I was trying to fit Cox Regression (aka Proportional Hazard) model on some cancer data (N=2288). I got the following output from SAS proc phreg:
Parameter Chi-Square p HR RaceN 3.7375 0.0532 1.198 Chemo 51.2541 <.0001 0.474 Surgery 251.6561 <.0001 0.211 ChSu 29.4288 <.0001 2.000 Age 53.1842 <.0001 1.018 Stage 1 220.5925 <.0001 0.133 Stage 2 66.7599 <.0001 0.353 Stage 3 24.3555 <.0001 0.720
All variables but Age are categorical. To make sure the model is valid, I tried the following two methods:
- log-log plot for categorical variables
- plotting Schoenfeld residuals of the model and then fit a line across it, looking at p-value of its slope not being 0
I got the following results:
Race Chemo Surgery Stage Age Test 1: ok BAD ok 2 n 3 cross NA Test 2: 0.2674 p<.0001 p<.0001 0.4622 0.0655
Following the advice here (http://statistics.ats.ucla.edu/stat/examples/asa/test_proportionality.htm), I created Race_t, Chemo_t, Surgery_t, Age_t, ChSu(interaction of Chemo and surgery) and do another Cox Regression, here's what I got:
Parameter Chi-Square p HR RaceN 27.1173 <.0001 1.888 Ra_t 57.5135 <.0001 0.999 ChemoN 0.4524 0.5012 1.086 Ch_t 36.6052 <.0001 0.999 Surgery 2.101 0.1472 1.195 Su_t 96.4175 <.0001 0.999 ChSu 14.9843 0.0001 1.687 Age 817.9242 <.0001 1.113 Age_t 1222.1119 <.0001 1 Stage 1 169.5012 <.0001 0.162 Stage 2 68.4689 <.0001 0.29 Stage 3 6.6744 0.0098 0.839
ALL the time-dependent covariates are statistically significant, while the original ChemoN and Surgery is no longer!!(and the implication goes the other direction!! --> surgery, chemo both lead to higher risk!!) Surprised to see that Ra_t is statistically significant. I am not sure what to make of my results.
Here are my main question:
- How should I proceed for my model? What should I look at to decide what to do?
- Is there a (or a set of) conclusive test for the proportionality assumption for Cox Regression? If so, how to implement it in SAS?
- For the subjective / graphical test, how far a departure from expected is too far?
- How 'good' (not sure what the statistics terminology is, in terms of Type I and Type II errors?) is the "Including Time Dependent Covariates in the Cox Model" test? E.g. why would Ra_t be significant even if Race1 looks fine in both subjective tests?
- Have anyone heard of the Schoenfeld's Global Test of Fitness (http://www.sljol.info/index.php/JNSFSL/article/view/456) I am having difficulty figuring out the expected count in the cells. Any help would be appreciated.
Thank you very much!