Simultaneous bands for event time percentiles in Cox models with an extension to recurrent events
Creators: name: Ahrens, Monica
Publisher: name: University of Iowa
Year: 2023
Subjects: Confidence Bands
End Stage Renal Disease
Survival analysis
Time-to-Event Percentiles
public abstract

description: A common method in survival analysis is Cox Proportional Hazards Regression (Cox PH). Cox PH models are used to describe a relationship between covariates and the event hazard, which can then be used to characterize the relationship between the covariates and time-to-event quantiles. Describing survival time quantiles as a function of covariates can give healthcare practitioners a helpful application in precision medicine.
description: The goal in precision medicine is to treat each patient, or a subgroup of patients, based on their individual characteristics instead of treating everyone in the same manner. This could be done through the use of genetic testing or by identifying subgroups of patients who would have more benefit from certain treatments than others. The median overall survival time is an overall assessment metric that shows little regard to key patient characteristics. A way to apply survival analysis to precision medicine is to assess the median survival time across a range of values for an important coefficient and add confidence bands. The confidence bands give a range of values that likely contain the true median.
description: The existing simultaneous band construction from Burr and Doss (1993) works only under settings that are unlikely in a real data scenario, such as a constant hazard or a coefficient that does not does not affect the event hazard in a clinically meaningful way. This dissertation proposes a simultaneous band that addresses the problems of the existing method and improves the overall coverage probabilities of confidence bands. The methods introduced, the Variance Stabilizing Transformation Band (VST) and the Corrected Variance Stabilizing Transformation Band (CVST), provide better coverage than that which is currently in the literature. These two bands are created using the Bartlett Approximation which allowed for a transformation of the asymptotic variance that stabilizes the variance to be constant. The CVST band also estimates a correction factor to account for the variability not attributed to the estimated percentile process. At 0% censoring, the CVST maintained near 95% coverage whereas the Burr and Doss method had coverage probabilities as low as 70% in the simulation study.
description: In addition to confidence bands for single event survival analysis, asymptotic results for recurrent event data are also presented. Recurrent event data breaks a main assumption used when developing the asymptotic results for the estimated percentile process, resulting in the need for all new asymptotic results. With the asymptotic results developed in this dissertation, confidence bands were created in the recurrent event case that assumed the event times are independent given the covariates accounted for in the Cox PH model. These bands are slightly conservative with coverage probabilities as high as 99% in simulations, but perform much better than their Burr and Doss counterpart at large effect sizes.
description: These methods were used to create confidence bands for median time between hospital visits as a function of age for patients with end-stage renal disease (ESRD). The bands showed that the length of time between hospital admissions is shorter for young patients with ESRD than it is for older patients. This finding could help health care practitioners develop ways to target specific patients that need added care in order to help them avoid re-hospitalization.