Assuming that the two failure times of interest with bivariate current status data follow a bivariate copula model, we propose a two‐stage estimation procedure to estimate the association parameter which is related to Kendall's tau. Asymptotic properties of the proposed semiparametric estimator show that, although the first‐stage marginal estimators have a convergence rate of only n^1/3, the resulting parameter estimator still converges to a normal random variable with the usual n^1/2 rate. The variance of the proposed estimator can be consistently estimated. Simulation results are presented, and a community‐based study of cardiovascular diseases in Taiwan provides an illustrative example.

Corporate bankruptcy prediction plays a central role in academic finance research, business practice, and government regulation. Consequently, accurate default probability prediction is extremely important. We propose to apply a discrete transformation family of survival models to corporate default risk predictions. A class of Box-Cox transformations and logarithmic transformations is naturally adopted. The proposed transformation model family is shown to include the popular Shumway model and the grouped relative risk model. We show that a transformation parameter different from those two models is needed for default prediction using a bankruptcy dataset. In addition, we show using out-of-sample validation statistics that our model improves performance. We use the estimated default probability to examine a popular asset pricing question and determine whether default risk has carried a premium. Due to some distinct features of the bankruptcy application, the proposed class of discrete transformation survival models with time-varying covariates is different from the continuous survival models in the survival analysis literature. Their similarities and differences are discussed.