
enter on or after:  time time0
exit on or before:  time .
if:  id<=2

------------------------------------------------------------------------------
16  total obs.
12  ignored per request (if(), etc.)
------------------------------------------------------------------------------
4  obs. remaining, representing
2  subjects
4  failures in multiple failure-per-subject data
508  total analysis time at risk, at risk from t =         0
earliest observed entry t =         0
last observed exit t =       310

and I get the correct total time at risk.

However, equivalently, I could do what I did before without the "enter(time0)":

. stset ttrxt, id(id) failure(fail) exit(time .)  if(id<=2)

id:  id
failure event:  fail != 0 & fail < .
obs. time interval:  (ttrxt[_n-1], ttrxt]
exit on or before:  time .
if:  id<=2

------------------------------------------------------------------------------
16  total obs.
12  ignored per request (if(), etc.)
------------------------------------------------------------------------------
4  obs. remaining, representing
2  subjects
4  failures in multiple failure-per-subject data
508  total analysis time at risk, at risk from t =         0
earliest observed entry t =         0
last observed exit t =       310

and I still get the correct time at risk.

Am I missing something? Shouldn't the total time at risk just be the sum of the "t's"?

Al

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Steven Samuels
Sent: Thursday, November 04, 2010 11:05 AM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: Survival analysis question

--
-Al and Chris:
I should correct a previous statement of mine.  You do formally
multiple-failure data, with a not-at-risk gap between test dates.  But
I think that the proper analysis is a "time from previous entry" as in http://www.stata.com/support/faqs/stat/stmfail.html#cond2
, Section 3.2.4.  The approach there of putting the second test data
into a separate stratum won't work, because you want to compare the
first and second times.

Steve

> Steve - I think there is a communication problem here. The event is
> a subject reaching a state of presyncopy during an upright tilt.
> Subjects are given the tilt test with Treatment 1 ("pre"), then one
> week later they are given the test with Treatment 2 ("post").
> Subjects aren't at risk during the week in between because they
> aren't doing the tilt test. But I see there is no way you would know
> this from the data alone. Therefore I would like to claim that in
> effect "times" can be considered as building up consecutively. Does
> this make sense?
>
> Al
>

It doesn't make sense to me, Al. Assume that there was no treatment
(or that the treatments were the same). For the times to be considered
as "building up consecutively,"  an individual's inherent survival
curve for the second test would continue  where the first curve left
off.  The length of time between the two tests make this very
unlikely. Too many (unmeasured) factors  that affect response will
differ between the tests. I think this would be true even if the tests
were separated by just a few hours, though here issues of treatment
order, carry-over, changed physiological state, and prior outcome
would also enter.

Put it another way: Suppose you were measuring an outcome that was not
censored. Wouldn't you do a standard paired-data analysis? Let's
happens if I do this, ignoring the censoring,  and compare the results
to those from a clustered regression of the individual times.

. bys subjectid: gen diff = time[2] - time[1]
. preserve
. bys subjectid: keep if _n==1
(8 observations deleted)

. mean diff   //paired analysis

Mean estimation                     Number of obs    =       8
--------------------------------------------------------------
|       Mean   Std. Err.     [95% Conf. Interval]
-------------+------------------------------------------------
diff |   -281.625   114.6071     -552.6277   -10.62231
--------------------------------------------------------------
. restore
reg time treatment, cluster(subjectid)

Linear regression                                      Number of obs
=      16
[output skipped]
(Std. Err. adjusted for 8 clusters in
subjectid)
------------------------------------------------------------------------------
|               Robust
time |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
Interval]
-------------
+----------------------------------------------------------------
treatment |   -281.625   118.6296    -2.37   0.049    -562.1394
-1.110568
_cons |     491.25   133.6418     3.68   0.008     175.2374
807.2626
------------------------------------------------------------------------------

The point estimates are the same, and the standard errors are close.
(In fact, if you jackknife the clusters, the standard errors are
identical.)   By analogy, clustered -stcox- on the individual times is
the way to go. The fact that you can't get sensible survival curves
for your approach just reinforces this conclusion.

Steve

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu
] On Behalf Of Steven Samuels
Sent: Wednesday, November 03, 2010 2:40 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: Survival analysis question

--

Al,

I don't think that the two times are consecutive: they are recorded as
seconds, but the the two observations on each subject were separated
by a week.

Steve

On Nov 3, 2010, at 2:50 PM, Feiveson, Alan H. (JSC-SK311) wrote:

Steve - In my opinion this is multiple failure data. Each subject is
subjected to two consecutive exposures, and a subject can "fail" on
none, either, or both of these tests. So the variable ttrxt at a given
observation is the total time that the particular subject has been at
risk up through that observation. Therefore I think the stset command

. stset ttrxt, id(id) failure(fail) exit(time .)

id:  id
failure event:  fail != 0 & fail < .
obs. time interval:  (ttrxt[_n-1], ttrxt]
exit on or before:  time .

------------------------------------------------------------------------------
16  total obs.
0  exclusions
------------------------------------------------------------------------------
16  obs. remaining, representing
8  subjects
13  failures in multiple failure-per-subject data
5607  total analysis time at risk, at risk from t =         0
earliest observed entry t =         0
last observed exit t =      1198

is correct. I agree that ideally, one should try a frailty model on
this data, but it doesn't work well with only 8 subjects.

Al Feiveson

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu
] On Behalf Of Steven Samuels
Sent: Wednesday, November 03, 2010 12:35 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: Survival analysis question

Chris Westby:

You don't have multiple-failure data, because the start time for the
two tests should be zero. The correct statement is:

stset t, failure(fail)

This will change the -stcox- results as well. Also try -stsum,
by(treatment)- after the two versions of -stset--.  I suggest that you
consider the -shared-  option in -stcox- to allow for the possibility
of person-specific baseline hazards. Note that eight subjects is
probably not enough for the standard errors to be reliable.

Steve

Steven J. Samuels
sjsamuels@gmail.com
18 Cantine's Island
Saugerties NY 12477
USA
Voice: 845-246-0774
Fax:    206-202-4783

On Nov 3, 2010, at 8:35 AM, Westby, Christian Michael. (JSC-SK)[USRA]
wrote:

Dear Statalisters,

I am working on comparing survival times in one group of subjects
before and after treatment and am having a hard time with the "stset"
code.

Using the following data set where testing was separated by 1 week, t
is time of task before and after treatment (seconds) and ttrxt is time
calculated to prevent time from being treated as continuous and fail
is 0=completed, 1=not completed.

subjectid       treatment       fail                    t       ttrxt
-----------------------------------------------------------------
1               pre             failed          169     169
1               post            failed          141     310
2               pre             failed          114     114
2               post            failed          84      198
3               pre             failed          564     564
3               post            failed          296     860
4               pre             failed          168     168
4               post            failed          332     500
5               pre             failed          215     215
5               post            failed          50      265
6               pre             completed               900     900
6               post            failed          196     1096
7               pre             completed               900     900
7               post            failed          298     1198
8               pre             completed               900     900
8               post            failed          280     1180
-----------------------------------------------------------------

I used

. stset ttrxt, id(subjectid) failure(fail) exit(time .)

id:  subjectid
failure event:  fail != 0 & fail < .
obs. time interval:  (ttrxt[_n-1], ttrxt]  exit on or before:  time .

------------------------------------------------------------------------------
16  total obs.
0  exclusions
------------------------------------------------------------------------------
16  obs. remaining, representing
8  subjects
13  failures in multiple failure-per-subject data
5607  total analysis time at risk, at risk from t =         0
earliest observed entry t =         0
last observed exit t =      1198

I then ran

. stcox treatment, cluster(subjectid)

failure _d:  fail
analysis time _t:  ttrxt
exit on or before:  time .
id:  subjectid

Iteration 0:   log pseudolikelihood = -20.175132
Iteration 1:   log pseudolikelihood = -18.079165
Iteration 2:   log pseudolikelihood = -18.026011
Iteration 3:   log pseudolikelihood = -18.025935
Refining estimates:
Iteration 0:   log pseudolikelihood = -18.025935

Cox regression -- no ties

No. of subjects      =            8                Number of obs
=        16
No. of failures      =           13
Time at risk         =         5607
Wald chi2(1)
=      4.22
Log pseudolikelihood =   -18.025935                Prob > chi2
=    0.0399

(Std. Err. adjusted for 8 clusters in
subjectid)
------------------------------------------------------------------------------
|               Robust
_t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+----------------------------------------------------------
-------------+------
treatment |   4.610013   3.428317     2.05   0.040     1.073226
19.80218
------------------------------------------------------------------------------

I believe that the output and results are accurate however, I am
unable to get Stata to correctly graph the survival curves using the
following code

. stcurv, surv at1(treatment=0) at2(treatment=1)

the resulting graph incorrectly plots both groups starting at less
than 100% at a time=0 and the x-axis scale is incorrect.

Any thoughts?

Chris

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```