Causal models and prediction in cell line perturbation experiments

In cell line perturbation experiments, a collection of cells is perturbed with external agents and responses such as protein expression measured. Due to cost constraints, only a small fraction of all possible perturbations can be tested in vitro. This has led to the development of computational models that can predict cellular responses to perturbations in silico. A central challenge for these models is to predict the effect of new, previously untested perturbations that were not used in the training data. Here we propose causal structural equations for modeling how perturbations effect cells. From this model, we derive two estimators for predicting responses: a Linear Regression (LR) estimator and a causal structure learning estimator that we term Causal Structure Regression (CSR). The CSR estimator requires more assumptions than LR, but can predict the effects of drugs that were not applied in the training data. Next we present Cellbox, a recently proposed system of ordinary differential equations (ODEs) based model that obtained the best prediction performance on a Melanoma cell line perturbation data set (Yuan et al. in Cell Syst 12:128-140, 2021). We derive analytic results that show a close connection between CSR and Cellbox, providing a new causal interpretation for the Cellbox model. We compare LR and CSR/Cellbox in simulations, highlighting the strengths and weaknesses of the two approaches. Finally we compare the performance of LR and CSR/Cellbox on the benchmark Melanoma data set. We find that the LR model has comparable or slightly better performance than Cellbox.