# st: RE: left-truncation of entry in survival analysis

 From "Newson, Roger B" To Subject st: RE: left-truncation of entry in survival analysis Date Wed, 22 Mar 2006 15:31:45 -0000

```I am assuming that the covariates in the 2 models are all
time-independent. In general, the 2 models are not equivalent. However,
it is entirely possible that they might give the same parameter
estimates, in at least some specific sets of data.

Survival analyses (as their name suggests) are based on events whereby
one subject is observed to survive another, ie one subject at risk on a
particular day survives to the end of that day and another subject at
risk on the same day is dead by the end of that day. The two models are
different in what is meant by "the same day" for the two subjects. In
the first model, we compare the fate of Subject A on Day X of the life
of Subject A with the fate of Subject B on Day X of the life of Subject
B, for all pairs of Subjects A and B who were both under observation in
the study on Day X of their respective lives. In the second model, we
compare the fate of Subject A on Day Y of Subject A's study time
(measured from Subject A's entry into the study) with the fate of
Subject B on Day Y of Subject B's study time (measured from Subject B's
entry into the study), for all pairs of Subjects A and B who were both
under observation on Day Y of their respective study time windows.

In a specific study, it might be the case that, for each Subject A who
died on Day X of his/her life and Day Y of his/her study time, the set
of Subjects B who survived through the Days X of their respective lives
in the study might be the same set as the set of Subjects B who survived
through the Days Y of their respective study times in the study. This
might especially be the case if the number of subjects is small and/or
deaths in the study are sparse. For such a specific study, the two Cox
regressions will give the same parameter estimates. However, this will
not be the case for all studies. For instance, in some studies, there
will be pairs of Subjects A and B, such that Subject A dies in the study
at 100 years of age after having entered the study at 99 years of age,
whereas Subject B dies in the study at 40 years of age after having
entered the study at 30 years of age. In this case, the first model will
assume that neither patient was observed to survive the other, whereas
the second model will assume that Subject B has survived Subject A, even
though Subject B died younger.

I hope this helps.

Roger

Roger Newson
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute at Imperial College London
St Mary's Campus
Norfolk Place
London W2 1PG
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute at Imperial College London
47 Praed Street
London W1 1NR
TELEPHONE: (+44) 020 7594 0939
FAX: (+44) 020 7594 0942
EMAIL: r.newson@imperial.ac.uk
WEBSITE: http://www.imperial.ac.uk/nhli/r.newson/
Opinions expressed are those of the author, not of the institution.

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Sue Chinn
Sent: 22 March 2006 12:47
To: statalist@hsphsun2.harvard.edu
Subject: st: left-truncation of entry in survival analysis

Reports of survival analysis which use age as the time scale rather than

time-on-study often 'adjust for delayed entry'. In Stata this is
achieved by:

stset age, fail(died) enter(ageatentry)

(see recent e-mail from Dawn Teele, or reply to st: streg from
rgutierrez@stata.com on 19th September 2002.)

However, a model fitted with the above stset gives exactly the same
as one with

stset timeonstudy, fail(died)

provided timeonstudy=age-ageatentry (as it normally would, but might not

exactly depending how variables were calculated) and the models are
exactly
the same. In the second model it is usual to adjust or stratify on age,
while in the first it isn't as age is taken into account, supposedly, so

researchers may not have realised the equivalence.

So, am I missing something, or are advocates of the first model deluding

themselves? Can left truncation be ignored with age as the timescale?

Thanks

Sue

Sue Chinn
Professor of Medical Statistics
Division of Asthma, Allergy and Lung Biology
King's College London
5th Floor Capital House
42 Weston Street
London SE1 3QD

tel no. 020 7848 6607
fax no. 020 7848 6605

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