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I'm analyzing the results of some simulation work using a Cox proportional hazard model, and I have what I perceive are a great many ties in the data, representing when a particular individual in the simulation was infected. For example, one of the (many) runs of this model:

Time, Freq
1, 8
2, 9
3, 5
4, 5
5, 6
6, 4
7, 1
8, 6
9, 4
10, 1
11, 3
12, 2

Followed be sporadic ties of two or three individuals all the way up to Time = 55. Worried about ties, I've analyzed the data using coxph() using both the Breslow and Efron methods.

The Breslow method for this particular data has a log(HR) of 1.95 with a standard error of 4.73. The Efron method produces a log(HR) of 1.75 with the same standard error. Ignoring for a moment the quality of those results in a general sense, they are slightly different, so I'd like to be able to check by using the Exact method. However, this seems to be extremely computationally intensive, and a small data set of ~200 individuals has taken over 24 hours to run.

How important is it to use the exact method for handling ties in this analysis? Is there another method someone would suggest? Do parametric models suffer from the same problems with tied data?

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Since you are simulating, do you know the true hazard ratio? – jkd Jul 25 '12 at 3:13
Also, the R help for coxph() states, "The Efron approximation is used as the default here, as it is much more accurate when dealing with tied death times, and is as efficient computationally." – jkd Jul 25 '12 at 3:14
@jkd Unfortunately no - simulating it on a network, and the effect of the network on the hazard is unknown. – EpiGrad Jul 25 '12 at 23:10

1 Answer

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It is normal that the exact method takes such a long time: it has to do quite a lot. My own experience is that the approximate methods you refer to can be quite poor (i.e., leading to substantively different conclusions to the use of exact methods), but my own experiences are a bit atypical as they involve the application of these methods to logit regression rather than the cox model.

If you do a google for PHREG and Paul D Allison, who has written a bit on this topic, you will find more information.

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I ended up turning to Paul Allison's book, as I always seem to, and implementing a conditional logistic regression model for this particular problem. – EpiGrad Jul 27 '12 at 21:57

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