st: RE: Many strata in Cox proportional hazard models

["Steve Rothenberg" <drlead@prodigy.net.mx>]

Given the very large range of age (49-94 years) in this mortality study and
the fact that there is a positive association between the exposure variable
of interest and age, it would seem a reasonable assumption that baseline
hazard will vary with age.  Specifying age strata allows different baseline
hazards for each age group while constraining the coefficients across strata
to be equal.  The question regarding the validity of proportional odds
assumption with this data set, especially among the different exposure
groups, is a matter for diagnostic tests; it may hold for the different
exposure groups or it may not.

With 9 5-year age strata it is feasible to test the proportional odds
assumption for the exposure variable in each strata; with 353 monthly age
strata it is much more difficult, not to mention the many one or two subject
monthly strata in which no one dies during the observation interval and the
hazard function is flat.

I welcome comments on this issue, as well as the two questions I raised in
the first post of this thread.

Steve Rothenberg
National Institute of Public Health
Cuernavaca, Morelos
Mexico


Steve,

Also I don't think you need to consider that the hazard varies with age.
I think the proportional hazards takes care of this.


David J Svendsgaard, PhD
Biostatistician
EPA/ORD/NCEA/RTP, Mail Drop B-243-01
Research Triangle Park, NC 27711
Phone (919) 541-4186
Fax (919) 541-1818

-----Mensaje original-----
De: Steve Rothenberg [mailto:drlead@prodigy.net.mx] 
Enviado el: Friday, July 15, 2011 1:23 PM
Para: 'statalist@hsphsun2.harvard.edu'
Asunto: RE: Many strata in Cox proportional hazard models

All variables except date and cause of death and date of right-censoring
were collected at baseline (entry to study).  The models were built on the
command line and no variables were identified as time varying.

Steve Rothenberg
National Institute of Public Health
Cuernavaca, Morelos
Mexico 

Did you check the  time-varying covariates box?
David J Svendsgaard, PhD
Biostatistician
EPA/ORD/NCEA/RTP, Mail Drop B-243-01
Research Triangle Park, NC 27711
Phone (919) 541-4186
Fax (919) 541-1818

-----Mensaje original-----
De: Steve Rothenberg [mailto:drlead@prodigy.net.mx] 
Enviado el: Friday, July 15, 2011 12:55 PM
Para: 'statalist@hsphsun2.harvard.edu'
Asunto: Many strata in Cox proportional hazard models

I'm trying to diagnose the proportional hazards assumption (and other
diagnostics) on Cox PH models.  I use a data set of mortality in  1154
subjects, with only baseline data measured at entry, and 185 failures during
the ~8 year follow up.  The age range of the group at entry is 49 to 94
years and there are three ordered categories of exposure to the variable of
interest.  All other independent variables in the model are dichotomous.

Since I expect baseline hazard to differ by age, I'm using age as the
stratification variable in stratified estimation.  A colleague has suggested
I use monthly age strata.  I obtain 353 monthly strata each with from 1 to
10 subjects, an average N in each strata ~ 3.  I've tried an alternative
strata division of 5-year age periods, 9 stratum groups in all with from 5
to 282 subjects in each group, an average N in each strata ~ 125.

The models with the monthly age strata all return hazard ratios for the
exposure variable below 1, compared to the lowest, reference exposure
variable.  The models with the 5-year age strata all return hazard ratios
for the exposure variables higher than 1.  Fit measures, such as AIC and BIC
are far better in the monthly stratified model than in the 5-year stratified
model.  The concordance index (Harrold's C) is .602 for the 5-year age
strata model and .615 in the monthly age strata model. 

I've checked proportional hazards assumptions for the exposure variables on
the each stratum of the 5-year strata model (along with other diagnostics)
and get good compliance on 7 of the 9 strata.  I don't know where and how to
begin checking the PH assumption on the monthly age strata model, due to the
large number of strata and the fact that there are so many strata with just
1 or 2 subjects.

I suspect overkill with monthly strata but wonder:

Question 1: Are there statistical drawbacks (other than diagnostic) to using
so many strata for survival models, especially with many singleton strata?

Question 2: Can anyone suggest available literature that discusses this
issue?

Steve Rothenberg
National Institute of Public Health
Cuernavaca, Morelos
Mexico

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/