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My question is about survival analysis.

According to this censoring is a condition in which the value of a measurement or observation is only partially known. For example, suppose a study is conducted to measure the impact of a drug on mortality rate. In such a study, it may be known that an individual's age at death is at least 75 years (but may be more). Such a situation could occur if the individual withdrew from the study at age 75, or if the individual is currently alive at the age of 75.

There are numerous techniques in the literature for handling such data.

Question

What type of data would we have if people are allowed to join the study? Is there a name for such a phenomenon? How do we analyze such data when there is withdrawal/censorship and at the same time people are allowed to join the study at various times.?

I really hope my question is clear.

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I think you are looking for the phenomenon of left truncation, or "delayed entry". In this case, if an individual joins the study at a later age, then that is a left truncated entry time.

There are many resources online for this. A good point to start is also in Klein & Moeschberg's Survival Analysis book. If you use R, then this can be easily handled with the survival package.

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