Influence diagnostics in regression with censored data
The work in this thesis is concerned with the development and extension of techniques for the assessment of influence diagnostics in data that include censored observations. Various regression models with censored data are presented and we concentrate on two models which are the accelerated failure time model, where the errors are generated by mixtures of normal distributions,and the Cox proportional hazards model. For the former, both finite discrete and continuous mixtures are considered, and an EM algorithm is used to determine measures of influence for each case. For the Cox proportional hazards model, various approaches to approximating influence curves are investigated. One-step or few-step approximations are developed using an EM algorithm and compared with a Newton-Raphson approach. Cook's measures of local influence are also investigated for the detection of influential cases in the data. The validity of the proportional hazards assumptions is also investigated. The residuals of Schoenfeld are examined for the possibility of being used to detect time dependence of the covariates in the proportional hazards model. Estimates to describe the nature of the time dependency computed from these residuals are presented.