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Such survival times are considered to be censored. With survival times of an individuals, who have not experienced the event of interest by the end of the study will recorded as censored that is called right-censoring. Three different scenarios involving censored data Which depended on the follow-up times are in existence. While, this depends largely on the risk and stage level for the patient. These scenarios can be summarized as follows:
• Right censoring is the most widely used for analyzing. That occurs when an individual may not encounter a time failure for the event-of interest until the follow-up duration elapses or drop out of the study before the end. • Left censoring arises when the event of interest(for example, death) has been occurred for the individual before observation time. This technique is not common. • Interval censored refer to that case, when an event-under-interest has a tendency of occurring in an interval time.
By taking the heroin addicts as an example, the survival times of 88 patients are censored. Generally, being unable to observe the event of interest is the major reason for censoring. In the maintenance treatment study, the mainly interested in addicts who drop out of maintenance treatment and who were remaining by the end of the study, which their survival times was right censored. By looking more closely to the censoring, it assumed that having uncensored, independent survival times T? 1,T? 2,…,T? n for n patients, and h(t) is the hazard function of i?th patient. Then, it can observed a right-censored survival time ˜ Ti with an indicator Di, where Di = 1 or 0 when ˜ Ti = T? i or ˜ Ti < T? i respectively. The following section gives a clear view of it.
2.2.1 Right Censoring
The random variables represent failure times as X1,X2,…,Xn. These variables assumed to be independent and identically distributed with probability density function f(x) and

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