How does lifelines model for left truncation?

[johol355]

Hello friends,

I do understand the bias that left truncation causes. After reading the documentation several times, I'm still having difficulties understanding how lifelines models for left truncation. Also, I did take a look at the source code without being able to tell what is going on. I would really appreciate any explanation or pointer to understand this matter.

[CamDavidsonPilon]

Hi @johol355, are you interested in a particular survival model in particular, like the Kaplan Meier?

[benslack19]

@CamDavidsonPilon should we expect that a CPH model and a CTV model give exactly the same summary values, all else being equal (one value per subject, etc.)? I'm seeing coefficients match up exactly but not the SEs. Not sure why SEs would be different, especially if left truncation is essentially using the CTV model under the hood.

[CamDavidsonPilon]

We have tests that confirm the coefficients should be the same. I'm not sure why the SEs are different though...
https://github.com/CamDavidsonPilon/lifelines/blob/master/lifelines/tests/test_estimation.py#L5252-L5284

[CamDavidsonPilon]

does one model have strictly greater SE than the other?

[benslack19]

No, sometimes it's the CPH model and sometimes it's CTV that has a higher SE. Thanks for sharing the links to the tests.

[benslack19]

I believe I figured out what happened after thinking that left truncation was a factor in the difference in standard errors. It wasn't. It was because I was using cluster_col in the CoxPHFitter and saw in the documentation that the sandwich estimator gets used and that's why the SE changes. I found a few issues while investigating this, though, and I added my observations to issue #544 and created issue #1598 and issue #1599.