Estimation of monotone bivariate quantile inactivity time with medical applications

In most lifetime models, the bivariate $\alpha$-quantile inactivity time is a vector of increasing functions. A novel estimator of this vector was created and investigated under this assumption. It was expected that the application of this knowledge would improve the efficiency of the estimator. It was proven that the proposed estimator is consistent and converges weakly to a bivariate Gaussian process under a suitable transformation. A simulation study was conducted to compare the performance of the proposed estimator with that of the usual estimator. Finally, the application of the proposed estimator is illustrated by analyzing a dataset comprising the time to blindness in patients with diabetic retinopathy.