Both the GSEA and hierarchical modeling approaches can be thought of as “empirical” as they use external information only to guide the selection of terms to include in a model or to stabilize their estimation. These approaches do not fit strong mechanistic models directly — our understanding of the basic biology is too primitive — although there have been notable successes. Some of the earliest were stochastic models for multistage carcinogenesis74,75, but they have not been applied to pathways involving specific genes. Another area that has seen extensive mathematical modeling is the pharmacokinetics and pharmacodynamics of drug metabolism76, exposure to toxic substances77,78, and normal metabolism79,80. While inter-individual variation in metabolic rate parameters has long been recognized, their genetic basis has only recently been incorporated into this kind of modeling81,82.
