[Paper Review] Nonparametric causal discovery with applications to cancer bioinformatics

Jean‐Pierre Gomez|arXiv (Cornell University)|Jun 28, 2023

Bioinformatics and Genomic NetworksBiochemistry, Genetics and Molecular Biology3 citations

TL;DR

This paper proposes a nonparametric causal discovery algorithm based on probabilistic causality and causal sufficiency to identify cause-effect relationships in binary gene expression data from prostate cancer and normal tissues. The method constructs causal graphs by detecting transitive and redundant arcs, eliminating spurious connections, and validating results against PCA-based gene rankings, achieving consistent top-ranking genes and a stable, interpretable network of genetic dysregulations linked to carcinogenesis.

ABSTRACT

Many natural phenomena are intrinsically causal. The discovery of the cause-effect relationships implicit in these processes can help us to understand and describe them more effectively, which boils down to causal discovery about the data and variables that describe them. However, causal discovery is not an easy task. Current methods for this are extremely complex and costly, and their usefulness is strongly compromised in contexts with large amounts of data or where the nature of the variables involved is unknown. As an alternative, this paper presents an original methodology for causal discovery, built on essential aspects of the main theories of causality, in particular probabilistic causality, with many meeting points with the inferential approach of regularity theories and others. Based on this methodology, a non-parametric algorithm is developed for the discovery of causal relationships between binary variables associated to data sets, and the modeling in graphs of the causal networks they describe. This algorithm is applied to gene expression data sets in normal and cancerous prostate tissues, with the aim of discovering cause-effect relationships between gene dysregulations leading to carcinogenesis. The gene characterizations constructed from the causal relationships discovered are compared with another study based on principal component analysis (PCA) on the same data, with satisfactory results.

Motivation & Objective

• To develop a nonparametric causal discovery method that avoids strong parametric assumptions and is scalable to large biological datasets.
• To model causal relationships between binary gene expression states in prostate cancer and normal tissues.
• To identify key genetic drivers of carcinogenesis through causal graph construction and validation against established methods like PCA.
• To address limitations in existing causal discovery tools, particularly in high-dimensional, complex biological data with unknown variable types.
• To provide a computationally efficient, interpretable framework for identifying minimal gene panels and causal chains relevant to cancer development.

Proposed method

• The algorithm uses a causal sufficiency framework based on probabilistic causality, modeling cause-effect relationships through material implication and contingency tables.
• It detects transitive paths and redundant arcs via triangle analysis, applying a priority-based elimination order to remove spurious and redundant connections.
• The Loevinger coefficient is used to quantify causal strength between binary variables, guiding arc directionality and network construction.
• A graph simplification pipeline removes spurious arcs based on conflict resolution in adjacent triangles and enforces transitivity constraints.
• The method applies a pseudocode-based implementation in C++ with optimized data structures, including sorted adjacency lists and dictionary-based lookups.
• The algorithm incorporates a PageRank-based gene ranking system to identify central nodes in the causal network, validated against PCA-derived gene importance.

Figure 2.1: First case of adjacent triangles, with conflict for the elimination of spurious arcs

Experimental results

Research questions

• RQ1 Can a nonparametric causal discovery algorithm effectively identify cause-effect relationships in high-dimensional, binary gene expression data without assuming parametric distributions?
• RQ2 How does the proposed method compare to PCA in identifying biologically relevant genes associated with prostate cancer progression?
• RQ3 What is the impact of spurious and redundant arc elimination order on the stability and interpretability of the resulting causal graph?
• RQ4 Can the algorithm recover known or plausible causal chains of genetic dysregulation in carcinogenesis?
• RQ5 To what extent does the causal graph structure converge with increasing sample size, and how robust are the identified causal relationships?

Key findings

• The algorithm successfully constructed a causal graph of genetic alterations in prostate adenocarcinoma, with 15 top-ranked genes by PageRank matching or overlapping with those identified in PCA-based analyses.
• Genes such as SLC39A2, ACTC1, and SEMG1 showed high PageRank scores (e.g., 43, 159, 24 respectively) and were consistently ranked highly across multiple analyses.
• The subgraph induced by genes with contrast >5% showed a scale-free degree distribution, indicating the presence of highly connected hub genes in the causal network.
• The method identified 8 genes with contrast >5% in the simplified graph, including known cancer-related genes like P63 and KRT5, suggesting biological plausibility.
• The PageRank rankings from the causal graph showed strong correlation with those from PCA, validating the algorithm’s ability to recover biologically meaningful gene importance.
• The algorithm demonstrated stability in graph structure across different sample subsets, with convergence patterns suggesting reliable inference as sample size increased.

Figure 2.2: Second case of adjacent triangles, with conflict for the elimination of spurious arcs