Abstract
Many fields including clinical and manufacturing areas usually perform life-testing experiments and accelerated failure time models (AFT) play an essential role in these investigations. In these models the covariate causes an accelerant effect on the course of the event through the term named acceleration factor (AF). Despite the influence of this factor on the model, recent studies state that the form of AF is weakly or partially known in most real applications. In these cases, the classical optimal design theory may produce low efficient designs since they are highly model dependent. This work explores planning and techniques that can provide the best robust designs for AFT models with type I censoring when the form of the AF is misspecified, which is an issue little explored in the literature. Main idea is focused on considering the AF to vary over a neighbourhood of perturbation functions and assuming the mean square error matrix as the basis for measuring the design quality. A key result of this research was obtaining the asymptotic MSE matrix for type I censoring under the assumption of known variance regardless the selected failure time distribution. In order to illustrate the applicability of previous result to a study case, analytical characterizations and numerical approaches were developed to construct optimal robust designs under different contaminating scenarios for a failure time following a log-logistic distribution.
Highlights
Failure time data, called time-to-event data or survival data, arise in many areas, including medical follow-up studies and reliability research
The emphasis of this work will be on the analysis of data from a experiment which stops at a predetermined time, so that the survival time of any subjects remaining at this point are right-censored
The key result of this work is presented in Section 3: an analytical expression of the asymptotic mean squared error matrix for type I censoring which does not depend on the assumed distribution
Summary
Called time-to-event data or survival data, arise in many areas, including medical follow-up studies and reliability research. Motivated by the gap in literature on the construction of robust designs for AFT models for a wider and not-predetermined class of possible departures from the considered model when AF is partially known, the present work arises. Nelson [24] holds that the Acceleration Factor (AF) is only partially known in most of practical cases, so that a better analysis would include the uncertainty in it Under this framework, this work provides theory and methods for constructing robust designs when the AF is misspecified and the variance of the time-to-event variable is known.
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