Sample size calculation example

[Oliver Scott]

Hi all,

I am writing a postdoc grant application right now and I have written a paragraph on a sample size calculation example, as follows:

"Assuming I wanted to detect a hazard ratio of 0.91 for overall survival in [X] patients associated with [X] use, at 80% power, with a 5% level of significance, and assuming a 10-year survival rate of 10% and prevalence of [X] use among [X] of ~25%, I would need a sample size of 5,230 patients. As I have identified 33,500 [X] from in my cohort (and assuming that ~30% of [X] are diagnosed with [X]), the sample size will be sufficient to detect HRs closer to the null (1) if the protective effect of [X] is not as strong among [X]. In fact, given my sample size of ~10,050 [X], the size of my cohort will be sufficiently powered (at 80% power) to detect a reduction in risk as small as 7% (i.e., a HR of 0.93)".

The [X]'s simply represent my cohort and exposure of interest-I didn't think they were relevant to include.

The commands I used in STATA are as follows:

power cox -0.094310679, p(0.8) eventpr(0.90) sd(0.433012701)

In this command, I took the natural log of the HR (0.91) and derived the standard deviation from the square root of 0.25*(1-0.25) (i.e., the prevalence of the exposure multipled by 1 minus the prevalence).

power cox, n(10050) p(0.8) eventpr(0.90) effect(hr) sd(0.433012701)

In this command, I took the sample size as 30% of 33,500 (10,050).

Do these commands/calculations look correct? Any help would be appreicated, because I'm not very used to using power cox in STATA.

Warm regards, Oliver

[Clyde Schechter]

I ran this in PASS 2025 and came out with essentially the same results, presented here lightly edited for simplicity:

A parallel, 2-group design (with one control group and 1 treatment groups) will be used to test whether the hazard rate for the treatment group is different from the control group hazard rate (H0: HR = 1 versus H1: HR ≠ 1, HR = treatment hazard rate/ control hazard rate). The hypotheses will be evaluated using 1 two-sided, two-sample ... Cox's proportional hazards regression term Z-tests, with an overall (experiment-wise) Type I error rate (α) of 0.05. ... It is anticipated that the proportion of subjects in each group that will have an event during the course of the study ... will be 0.9 . To detect the treatment to control hazard ratio 0.91 with at least 80% power ..., the control group sample size needed will be 3924 and the number of needed subjects for the treatment groups will be 1308 (totaling 5232 subjects overall). The corresponding total number of events is 4708.8. These results assume that the hazard ratio is constant throughout the study. The group sample sizes were computed using PASS 2025, version 25.0.3. [Emphasis added]

(N.B. PASS assumes a randomized design, and so refers to treatment and control rather than exposed and unexposed groups.)