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I am reading Dirk Moore's Applied Survival Analysis 11.2.

"...However, patients actually enter over an accrual period of length a, and then, after accrual to the trial has ended, they are followed for an additional time f...."

Is this asserting all trials are left truncated? Since you will not start treatment until the end of accrual period, there is possibility of patient dying during that accrual period. Hence we can only follow people not dying during accrual period.

If the treatment starts right at beginning of accrual period, I would say this is right censored. However, I am not sure what is accrual period for here. Is it only used for accumulating enough patient to start trial? Or one can start trial right at the beginning of accrual period?

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That "you will not start treatment until the end of accrual period" is not the case.

Participants enroll in clinical trials over time. The total time over which all participants enroll is the accrual time. Nevertheless, each individual begins treatment soon after enrollment, according to the terms of the trial design. The starting time = 0 for each participant might be defined as the date of the start of that participant's therapy. So there is no left truncation with respect to that choice of time = 0 in that situation.

There's a possibility of left truncation if you define time = 0 to be the date of initial diagnosis and there's a delay between diagnosis and study enrollment. Therneau and Grambsch discuss that in Section 3.7.3 of "Modeling Survival Data," for an example when a patient entered a study at the Mayo Clinic referral center 1175 days after initial diagnosis at a local healthcare provider

the patient was not at risk for an observable death during the first 1,175 days of that interval. Such data, where the patient enters the risk set after time 0, is said to be left truncated.

Usually there isn't such a large time difference between diagnosis and enrollment, so any minor left truncation might be ignorable.

Left truncation can also be an issue when you define time = 0 to be date of birth or something similar. Klein and Moeschberger provide many examples of different types of censoring and truncation and how to deal with them.

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