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Title: Development of robust designs for accelerated failure time models with Type I censoring Authors:  M Jesus Rivas-Lopez - University of Salamanca (Spain)
Raul Martin-Martin - University of Castilla-La Mancha (Spain)
Irene Garcia-Camacha Gutierrez - University of Castilla-La Mancha (Spain) [presenting]
Abstract: Accelerated Failure Time (AFT) models are commonly used in the field of manufacturing, but they are more and more frequent for modeling clinical trial data. These models are defined through the survival function of the time-to-event variable, $T$. The construction of robust designs for AFT models is considered, with the possibility that the Acceleration Factor (AF) is misspecified when the variance of $T$ is known. In particular, the ``true'' AF is allowed to vary over a neighbourhood of possible functions, $AF(\mathbf{x}, \mathbf{\theta}) = \exp ( \mathbf{\theta}^T \mathbf{x} + g_n(\mathbf{x}) ),$ for some unknown perturbation function $g_n$. Thus the efficiency of a design cannot be assessed through the covariance matrix of the Maximum Likelihood Estimator (MLE). Still, the estimate is subject to both ``bias error'' due to the inadequacy of the model as well as ``variance error'' due to sampling. The asymptotic mean squared error matrix (MSE) of the parameter estimates is obtained for right-censored observations. D- and I-optimal robust designs are derived from the above result considering the log-logistic distribution for illustration.