Abstract
Parametric models for analysis of survival data with possible crossing of hazard rates related with two treatment groups are introduced. Strategy for survival improvement through application of time-varying treatment is discussed. Complete and right-censored data with possible confounding covariates are considered. Estimators of the crossing points are given. Chi-square type goodness-of-fit tests for the considered models are given. Parametric tests for the absence of crossing of survival functions (and also for crossing of the hazard functions) hypothesis are proposed.