A Bayesian hierarchical model for signal extraction from protein microarrays

Abstract

Protein microarrays are a promising technology that measure protein levels in serum or plasma samples. Due to their high technical variability and high variation in protein levels across serum samples in any population, directly answering biological questions of interest using protein microarray measurements is challenging. Analyzing preprocessed data and within-sample ranks of protein levels can mitigate the impact of between-sample variation. As for any analysis, ranks are sensitive to preprocessing, but loss function based ranks that accommodate major structural relations and components of uncertainty are very effective. Bayesian modeling with full posterior distributions for quantities of interest produce the most effective ranks. Such Bayesian models have been developed for other assays, for example, DNA microarrays, but modeling assumptions for these assays are not appropriate for protein microarrays. Consequently, we develop and evaluate a Bayesian model to extract the full posterior distribution of normalized protein levels and associated ranks for protein microarrays, and show that it fits well to data from two studies that use protein microarrays produced by different manufacturing processes. We validate the model via simulation and demonstrate the downstream impact of using estimates from this model to obtain optimal ranks.

Keywords: Bayesian models; bioinformatics; optimal ranks; preprocessing; protein microarrays.

FIGURE 1

Posterior distributions for four different active spots ($t=a$) of $S$ on four malaria arrays (A,B,C,D) and four HuProt^™ arrays (E,F,G,H) fit with Model 1. Vertical dashed lines are at mean of values $Y_{i,t=a,p,j}$ corresponding to the protein $p$.

FIGURE 2

Posterior distributions for means, ${\mu }_{i,t}$ of four different control spots on four malaria arrays (A, B, C, D) and four HuProt^™ arrays (E, F, G, H) fit with Model 1. Vertical dashed lines are at mean values of $Y_{i,t,p,j}$ for a particular type of control protein, $t\in 1,\dots ,T$.

FIGURE 3

$P^{‡}$ for all 503 malaria arrays and 5 of the 100 HuProt^™ arrays fit with Models 1, 2, and 3. The red line is $y=x$.

FIGURE 4

Percentile residuals ($P^{‡}$) for 10 simulated arrays under generating models A, B, C, D, E, and F (Section 3.3), analyzed with Models 1 and 2 respectively.

FIGURE 5

Each color is a protein simulated under generating mechanism A, B, C, D, E, or F each column shows one of the true ranks of $S$, the Squared error loss ranks $\ddot{T}$, obtained from posterior distributions under Model 1 or Model 2. Lines represent how the protein ranks change from the top 30 true values to those under the two analysis models.

FIGURE 6

Each color is a protein on the original malaria or HuProt^™ array, each column shows one of: the published ranks from Kobayashi et al, the ranks of fluorescent intensity preprocessed according to the procedure described in Bérubé et al, the squared error loss ranks, $\ddot{T}$, and the gamma ($\gamma =3$) ranks, $\ddot{Q}$. Lines represent how ranks of proteins change across each method of preprocessing and ranking.