**Protein Ratio Statistics:**

Overall protein ratios and their standard errors were calculated using a hierarchical model combined with bootstrap estimates and pooled variance estimates at the peptide level. Briefly, a global estimate of measurement error is calculated using pooled variance from the protein ratio in each replicate. Next, a hierarchical model of the overall protein ratio is calculated by first calculating the protein replicate ratio as the median of the peptide ratios in each replicate and then calculating the overall protein ratio as the mean of the protein replicate ratios. Finally, the standard error of the overall protein ratio is calculated using a bootstrap procedure where resampling with replacement occurs within the hierarchical model at both the replicate and peptide level and each peptide ratio in the bootstrap procedure is augmented by adding a random â€œnoiseâ€ effect drawn from a normal distribution with mean zero and standard deviation equal to the previously calculated global estimate of measurement error. In total, 1000 bootstrap iterations are performed. The standard error of the overall protein ratio is then calculated as the standard deviation of the bootstrapped overall protein ratios. Z-tests can then be used to calculate p values of overall protein ratios with respect to a 1-to-1 ratio.

Overall protein ratios and their standard errors were calculated using a hierarchical model combined with bootstrap estimates and pooled variance estimates at the peptide level. Briefly, a global estimate of measurement error is calculated using pooled variance from the protein ratio in each replicate. Next, a hierarchical model of the overall protein ratio is calculated by first calculating the protein replicate ratio as the median of the peptide ratios in each replicate and then calculating the overall protein ratio as the mean of the protein replicate ratios. Finally, the standard error of the overall protein ratio is calculated using a bootstrap procedure where resampling with replacement occurs within the hierarchical model at both the replicate and peptide level and each peptide ratio in the bootstrap procedure is augmented by adding a random â€œnoiseâ€ effect drawn from a normal distribution with mean zero and standard deviation equal to the previously calculated global estimate of measurement error. In total, 1000 bootstrap iterations are performed. The standard error of the overall protein ratio is then calculated as the standard deviation of the bootstrapped overall protein ratios. Z-tests can then be used to calculate p values of overall protein ratios with respect to a 1-to-1 ratio.

Can somebody tell me more about this method including hierarchical model construction ? pointer to any article, book, example code is highly appreciated.

The original article can be accessed here(free PMC pdf)

http://www.ncbi.nlm.nih.gov/pubmed/24563536