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Hello,

One of my long-time clients (a CRO) recently asked for my help with a sample size calculation for a prospective study to time to cure of a mild condition. Subjects are randomized into two treatments (experimental and current standard-of-care) when they develop the condition, then treated and followed for 7 days to see if they attain a cure. The primary endpoint is time to cure. My client stated that XXX subjects would be randomized to detect an effect size of 0.25 with 80% power and 2-sided alpha of 0.05, but the method used to calculate this was not provided to me at that time.

After checking the literature to get estimates of the median time to cure in the standard-care population, I used nQuery Advisor to calculate the sample size using the alpha and beta above and assuming a 24-hour improvement in median time to cure in the experimental group, with analysis to be done using the log-rank test. My calculated total sample size was about 10% larger than what my client had told me. When I asked where the figure of XXX had come from, they told me that another statistical consultant had calculated it (they sent me screenshots of his results). They also told me that a second statistician had independently come up with a slightly smaller n than the first statistician. When I looked at the first statistician's results, it was apparent that he had used an effect-size calculation and the t distribution to calculate the sample size (that is, he treated the time-to-event outcome, in hours, as an intervally scaled dependent variable and the analysis as a comparison of mean time to cure in the 2 groups). I was able to confirm his result using nQuery, the t distribution, and the same parameters he used. I was told that the second statistician also used the t distribution for his calculations.

Since I've been out of grad school for a long time, I thought that there might have been some kind of breakthrough in sample size calculations that I wasn't aware of, that made the t distribution appropriate for calculation of time-to-event sample size - maybe for very short studies only?. However, a literature search has not turned up anything of the sort, only the expected warnings against treating time-to-event data as intervally scaled. I am now helping my client deal with their client regarding the necessity for a larger sample size than they budgeted for. My question is, is there ever any justification for treating time-to-event data as intervally scaled and using an effect size approach? I have never heard of this before and don't see how it can be justified given censoring and non-normality, but the argument is currently two against one, and I certainly don't want my client's client to over-enroll their study, nor do I want them to embark on an underpowered study!. Thanks for your help.

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Morgan Stewart
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Well, it depends. 2 issues.

(1) Distribution of the time-to-event outcome

Not all such outcomes are skewed (eg, exponential). For example, some Weibull distributions look VERY symmetric. In this case, a t-test might not be so far off (it is fairly robust to departures from normality as long as the distribution is reasonably symmetric). If you have prior data (say, of the current-standard-of-care patients), you may look at the distribution of cure times and see what it looks like.

(2) Censoring

If there is censoring (say, >5%), you might need to go to survival analyses. If the follow-up ends at 7 days, that might indeed be the case. But then, you would have to do power calculations accounting for the censoring rate etc.

So, if the distribution is nice and symmetric, and there will be no censoring to speak of, t-test might not be so unreasonable. Also, plus/minus 10% on sample size is a trivial difference IMO. Practically, it may  not seem trivial, but when you consider how much hand-waving and approximations and assumptions go into all our power calculations, plus/minus 10% is nothing.

Best,

Constantine

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Constantine Daskalakis
Thomas Jefferson University, Philadelphia, PA

Does your client have preliminary data that you can look at? Perhaps in the form of Kaplan-Meier curves of the two treatments? Because if the Kaplan-Meier curves look like they follow a location-shift model better than a proportional-hazards model, then that suggests that the Wilcoxon test would be more powerful than the log-rank test in detecting the difference between the curves. Which, in turn, may have provided the motivation for the previous statistician to go in a t-test direction rather than the log-rank-test direction.  

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Eric Siegel, MS
Research Associate
Department of Biostatistics
Univ. Arkansas Medical Sciences