How important is using the exact method for ties in a Cox model, and how long should this take?

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