# RE: st: R: Problem with Left Truncation

 From "Feiveson, Alan H. (JSC-SK311)" To "statalist@hsphsun2.harvard.edu" Subject RE: st: R: Problem with Left Truncation Date Fri, 23 Oct 2009 08:13:34 -0500

```I think the only safe conclusion that can be made by analyzing this data alone is that the survival analysis is valid conditional on the event (e.g. a death) occurring. In other words the distribution that is estimated is the time to the event given that the event has occurred. In most cases this would not be the same as the unconditional distribution of time to the event.

Al Feiveson

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Antoine Terracol
Sent: Friday, October 23, 2009 5:06 AM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: R: Problem with Left Truncation

Hi,

Carlo Lazzaro wrote:
> Dear Elaine,
>
> <We are doing survival analysis, but unlike other dataset, our dataset
> only includes observations that have failed.>
>
> I would not be concerned about all failure=1; how long patient takes to
> failure (failure time (tn)- risk onset (t0)) it's the relevant issue.

I haven't done the math, but my intuition is the following.

If Elaine's dataset can be considered as a random sample from the
population, then she can use -stset- and proceed as usual.

I can think of one case where it would not be true: Consider the case
where individuals cannot be at risk before a certain calendar date t0
(say, because she is studying spells in a social program that did not
exist before). If Elaine's observation window is relatively (compared to
the average real duration in the state under study) short, and begins
relatively (again, compared to the real durations) close to t0, then
Elaine's sample will only contain spells short enough to have failed
during the observation window. In this cas, the coefficients will be
biased (although I'm not quite sure if there is a way to handle that
with Stata).

On the other hand, if the spells could have started at any given date
before the observation window (or long enough before the start of the
observation window, relatively to the real durations), then I think her
sample will be random and can be analysed as usual.

HTH,
Antoine

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