# Any model for an increasing-constant-increasing cumulative hazard?

Discussion in 'Scientific Statistics Math' started by Jennifer, May 20, 2006.

1. ### JenniferGuest

I use SAS's PROC LIFETEST with method=Kaplan-Meier to analyze a data set
with censored and uncensored observations. The plot of the cumulative
hazard (negative of the log of the survival) versus the survival time
shows an increasing-constant-increasing curve. It looks like a 45 degree
(slope=1) line from t0 to t1, a horizontal line from t1 to t2, and then a
45 degree (slope=1) line from t2 to infinity.
something wrong on the analysis?
Thanks.

Jennifer

Jennifer, May 20, 2006

2. ### Richard UlrichGuest

The more familiar basis for a model is the hazard, to my mind.

You describe a constant hazard, zero hazard, constant hazard.
The obvious model for risks is simply this -- On/off/on.

I will repeat what a common opinion: One very important
question for initial selection or first evaluation of a model is,
"What generates the observations?"

There are a lot of models that generate U-shaped hazard
curves, so I wonder how abrupt your transitions are (On/off/on)
and whether your description is based on a small amount of data

Richard Ulrich, May 21, 2006

3. ### Bill HGuest

Jennifer, you could use the PHREG procedure to fit time-dependent
covariates for the three intervals. Otherwise, if you are comparing
the survival of groups, the logrank test averages the baseline hazards
over the entire time interval, which might or might not be a bad thing
for you data. The book by Paul Allison, Survival Analysis with SAS (or
something like that) has a good discussion of the diagnostics for
proportional hazards.

Bill H, May 22, 2006
4. ### David WinsemiusGuest

"The plot of the cumulative hazard (negative of the log of the survival)
versus the survival time shows an increasing-constant-increasing curve."

Another reference to consider is Thernau and Grambsch's "Modeling
Survival Data". Their chapter on analyzing "functional form" of the Cox
model includes worked examples using the widely available PBC (Primary
biliary cirrhosis) data with regression spline fits of the hazard
yielding results looking similar to the results you describe. The book
uses both S and SAS code. Their section on regression splines references
the use of "the supplied macro", %daspline". In their appendix on SAS
macro it becomes clear that the author of %daspline is Frank Harrell.

The link given in that book to SAS code is out of date. The current
location is:
http://mayoresearch.mayo.edu/mayo/research/biostat/sasmacros.cfm.

Harrell has a page for some SAS macros including %daspline at:
http://biostat.mc.vanderbilt.edu/twiki/bin/view/Main/SasMacros

His page says he is no longer supporting these, presumably because he
moved his analyses to the R/S framework, rather than because he thinks
the methods are deficient in some way.

David Winsemius, May 30, 2006