Sequential Experimental Design for Optimal Structural Intervention in Gene Regulatory Networks Based on the Mean Objective Cost of Uncertainty

Scientists are attempting to use models of ever increasing complexity, especially in medicine, where gene-based diseases such as cancer require better modeling of cell regulation. Complex models suffer from uncertainty and experiments are needed to reduce this uncertainty. Because experiments can be costly and time-consuming it is desirable to determine experiments providing the most useful information. If a sequence of experiments is to be performed, experimental design is needed to determine the order. A classical approach is to maximally reduce the overall uncertainty in the model, meaning maximal entropy reduction. A recently proposed method takes into account both model uncertainty and the translational objective, for instance, optimal structural intervention in gene regulatory networks, where the aim is to alter the regulatory logic to maximally reduce the long-run likelihood of being in a cancerous state. The mean objective cost of uncertainty (MOCU) quantifies uncertainty based on the degree to which model uncertainty affects the objective. Experimental design involves choosing the experiment that yields the greatest reduction in MOCU. This paper introduces finite-horizon dynamic programming for MOCU-based sequential experimental design and compares it to the greedy approach, which selects one experiment at a time without consideration of the full horizon of experiments. A salient aspect of the paper is that it demonstrates the advantage of MOCU-based design over the widely used entropy-based design for both greedy and dynamic-programming strategies and investigates the effect of model conditions on the comparative performances.