A bivariate Weibull model is proposed for censored survival data when there may be dependence between the survival and censoring random variables. The model is based on marginal transformations of the Pickands class of bivariate exponential distributions. Assuming the model to hold, the joint distribution of survival and censoring times is shown to be identifiable, and the maximum likelihood estimator of the parameters is shown to be consistent.
"A Weibull Model for Dependent Censoring." Ann. Statist. 18 (4) 1556 - 1577, December, 1990. https://doi.org/10.1214/aos/1176347866