Difference between survival confidence bands generated in PHREG vs. LIFETEST?

[mconover]

Hello,

I am trying to migrate a survival analysis out of PROC LIFETEST and into PROC PHREG and ran into some incongruencies that I want to make sure I understand. Specifically, I am confused by the difference between the confidence bands generated for my survival curves when I use PROC LIFETEST and PROC PHREG. Any feedback would be hugely appreciated (including links to technical documentation if that would help).

The options for survival confidence bands under PROC LIFETEST are Hall Wellner bands (cb=hw) or equal precision bands (cb=ep). 

The options for survival confidence bands under PROC PHREG are log (clytpe=log), loglog (clytype=loglog), and normal (cltype=normal). It seems like when I specify cltype=log in PROC PHREG, my confidence intervals are close to the Hall Wellner bands I get from PROC LIFETEST.  However they are not exactly the same.  While I would love to have a conceptual understanding of the difference between these two procedures, the important question is this: Is this variation that I need to be concerned about or is it simply because the two procedures are using slightly different (but similarly valid) approaches to calculating confidence intervals?  Also a secondary question: Are there settings that I can apply in LIFETEST and PHREG that will generate identical survival functions and confidence bands?

Here are some things I think I understand to be true:

• Neither PHREG nor LIFETEST confidence bands will necessarily reflect the point-wise confidence intervals.
• All three PHREG options use some form of normal theory approximation.  The three different options allow transformations before assuming normality and calculating the corresponding confidence limits.
• Hall Wellner bands, estimated from PROC LIFETEST, also assume normality using the Miller and Siegmund equation (see lifetest reference below).
• I did at one point see a note in my log for PROC LIFETEST that said: "The LOGLOG transform is used to compute the confidence limits for the quartiles of the survivor distribution." 

Two releveant references that I found informative:

1. Description of PHREG confidence limit types (see entry for "CLTYPE=method" on page 12):
   • http://www.okstate.edu/sas/v8/saspdf/stat/chap49.pdf
2. Description of equal precision and Hall Wellner confidence bands calculated in PROC LIFETEST:
   • https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_lifetest_a0...

[JacobSimonsen · Accepted solution]

Some of the difference between the result is that it is not estimating the same thing. The confidence intervals you get from PHREG is pointwise confidence intervals, calculated on some specific scale (log, logit or loglog).

But this Hall Wellner bands should be interpretated uniformly in the sense that with 5% probability there is some point where the true curve is outside the band.