Thoracic endovascular aortic repair (TEVAR) is a commonly used, minimally invasive approach for treatment of thoracic aortic aneurysms (TAA). As there have been no randomized clinical trials, we often extract information for this treatment from observational data, such as the Vascular Quality Initiative registry of TEVAR patients. However, evaluating the effectiveness of the treatment using observational data can be challenging when there is no data on the untreated group (e.g TEVAR registry), and no reliable information on the cause of death. To address these issues, we propose using the relative survival approach, in which one estimates the excess mortality hazard attributable to a disease by comparing disease registry survival data to general-population control data.

Popular modeling methods of estimating the relative survival have two shortcomings that render them unsuitable in some cases. First, they assume the excess hazard is positive, which is undoubtedly true for cancer, but may not hold for diseases treated with potentially curative therapy. Second, they consider survival to be continuous, whereas population control data is often available only in discrete form, rounded to the nearest year. To address these concerns, in Chapter 1, we propose describing discrete mortality hazards with a flexible logistic regression model that permits the registry hazard to be either larger or smaller iv than the population hazard. We apply our approach to analyze relative survival of patients who underwent thoracic endovascular aortic repair (TEVAR) for thoracic aortic aneurysm (TAA). Our results show that relative survival is favorable for the youngest and oldest TEVAR recipients and unfavorable for those in between.

We hypothesized that the superior survival at older ages occurred because surgeons were recommending only the hardiest older TAA patients for TEVAR. Thus, some older patients may have been excluded from a treatment that could have increased their survival time. It is not possible to evaluate this bias directly because the registry includes only those TAA patients who underwent TEVAR. In Chapter 2, we address this bias by proposing the use of sensitivity analysis to investigate the extent at which results are sensitive to potential biases in sampling. Our model has two components: First, a one-parameter selection model posits a pool of “potential patients” who could have received the treatment but did not, with selection probability depending on age. Second, a mortality hazard model for the on-surgery potential outcomes of the excluded patients extends the hazard model that we used to describe mortality in the registry. We identify combinations of parameters of the models that eliminate the relative survival advantage in the older patients. The analysis confirms, and places a magnitude on, a “healthy screening effect”, which posits that older TEVAR patients are screened for hardiness more critically than younger patients.

The size of the thoracic aneurysms is an important criterion for deciding whether and when to conduct the TEVAR. Although previous analyses have sought to identify the ideal TAA size at which to apply TEVAR, none have properly accounted for potential confounding of the size of the aneurysm with treatment outcome. In Chapter 3, we aim to study the marginal effect of aneurysm size on post-procedure survival in causal inference framework. We estimate a marginal structural model (MSM) using inverse propensity score weighting, and model nonlinearity in the effect of aneurysm size with a flexible fractional polynomial form for the MSM. We find that patients who are asymptomatic at presentation and undergo elective surgery have better survival outcomes if the operation takes place when the TAA size is near 60mm.

Degree Date

Spring 2023

Document Type


Degree Name



Statistical Science


Daniel F. Heitjan

Subject Area


Number of Pages




Creative Commons License

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License