Quantile inference, regression and additive hazards models in multivariate survival analysis

• Main Author: Yin, Guosheng
• Format: Dissertation
• Language: English
• Published: ProQuest Dissertations & Theses 01.01.2003
• Subjects: Additives; Multivariate analysis; Public health; Regression analysis
• ISBN: 9780496344529; 0496344528

Multivariate failure time data often arise in biomedical and epidemiological studies. For example, each patient might experience multiple events which may be of the same type (recurrent) or distinct types, and there could be correlated observations due to natural or artificial clustering. Quantiles, especially the medians, of survival times are often used as summary statistics to compare the survival experiences among different groups. They are robust against outliers and preferred to the mean survival times. We propose nonparametric procedures for the estimation of quantiles and show that the proposed estimators asymptotically follow a multivariate normal distribution. The asymptotic variance-covariance matrix is estimated based on the kernel smoothing and bootstrap techniques. The methods are applied to data from burn-wound infections study and Diabetic Retinopathy Study (DRS). As an alternative to the mean regression model, the quantile regression model has been studied extensively with independent failure time data. For clustered survival data, we study quantile regression models and propose an estimating equation approach for parameter estimation. The regression parameter estimates are shown to be asymptotically normally distributed. The variance estimation based on asymptotic approximation involves nonparametric functional density estimation. Alternatively, we apply and compare the bootstrap and perturbation resampling methods for the estimation of the variance-covariance matrix. The new proposal is illustrated with a data set from a clinical trial about ventilating tubes for otitis media. Under general dependence structure with multiple parallel events involving clustered subjects (e.g. siblings) contributing to each event type, both the between-failure-type correlation and the within-cluster correlation need to be adjusted to ensure valid statistical estimation and inference. We study the additive hazards model and propose estimating equations for parameter estimation. The regression coefficient estimates are shown to follow multivariate normal distribution asymptotically with mean zero and a sandwich-type variance-covariance matrix that can be consistently estimated. Furthermore, jointly across all the failure types, the estimated baseline and subject-specific cumulative hazard processes are shown to converge weakly to a zero-mean Gaussian random field. Through a resampling technique, we propose the procedures to construct simultaneous confidence bands for the survival curve of a given subject. Monte Carlo simulation studies are conducted to assess the finite-sample properties and the proposed method is illustrated with a data set from the Framingham Heart Study.