Modeling Tumor Growth Using Partly Conditional Survival Models: A Case Study in Colorectal Cancer

Abstract

PURPOSE There are multiple approaches to modeling the relationship between longitudinal tumor measurements obtained from serial imaging and overall survival. Many require strong assumptions that are untestable and debatable. We illustrate how to apply a novel, more flexible approach, the partly conditional (PC) survival model, using images acquired during a phase III, randomized clinical trial in colorectal cancer as an example. METHODS PC survival approaches were used to model longitudinal volumetric computed tomography data of 1,025 patients in the completed VELOUR trial, which evaluated adding aflibercept to infusional fluorouracil, leucovorin, and irinotecan for treating metastatic colorectal cancer. PC survival modeling is a semiparametric approach to estimating associations of longitudinal measurements with time-to-event outcomes. Overall survival was our outcome. Covariates included baseline tumor burden, change in tumor burden from baseline to each follow-up time, and treatment. Both unstratified and time-stratified models were investigated. RESULTS Without making assumptions about the distribution of the tumor growth process, we characterized associations between the change in tumor burden and survival. This change was significantly associated with survival (hazard ratio [HR], 1.04; 95% CI, 1.02 to 1.05; P < .001), suggesting that aflibercept works at least in part by altering the tumor growth trajectory. We also found baseline tumor size prognostic for survival even when accounting for the change in tumor burden over time (HR, 1.02; 95% CI, 1.01 to 1.02; P < .001). CONCLUSION The PC modeling approach offers flexible characterization of associations between longitudinal covariates, such as serially assessed tumor burden, and survival time. It can be applied to a variety of data of this nature and used as clinical trials are ongoing to incorporate new disease assessment information as it is accumulated, as indicated by an example from colorectal cancer.