# Sample Size Calculation for Gene and Protein Biomarker Study

The PIs are looking for biomarkers in pre and post-trauma individuals. I need to calculate a sample size for a microarray study of 10 genes and the top 5 up- and down-regulated proteins and metabolites. Each subject will be sampled twice: pre-exposure and post-exposure. I've calculated sample sizes of non-genomic studies before, but would appreciate guidance on where to start. I am fluent in the R programming language and welcome suggestions for packages and/or techniques specific to genomic studies and sample size calculation.

EDIT

I'm getting 69 for sample size. Here's my process to ensure I'm on the right path:

The study's design includes pre and post gene expression values for each subject. Thus, we anticipate a series of paired t-tests over 30 variables, so we must adjust the p-value for multiple comparisons. FDR is the standard p-value adjustment in genetic expression studies. However, since we cannot do FDR without the raw p-values from the experiment, I set alpha to 0.05/30. This Bonferroni-like adjustment is more conservative than FDR, so the resulting sample size will be a bit higher than the PIs need, which may be desirable overall.

The PIs had no specific effect size in mind, so I set the effect size (Cohen's d) to a moderate 0.5.

I assumed 0.5 for the correlation between the paired measurements since we do not have pilot data to guide us.

Finally, I incorporated a standardized standard deviation sqrt(1/(2*(1-0.5))) in the absence of specific experimental means and standard deviations.

library(pwrss)

effect_size <- 0.5
power_experiment <- 0.80
paired_correlation <- 0.5
SD_standardized <- sqrt(1/(2*(1-0.5)))

mu2 = 0,
sd1 = SD_standardized,
sd2 = SD_standardized,
paired = TRUE,
paired.r = paired_correlation,
power = power_experiment,
alternative = "not equal")

Difference between Two means
(Paired Samples t Test)
H0: mu1 = mu2
HA: mu1 != mu2
------------------------------
Statistical power = 0.8
n = 69
------------------------------
Alternative = “not equal”
Degrees of freedom = 68
Non-centrality parameter = 4.153
Type I error rate = 0.002
Type II error rate = 0.2


Some statements are key:

The PIs had no specific effect size in mind, so I set the effect size (Cohen's d) to a moderate 0.5.

I assumed 0.5 for the correlation between the paired measurements since we do not have pilot data to guide us.

Finally, I incorporated a standardized standard deviation sqrt(1/(2*(1-0.5))) in the absence of specific experimental means and standard deviations.

Although you seem to be performing FWER calculations properly under those assumptions, the sample size that you get depends heavily upon them. The risk you run is that those assumptions will lead either to a much larger or a much smaller sample size than necessary. Part of the job is helping the client to think through the experimental design in a way that minimizes such problems.

Ask the PIs what effect size they have in mind and what data might be available on correlations and standard deviations in such studies. This is not the first time anyone has done microarray, protein-expression, or metabolite-level analyses, presumably even in this particular field of study. There are large repositories of data from such studies, like the NIH Gene Expression Omnibus, that can provide a basis for better estimates.

Furthermore, you don't necessarily have to replace the FDR criterion with a conservative FWER criterion. A web search on "power analysis FDR" shows several papers dealing with this issue, for example:

Practical guidelines for assessing power and false discovery rate for a fixed sample size in microarray experiments, Tiejun Tong & Hongyu Zhao, Stat Med. 27: 1960–1972 (2008)

Sample size calculation while controlling false discovery rate for differential expression analysis with RNA-sequencing experiments, Ran Bi & Peng Liu, BMC Bioinformatics 17: Article 146 (2016)

I don't have experience with that type of power analysis, but those and similar references should point you in a better direction--if you can get the PIs to tell you what their expectations are.

• Thank you so much @EdM! These are great resources and I super appreciate your insights. Dec 8, 2023 at 20:24