Reliable information on growth rates and risk factors for growth of thoracic aortic aneurysms (TAA) is important for managing patients with this potentially lethal condition. This article reviews existing procedures for ascertaining TAA growth rates and describes improved statistical methodologies. Using data from the Yale Center for Thoracic Aortic Disease, the article demonstrates that the statistical procedure of instrumental variables (IV) estimation leads to substantially more precise and robust estimates of TAA growth rates and associated risk factors. We recommend that IV estimation be routinely employed in estimating the progression of thoracic aortic aneurysms and in identifying risk factors for growth. The article also discusses the issue of sample selection effects that arise when patients receive graft surgery and therefore are removed from the data set, and describes statistical procedures fro addressing this issue.