MixTwice: large-scale hypothesis testing for peptide arrays by variance mixing

Peptide microarrays have emerged as a powerful technology in immunoproteomics as they provide a tool to measure the abundance of different antibodies in patient serum samples. The high dimensionality and small sample size of many experiments challenge conventional statistical approaches, including those aiming to control the false discovery rate (FDR). Motivated by limitations in reproducibility and power of current methods, we advance an empirical Bayesian tool that computes local FDR statistics and local false sign rate statistics when provided with data on estimated effects and estimated standard errors from all the measured peptides. As the name suggests, the MixTwice tool involves the estimation of two mixing distributions, one on underlying effects and one on underlying variance parameters. Constrained optimization techniques provide for model fitting of mixing distributions under weak shape constraints (unimodality of the effect distribution). Numerical experiments show that MixTwice can accurately estimate generative parameters and powerfully identify non-null peptides. In a peptide array study of rheumatoid arthritis, MixTwice recovers meaningful peptide markers in one case where the signal is weak, and has strong reproducibility properties in one case where the signal is strong.

Automated summary

Peptide microarrays are a powerful tool in immunoproteomics, but face challenges with high dimensionality and small sample sizes in experiments. The MixTwice tool addresses limitations in reproducibility and power of current methods by computing local FDR statistics and local false sign rate statistics, effectively estimating generative parameters and identifying non-null peptides. Numerical experiments demonstrate its accuracy and reproducibility in identifying meaningful peptide markers in different signal strengths.