A new summary measure for time-to-event data, termed lost lifespan, is proposed in which the existing concept of reversed percentile residual life, or percentile inactivity time, is recast to show that it can be used for routine analysis to summarize life lost. The lost lifespan infers the distribution of time lost due to experiencing an event of interest before some specified time point. An estimating equation approach is adopted to avoid estimation of the probability density function of the underlying time-to-event distribution to estimate the variance of the quantile estimator. A K-sample test statistic is proposed to test the ratio of quantile lost lifespans. Simulation studies are performed to assess finite properties of the proposed statistic in terms of coverage probability and power. The concept of life lost is then extended to a regression setting to analyze covariate effects on the quantiles of the distribution of the lost lifespan under right censoring. An estimating equation, variance estimator, and minimum dispersion statistic for testing the significance of regression parameters are proposed and evaluated via simulation studies. The proposed approach reveals several advantages over existing methods for analyzing time-to-event data, which is illustrated with a breast cancer dataset from a Phase III clinical trial conducted by the National Surgical Adjuvant Breast and Bowel Project.
Public Health Significance: The analysis of time-to-event data can provide important information about new treatments and therapies, particularly in clinical trial settings. The methods provided in this dissertation will allow public health researchers to analyze effectiveness of new treatments in terms of a new summary measure, life loss. In addition to providing statistical advantages over existing methods, analyzing time-to-event data in terms of the lost lifespan provides a more straightforward interpretation beneficial to clinicians, patients, and other stakeholders
