Sample size calculation: difference in geometric means

[Jill Korsiak]

Hello,
I am working on a sub-study of a pre-existing clinical trial in which women were supplemented with vitamin D or placebo (N~500). In the sub-study, we are wanting to look at the effect of vitamin D supplementation on hepcidin concentrations (likely just comparing mean hepcidin between placebo and treatment group). Due to the high cost and time needed to measure hepcidin in the lab, we were looking to measure hepcidin in only a subset of women. The relationship between vitamin D and hepcidin has not been studied much in a clinical trial setting, but I did find one study (Smith et al., 2016; reference below) which looked at this association. I was hoping to use the effect size found in this study to base our sample size calculation on.

The authors report the geometric mean of hepcidin among women treated with vitamin D supplements was 2.4 ng/mL (95% CI: 0.8-7.4), while the geometric mean hepcidin concentrations was 9.0 ng/mL (95% CI: 4.8-16.7) among those in the placebo group. The authors then report a geometric mean ratio of 0.27 (95% CI: 0.08-0.96).

How can I conduct a sample size calculation based on this information? I have never had to do a sample size calculation using geometric means and 95% CI before- I have only used arithmetic means and SD when looking for a change in means. Alternatively, we are also open to doing a power calculation (with a pre-determined sample size of ~50-100 per group, maybe).

Thank you!


Reference:
Smith et al., 2016. High-dose vitamin D3 reduces circulating hepcidin concentrations: A pilot, randomized, double-blind, placebo-controlled trial in healthy adults. Clinical Nutrition. doi: 10.1016/j.clnu.2016.06.015

[Clyde Schechter]

Well, the geometric mean is the exponential of the mean of the natural logarithms. So you can just do your power analysis as if your outcome variable were log(hepcidin concentration).

Most likely Smith obtained the 95% CIs by exponentiating CIs obtained from the logarithms. So on the log scale, the width of the CI would be log(0.96)-log(0.08) = 2.485. And since that is presumably 1.96 standard errors, the standard error on the log scale would have been about 1.27. On the other hand, within each group, the standard errors calculated in the same way are 2.22 and 1.25, the first being appreciably wider. (Different sample sizes perhaps?) Anyway some figure in the 1.25-2.22 range, probably closer to the lower end, would be a reasonable guess for the pooled standard error.

Assuming your proposed design is reasonably similar to Smith's, you could appropriate that value as an anticipated standard error for your study. Then you just have to decide what an appropriate minimum clinically significant difference is and feed those things into your favorite sample size/power calculating program (which might be Stata). Since this is taken only from one other study, and who knows if the assays are different, or the populations differ in some relevant way, you probably want to do a sensitivity analysis around this value as well.

[Jill Korsiak]

Thank you very much for this response!

[Clifford Banda]

Jill Korsiak : what syntax in Stata did you use in the end for this calculation?

@Clyde Schechter: Would this be any different if the means were paired, that is assuming, in the example above, the participants were self-matched and had hepcidin levels before and after taking vit D and the reported mean and geometric mean ratios were a comparison between the two periods

[Clyde Schechter]

The basic principle would be the same: do the calculations based on the logarithm of hepcidin levels. But the calculation of sample size/power for a paired design is different from that for a two independent arms study. The Stata -sampsi- command handles both of these designs.

[Clifford Banda]

Thanks a lot.