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

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 POSTAL ADDRESS: Respiratory Epidemiology and Public Health Group National Heart and Lung Institute at Imperial College London St Mary's Campus Norfolk Place London W2 1PG STREET ADDRESS: Respiratory Epidemiology and Public Health Group National Heart and Lung Institute at Imperial College London 47 Praed Street Paddington 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 answer 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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