Diagnostic tools for bivariate accelerated life regression models

Abstract

We propose graphical diagnostic tools to assess the fit of a bivariate accelerated lifetime regression model. Using univariate residuals for each response measurement in a pair, we assess their dependence structure via the bivariate probability integral transformation of univariate residuals, which we call V-residuals. To reduce the computational burden associated with plots of V-residuals, as well as some uncertainty associated with parameter estimation, we next develop K-residuals. We also devise adjusted V- and K-residuals to account for right censoring of any response. Via simulation studies, we examine the statistical behaviour of Q–Q plots of the estimated K-residuals, and demonstrate the potential of these plots to identify an appropriate choice of frailty distribution in bivariate modeling. We apply our proposed diagnostic tools to the Diabetic Retinopathy Study and assess the goodness of fit of various models fitted to these study data using different choices of frailty distributions combined with several baseline survivor functions.