Defining and ranking effects of individual agents based on survival times of cancer patients treated with combination chemotherapies

An important problem in oncology is comparing chemotherapy (chemo) agents in terms of their effects on survival or progression-free survival time. When the goal is to evaluate individual agents, a difficulty commonly encountered with observational data is that many patients receive a chemo combination including two or more agents. Because agents given in combination may interact, quantifying the contribution of each individual agent to the combination's overall effect is problematic. Still, if on average combinations including a particular agent confer longer survival, then that agent may be considered superior to agents whose combinations confer shorter survival. Motivated by this idea, we propose a definition of individual agent effects based on observational survival data from patients treated with many different chemo combinations. We define an individual agent effect as the average of the effects of the chemo combinations that include the agent. Similarly, we define the effect of each pair of agents as the average of the effects of the combinations including the pair. Under a Bayesian regression model for survival time in which the chemo combination effects follow a hierarchical structure, these definitions are used as a basis for estimating the posterior effects and ranks of the individual agents, and of all pairs of agents. The methods are illustrated by a data set arising from 224 pediatric brain tumor patients treated with over 27 different chemo combinations involving seven chemo agents.