# Re: [R] Cox Proportional Hazards model with a time-varying covariate

From: Paul Miller <pjmiller_57_at_yahoo.com>
Date: Fri, 01 Apr 2011 07:28:57 -0700 (PDT)

Hi Terry and Kevin,

Thanks for your replies to my post. And thanks particularly to Terry for pointing out my confusion about the "exact partial likelihood" vs. the "exact marginal likelihood." I'm learning and so am likely to be confused about such things from time to time.
I had thought that a good way to see if I was replicating the results would be to use the Efron approximation in both R and SAS. I tried this just now and obtained a similar pattern of differences in the results. Please bear with me. I hope I'm not doing something silly.
Below are my results in each program. I got the results for R simply by running the code I sent earlier. I got the results in SAS by changing TIES = EXACT to TIES = EFRON.
Should I be getting results as different as these? Or does this suggest that there is some problem in how I've set up my data in R? I've looked over my data In R and everything looks fine, but maybe I've missed something.
Thanks,

Paul

> summary(model)

Call:
coxph(formula = Surv(START, STOP, STATUS) ~ TRT + DENS + INFCTN,

```    data = vitclear)
n= 167
coef exp(coef) se(coef)      z Pr(>|z|)
```
TRT     0.2913    1.3382   0.1782  1.635    0.102
```DENS   -0.1762    0.8384   0.1739 -1.013    0.311
INFCTN  0.1192    1.1266   0.1912  0.624    0.533
exp(coef) exp(-coef) lower .95 upper .95
```
TRT       1.3382     0.7473    0.9436     1.898 DENS      0.8384     1.1927    0.5963     1.179 INFCTN    1.1266     0.8876    0.7746     1.639 Rsquare= 0.024   (max possible= 0.999 )
```Likelihood ratio test= 4.12  on 3 df,   p=0.2486
Wald test            = 4.12  on 3 df,   p=0.2485
Score (logrank) test = 4.15  on 3 df,   p=0.2460
```

Cox Proportional Hazards Model 09:01 Friday, April 1, 2011 1 Example 22.2: Hyalurise in Vitreous Hemorrhage The PHREG Procedure
Model Information
Data Set WORK.VITCLEAR
Dependent Variable RSPTIM
Censoring Variable CENS
Censoring Value(s) 0
Ties Handling EFRON

Number of Observations Used 143

Summary of the Number of Event and Censored Values Percent
Stratum CENTER Total Event Censored Censored 1 A 60 45 15 25.00
2 B 37 30 7 18.92
3 C 46 39 7 15.22

Total 143 114 29 20.28

Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Cox Proportional Hazards Model 09:01 Friday, April 1, 2011 2 Example 22.2: Hyalurise in Vitreous Hemorrhage The PHREG Procedure
Model Fit Statistics
Without With
Criterion Covariates Covariates
-2 LOG L 711.142 706.171
AIC 711.142 712.171
SBC 711.142 720.379

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 4.9712 3 0.1739
Score 4.9604 3 0.1747
Wald 4.9151 3 0.1781

Analysis of Maximum Likelihood Estimates Parameter Standard Hazard
Parameter DF Estimate Error Chi-Square Pr > ChiSq Ratio TRT 1 0.34437 0.19562 3.0988 0.0783 1.411 DENS 1 -0.23832 0.19585 1.4807 0.2237 0.788 INFCTN 1 0.12819 0.27780 0.2129 0.6445 1.137

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