RE: COX Proportional Hazard Model with Time Dependent Covariate
Both Splus and SAS can do it. They both use the counting-process syntax.
In SAS, follow Example 54.5: Time-Dependent Repeated Measurements of a
Covariate:
proc phreg data=Tumor1;
model (T1,T2)*Status(0)=NPap;
OUTPUT OUT=Out1 SURVIVAL=sur/order=data;
id ID Time Dead;
run;
Even though SAS can correctly estimate the slope for the time-dependent
covariate, the survival prediction (SURVIVAL=sur) in the output file
(OUT=Out1) is wrong. SAS document explains how SAS calculates these
surivial predictions at
http://support.sas.com/onlinedoc/913/getDoc/en/statug.hlp/phreg_sect31.h
tm
http://support.sas.com/onlinedoc/913/getDoc/en/statug.hlp/phreg_sect31.
htm . Unfortunately, SAS doesn't follow the right equation described in
the docuemnt (Empirical Cumulative Hazards Function Estimates). Instead,
SAS calculates S(t,x)=S(t,0)**exp(beta*x), which only applies to
time-independent covariate. But S(t,0) is correct from SAS if a new
individual was created to have x=0 for all the time points. From S(t,0),
you can write some code to follow the right equation in the SAS document
to calculate S(t,x) correctly, which I tested to be consistent with
Splus results.
Nick and Rene:
With the predicted S(t,x), a step function instead of a smooth function,
you can simulate the event times. The hazard function can also be
calculated. Of course, it is also a step function, not a smooth
function. As a result, the integration step will be larger compared to
NONMEM assuming a parametric smooth hazard function.
Yaning
Yaning Wang, Ph.D.
Team Leader, Pharmacometrics
Office of Clinical Pharmacology
Office of Translational Science
Center for Drug Evaluation and Research
U.S. Food and Drug Administration
Phone: 301-796-1624
Email: [EMAIL PROTECTED]
"The contents of this message are mine personally and do not necessarily
reflect any position of the Government or the Food and Drug
Administration."
Quoted reply history
________________________________
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]
On Behalf Of Zhao, Liang
Sent: Tuesday, July 03, 2007 3:41 PM
To: Nanayakkara, Nuwan; [email protected]
Subject: RE: [NMusers] COX Proportional Hazard Model with Time Dependent
Covariate
Hi, Nuwan,
Just want to share what I just have found how to do it with S-pus for my
#2 question. It is easier to illustrate with an example.
data.cov <-data.frame(start=c(0, 1, 2, 3), stop=c(1, 2, 3, 4),
event=c(0, 0, 0, 1), age=(22, 23, 24, 25), transplant.surgery=c(0, 0, 1,
1), weight=c(70, 70, 69, 69))
survfit(your.previous.fit.outcome, data.cov, individual=T)
Here, "age", "transplant.surgery", and "weight" are the time-dependent
covariates that have been used to obtain "your.previous.fit.outcome".
It means that corresponding to time 0-1, age=22, transplant.surgery=0,
weight=70l; corresponding to time 1-2, age=23, transplant.surgery=0,
weight=70 ... .
Very important, the projected survival can only be obtained by flagging
"individual=T".
Cheers!
Liang
________________________________
From: Nanayakkara, Nuwan [mailto:[EMAIL PROTECTED]
Sent: Tuesday, July 03, 2007 1:54 PM
To: Zhao, Liang; [email protected]
Subject: RE: [NMusers] COX Proportional Hazard Model with Time Dependent
Covariate
For (2), take a look at Survival Analysis Using SAS: A Practical Guide:
Books: Paul D. Allison by Paul D. Allison.
________________________________
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]
On Behalf Of Zhao, Liang
Sent: Monday, July 02, 2007 2:34 PM
To: [email protected]
Subject: [NMusers] COX Proportional Hazard Model with Time Dependent
Covariate
Dear All,
I have the following questions regarding with COX survial model with
Time Dependent Covariate that needs your experience and expertise
(1) Even we can do it with S-Plus or SAS, it can not be handled by
NONMEM, am I right? If I am wrong, who has started the work?
(2) How to make predictions with time-variant covariates based on COX
model using S-plus or SAS, if not NONMEM?
The question is asked because certain epidemic diseases are
season-sensitive and none assumption on base hazard is advantageous over
parametric approaches. Thank you in advance!
Liang Zhao