Gene Set Priorization Guided by Regulatory Networks with p-values through Kernel Mixed Model

Abstract

The transcriptome association study has helped prioritize many causal genes for detailed study and thus further helped the development of many therapeutic strategies for multiple diseases. How- ever, prioritizing the causal gene only does not seem always to be able to offer sufficient guidance to the downstream analysis. Thus, in this paper, we propose to perform the association studies from another perspective: we aim to prioritize genes with a tradeoff between the pursuit of the causality evidence and the interest of the genes in the pathway. We introduce a new method for transcriptome association study by incorporating the information of gene regulatory networks. In addition to directly building the regularization into variable selection methods, we also expect the method to report p-values of the associated genes so that these p-values have been empirically proved trustworthy by geneticists. Thus, we introduce a high-dimension variable selection method with the following two merits: it has a flexible modeling power that allows the domain experts to consider the structure of covariates so that prior knowledge, such as the gene regulatory network, can be integrated; it also calculates the p-value, with a practical manner widely accepted by geneticists, so that the identified covariates can be directly assessed with statistical guarantees. With simulations, we demonstrate the empirical strength of our method against other high-dimension variable selection methods. We further apply our method to Alzheimer’s disease, and our method identifies interesting sets of genes.

Appendices

A Additional Simulation Experiments

Different Strengths of the Regulation. Further, we study how the strength of regulation will affect the performances of our methods, and we model this shift of strength with variations of the parameter r in the data generation process, while the rest of the configurations remain the same as the data generation process. Also, we continue to focus on the intermediate level of the previous example where we set $v=16$.

Fig. 2.

ROC curve of competing methods over different regulation strength of the TF.

Similarly, we repeat the experiments three times and plot the ROC curve with standard deviation plotted as the shady areas in Fig. 2.

As Fig. 2 shows, our method is on par with previous hypothesis testing methods over most correlation levels. When $r=1$, the regulated genes are distributed in the same way as the TF, although are associated with smaller effect sizes. Both LMM and KMM are good enough to uncover the associated genes in this case. When r is smaller (0.5 or 0.3), the regulated genes are less dependent on the TF, the hypothesis testing methods all perform similarly, probably because that when the regulated genes are more independent from the TF, the network structure does not introduce advantages. However, when $r=0.7$, the KMM method starts to show a clear advantage over other methods. In summary, our proposed method can outperform other methods when there is a strong correlation between the TF and regulated genes (but not too strong when the regulated genes and TF are identically distributed). We believe this is the most frequently seen scenarios in real-world data. In addition, in other scenarios, our method does not perform worse than other methods, so there is no loss in using our method in general. In fact, if one calculates the area under ROC curve for Fig. 2, our method performs the best in all these four tested scenarios, although the advantages of our method in the other three scenarios are marginal.

Misspecified Network Structure. Finally, as our method is built upon the knowledge of network structure, we are interested in knowing what if the network structure is misspecified since in practice, we may not always be able to obtain a network structure faithful to the underlying regulatory mechanism. To simulate this, we introduce another hyperparameter q in the data generation process. When we generate the network structure N, we drop the edges in the network structure with the probability $1-q$. The rest configuration of data generation is the same as the general one introduced in the preceding texts.

Fig. 3.

ROC curve of competing methods when the prior network is misspecified (the edges of a network is dropped with probability $1-q$).

Again, we repeat the experiments three times and plot the ROC curve with standard deviation plotted as the shady areas in Fig. 3.

As Fig. 3 shows, our method is surpringly robust to the misspefication of the prior network structure. When $q=1$, the input network is faithful to the underlying regulatory network, and the KMM method certainly outperforms the competing methods. Interestingly, the advantages of the KMM method maintain even when half of the edges of the input network are missing ($q=0.5$). When $q=0.3$, which means that 70% of the edges of the underlying regulatory network are missing in the input network for the model, the proposed method start to perform similarly to the previous hypothesis testing methods. Even this case, the calculated area under ROC score of KMM will be higher than those competing methods, although this advantage cannot be observed in the ROC curves.

B Covaraite Regressing

To demonstrate the success correction of these factors, we compared the Spearman’s correction between the expressions and the covariates before and after the correction. Figure 4 shows the comparison of the Spearman’s correlation between the gene expressions and the covariates before and after the regressing across the three different compartments studied in this work, and we can see that the correlation between each genes and the age covaraites drops significantly after the regression.

Fig. 4.

The comparison of the Spearman’s correlation between the gene expressions and the covariates before and after the regressing.