An investigation of gene-gene interactions in dose-response studies with Bayesian nonparametrics

Abstract

Background: Best practice for statistical methodology in cell-based dose-response studies has yet to be established. We examine the ability of MANOVA to detect trait-associated genetic loci in the presence of gene-gene interactions. We present a novel Bayesian nonparametric method designed to detect such interactions.

Results: MANOVA and the Bayesian nonparametric approach show good ability to detect trait-associated genetic variants under various possible genetic models. It is shown through several sets of analyses that this may be due to marginal effects being present, even if the underlying genetic model does not explicitly contain them.

Conclusions: Understanding how genetic interactions affect drug response continues to be a critical goal. MANOVA and the novel Bayesian framework present a trade-off between computational complexity and model flexibility.

Keywords: Bayesian nonparametric; Dose-response; Epistasis; Machine learning; Neural network.

Figure 1

Graphical depiction of a neural network with several output units. The blue nodes on the bottom represent SNPs in MAF coding, the orange nodes represent the hidden unit functions in Equation (3), and the red nodes at the top represent the estimated response for each of the concentrations measured. This architecture allows the network to model the response at each concentration as a nonlinear combination of the input SNPs.

Figure 2

Overview of the Bayesian neural network method for dose-response studies. First the network architecture is established and transferred along with the data to GPU memory. The HMC simulation is performed on the GPU and the samples are then transferred back to main memory. The posterior for each SNP’s ARD parameter is compared to the null distribution. Bayesian posterior probabilities are computed to assess how likely each SNP is to be involved in determing drug-response. In the right panel SNP 1 shows little evidence of being involved with this trait while SNP P has strong evidence of playing a role.

Figure 3

Power results for the additive model. The power for the Bayesian neural network (BNN) model is shown in blue while MANOVA is shown in orange. Solid lines indicate the power to detect both loci, while the dashed lines indicate power to detect at least one of the causal loci.

Figure 4

Power results for the additive model with interactions. The power for the Bayesian neural network (BNN) model is shown in blue while MANOVA is shown in orange. Solid lines indicate the power to detect both loci, while the dashed lines indicate power to detect at least one of the causal loci.

Figure 5

Power results for the purely interactive mode. The power for the Bayesian neural network (BNN) model is shown in blue while MANOVA is shown in orange. Solid lines indicate the power to detect both loci, while the dashed lines indicate power to detect at least one of the causal loci.