SUMMARY: We introduce Eliater, a Python package for estimating the effect of perturbation of an upstream molecule on a downstream molecule in a biomolecular network. The estimation takes as input a biomolecular network, observational biomolecular data, and a perturbation of interest, and outputs an estimated quantitative effect of the perturbation. We showcase the functionalities of Eliater in a case study of Escherichia coli transcriptional regulatory network. AVAILABILITY AND IMPLEMENTATION: The code, the documentation, and several case studies are available open source at https://github.com/y0-causal-inference/eliater.

Causal query estimation in biomolecular networks commonly selects a 'valid adjustment set', i.e. a subset of network variables that eliminates the bias of the estimator. A same query may have multiple valid adjustment sets, each with a different variance. When networks are partially observed, current methods use graph-based criteria to find an adjustment set that minimizes asymptotic variance. Unfortunately, many models that share the same graph topology, and therefore same functional dependencies, may differ in the processes that generate the observational data. In these cases, the topology-based criteria fail to distinguish the variances of the adjustment sets. This deficiency can lead to sub-optimal adjustment sets, and to miss-characterization of the effect of the intervention. We propose an approach for deriving 'optimal adjustment sets' that takes into account the nature of the data, bias and finite-sample variance of the estimator, and cost. It empirically learns the data generating processes from historical experimental data, and characterizes the properties of the estimators by simulation. We demonstrate the utility of the proposed approach in four biomolecular Case studies with different topologies and different data generation processes. The implementation and reproducible Case studies are at https://github.com/srtaheri/OptimalAdjustmentSet.

MOTIVATION: Estimating causal queries, such as changes in protein abundance in response to a perturbation, is a fundamental task in the analysis of biomolecular pathways. The estimation requires experimental measurements on the pathway components. However, in practice many pathway components are left unobserved (latent) because they are either unknown, or difficult to measure. Latent variable models (LVMs) are well-suited for such estimation. Unfortunately, LVM-based estimation of causal queries can be inaccurate when parameters of the latent variables are not uniquely identified, or when the number of latent variables is misspecified. This has limited the use of LVMs for causal inference in biomolecular pathways. RESULTS: In this article, we propose a general and practical approach for LVM-based estimation of causal queries. We prove that, despite the challenges above, LVM-based estimators of causal queries are accurate if the queries are identifiable according to Pearl's do-calculus and describe an algorithm for its estimation. We illustrate the breadth and the practical utility of this approach for estimating causal queries in four synthetic and two experimental case studies, where structures of biomolecular pathways challenge the existing methods for causal query estimation. AVAILABILITY AND IMPLEMENTATION: The code and the data documenting all the case studies are available at https://github.com/srtaheri/LVMwithDoCalculus. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Counterfactual inference is a useful tool for comparing outcomes of interventions on complex systems. It requires us to represent the system in form of a structural causal model, complete with a causal diagram, probabilistic assumptions on exogenous variables, and functional assignments. Specifying such models can be extremely difficult in practice. The process requires substantial domain expertise, and does not scale easily to large systems, multiple systems, or novel system modifications. At the same time, many application domains, such as molecular biology, are rich in structured causal knowledge that is qualitative in nature. This article proposes a general approach for querying a causal biological knowledge graph, and converting the qualitative result into a quantitative structural causal model that can learn from data to answer the question. We demonstrate the feasibility, accuracy and versatility of this approach using two case studies in systems biology. The first demonstrates the appropriateness of the underlying assumptions and the accuracy of the results. The second demonstrates the versatility of the approach by querying a knowledge base for the molecular determinants of a severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)-induced cytokine storm, and performing counterfactual inference to estimate the causal effect of medical countermeasures for severely ill patients.