st: Many strata in Cox proportional hazard models

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

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

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