Superposition of survival curves as a tool for epistasis analysis of longevity interventions

A long-standing problem in ageing research is to understand how different factors contributing to longevity should be expected to act in combination under the assumption that they are independent. Standard epistasis analysis compares the extension of mean lifespan achieved by a combination of interventions to the prediction under an additive or multiplicative null model, but neither model is fundamentally justified. Moreover, the target of longevity interventions is not mean life span but the entire survival curve. Here we formulate superposition principles that predict the survival curve resulting from a combination of two interventions based on the survival curves of the individual treatments, and quantify epistasis as the deviation from this prediction. We test the method on a published data set comprising survival curves for all combinations of 4 different longevity interventions in Caenorhabditis elegans. We find that epistasis is generally weak even when the standard analysis indicates otherwise.