Causal Discovery of Gene Regulation with Incomplete Data

Abstract

Causal discovery algorithms aim to identify causal relations from observational data and have become a popular tool for analysing genetic regulatory systems. In this work, we applied causal discovery to obtain novel insights into the genetic regulation underlying head-andneck squamous cell carcinoma. Some methodological challenges needed to be resolved first. The available data contained missing values, but most approaches to causal discovery require complete data. Hence, we propose a new procedure combining constraint-based causal discovery with multiple imputation. This is based on using Rubin's rules for pooling tests of conditional independence. A second challenge was that causal discovery relies on strong assumptions and can be rather unstable. To assess the robustness of our results, we supplemented our investigation with sensitivity analyses, including a non-parametric bootstrap to quantify the variability of the estimated causal structures. We applied these methods to investigate how the high mobility group AT-Hook 2 (HMGA2) gene is incorporated in the protein 53 signalling pathway playing an important role in head-and-neck squamous cell carcinoma. Our results were quite stable and found direct associations between HMGA2 and other relevant proteins, but they did not provide clear support for the claim that HMGA2 itself is a key regulator gene.

Multiple imputation and test-wise deletion for causal discovery with incomplete cohort data

“…However, it is not clear what a good pooling method would be. The other one is to pool at the test level, as proposed by Foraita et al (2020): First, m imputed datasets are generated using standard multiple imputation techniques. Then causal discovery is applied with the following modification: For each test, the test statistic is calculated using each of the m datasets in turn, and the m test statistics are pooled using appropriate rules.…”

“…Fisher's z-test can be applied to multiply imputed data using Rubin's rules, as follows (Schafer, 1997, page 109;Foraita et al, 2020).…”

“…Single imputation usually leads to underestimation of standard errors. Recently, two promising new strategies have been suggested for constraint-based causal discovery with missing values: (i) test-wise deletion (Strobl et al, 2018;Tu et al, 2019Tu et al, , 2020, where each conditional independence test is performed using the subset of records containing complete data for all variables involved in that particular test, and (ii) multiple imputation for Gaussian data (Foraita et al, 2020).…”

“…Building on Tu et al (2019), we establish necessary and sufficient conditions for the recoverability of causal graphs under test-wise deletion. Further, we extend the multiple imputation approach by Foraita et al (2020) to discrete and mixed variables, characterise situations in which multiple imputation is expected to outperform test-wise deletion, and discuss why selecting the imputation model is challenging in causal discovery. The performance of list-wise deletion, test-wise deletion, single imputation and multiple imputation is compared on simulated and real data.…”

A practical guide to causal discovery with cohort data

“…Therefore, information on the available causal discovery software packages are scattered across the literature (usually as software manual or R package vignette), which makes it more difficult for users to compare and contrast them. In this paper, we aim to provide a practical guide for carrying out causal discovery via three of the most popular software implementations: the Java-based TETRAD software package (Scheines et al, 1998), the R package bnlearn (Scutari, 2010), and the R package pcalg (Kalisch et al, 2012;Hauser and Bühlmann, 2012) with its add-ons tpc (Witte, 2021) and micd (Foraita et al, 2020;Witte et al, 2021). For simplicity, we will focus only on the constraint-based PC algorithm and how it is implemented in each software package.…”