DAGBagM: learning directed acyclic graphs of mixed variables with an application to identify protein biomarkers for treatment response in ovarian cancer

Abstract

Background Applying directed acyclic graph (DAG) models to proteogenomic data has been shown effective for detecting causal biomarkers of complex diseases. However, there remain unsolved challenges in DAG learning to jointly model binary clinical outcome variables and continuous biomarker measurements. Results In this paper, we propose a new tool, DAGBagM, to learn DAGs with both continuous and binary nodes. By using appropriate models, DAGBagM allows for either continuous or binary nodes to be parent or child nodes. It employs a bootstrap aggregating strategy to reduce false positives in edge inference. At the same time, the aggregation procedure provides a flexible framework to robustly incorporate prior information on edges. Conclusions Through extensive simulation experiments, we demonstrate that DAGBagM has superior performance compared to alternative strategies for modeling mixed types of nodes. In addition, DAGBagM is computationally more efficient than two competing methods. When applying DAGBagM to proteogenomic datasets from ovarian cancer studies, we identify potential protein biomarkers for platinum refractory/resistant response in ovarian cancer. DAGBagM is made available as a github repository at https://github.com/jie108/dagbagM.

Learning directed acyclic graphs for ligands and receptors based on spatially resolved transcriptomic analysis of ovarian cancer

“…Finally, the score of a graph G is the summation of individual node scores: where D denotes the data. We then search for the DAG that minimizes the above score function using an efficient implementation of the hill climbing algorithm that is modified from one of our recent works DAGBagM [28] – a DAG method for mixed types of nodes.…”

“…We conduct simulation experiments to examine the performance of LRnetST and further compare it with three alternative methods: DAGBagM, DAGBagM_C [28] and bnlearn [29]. Specifically, DAGBagM_C and bnlearn are applied to the Initial Neighbor Integrated Matrix ( Figure 1b ) before introducing the binary nodes.…”

“…Finally, we learn one DAG based on each bootstrap resample using the method described in the previous subsection. The resulting ensemble of DAGs are then aggregated following the aggregation procedure implemented in DAGBagM [28], where the hill climbing algorithm is (again) used to search for the DAG that minimizes an aggregation score based on the structural Hamming distance (SHD) while maintaining acyclicity.…”

“…Specifically, the DAGs are constructed by minimizing a score function, amounting to maximize a BIC penalized joint likelihood of all the random variables in the graph. Similar to a previous work [28], continuous variables conditioned on their parent nodes are modeled with Gaussian distributions, while a logistic model is employed to characterize the dependency of binary variables on their parent nodes. In addition, from the definition of the binary and continuous variable of each gene, it's obvious that the binary variable is a parent node of its corresponding continuous variable and the likelihoods of the continuous variables are evaluated only for spots where the corresponding binary nodes take the value 1 (i.e., when the continuous variables are defined).…”

“…We compared the performance of DAG construction based on initial-NIM and NIM to assess the advantage of using the paired binary and continuous nodes to facilitate the modeling of zero-inflation in ST data. Moreover, we compared the performance of LRnetST to alternative DAG construction methods including DAGBagM [28], DAGBagM_C [28], and bnlearn [29]. Note, DAGBagM, which can handle binary and continuous variables simultaneously, was applied to NIMs; while DAGBagM_C, which model continuous variables, were applied to the initial NIM before introducing the binary nodes.…”