Quantile regression models for current status data

Current status data arise frequently in demography, epidemiology, and econometrics where the exact failure time cannot be determined but is only known to have occurred before or after a known observation time. We propose a quantile regression model to analyze current status data, because it does not require distributional assumptions and the coefficients can be interpreted as direct regression effects on the distribution of failure time in the original time scale. Our model assumes that the conditional quantile of failure time is a linear function of covariates. We assume conditional independence between the failure time and observation time. An M-estimator is developed for parameter estimation which is computed using the concave-convex procedure and its confidence intervals are constructed using a subsampling method. Asymptotic properties for the estimator are derived and proven using modern empirical process theory. The small sample performance of the proposed method is demonstrated via simulation studies. Finally, we apply the proposed method to analyze data from the Mayo Clinic Study of Aging

QUANTILE REGRESSION MODELS FOR INTERVAL-CENSORED FAILURE TIME DATA

Quantile regression models the conditional quantile as a function of independent variables providing a complete association between the response and predictors. Quantile regression can describe the association at different quantiles yielding more information than the least squares method which only detects associations with the conditional mean. Quantile regression models have gained popularity in many disciplines including medicine, finance, economics, and ecology as they can accommodate heteroscedasticity. A specific type of failure time data is called interval-censored where the failure time is only known to have occurred between certain observation times. Such data appears commonly in medical or longitudinal studies because disease onset is known to have occurred between scheduled visits but the exact time is unknown. Quantile regression has been extended to survival analysis with random censoring time. Most methods focus on survival analysis with right-censored data while a few were developed for data with other censoring mechanisms. Despite the fact that the development for censored quantile regression flourishes, limited work has been done to handle interval-censored failure time data under the quantile regression framework. In this dissertation, we developed a new method to analyze interval-censored failure time data using conditional quantile regression models. Our method can handle both Case I and Case II interval-censored data and allow the censoring time to depend on covariates. We developed an estimation procedure that is computationally efficient and easy to implement with inference performed using a subsampling method. The consistency and asymptotic distribution of the resulting estimators were established using modern empirical process theory. The developed method was extended as a computational tool to analyze interval-censored data for accelerated failure time models. The estimators from different quantiles were combined to increase the efficiency of the estimators. The small sample performances were demonstrated via simulation studies. The proposed methods were illustrated with current status datasets, data from the Voluntary HIV-1 Counseling and Testing Efficacy Study Group and calcification study, and Case II interval-censored data, data from the Atherosclerosis Risk in Communities Study and breast cosmesis data.Doctor of Philosoph