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Most standard statistical methods for the analysis of right-censored survival data fail to be consistent if the censoring is not independent of survival. The independence assumption cannot be tested with right-censored data unless the additional data are collected or assumptions are made about an underlying statistical model. In 1998 Lee and Wolfe proposed a two-stage sampling method for testing dependent censoring. The model for dependent censoring specified by the conditional hazard function for T is λ(t|C)=λ1 (t)I(C≥t)+λ2 (t,C) I(C < t), here λ11 (t) is a hazard function before the dependent censoring event and λ2 (t,C) is a family of hazard functions after the dependent censoring event. Under two-stage sampling technique, a non-parametric estimator under Non-homogenous model with λ2 (t,C)=λ2 (t) was proposed and compared to Empirical estimator, Semi-Markov estimator and Kaplan-Meier estimator. Two real data examples and one simulation one have been applied to generate these estimators. Also parametric estimation of one special case λ1 (t)=λ1λ2 (t,C)=λ2, and one general case λ1 (t)=λ1 t,λ2 (t,C)=λ2λ1λ2 are constants are conducted in this paper. Two different methods full information maximum likelihood estimation (FIML) and expectation-maximization (EM) algorithm had been compared under these two cases to see which method provide better estimation.