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.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.