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Notation and Example Datasets

Notation

Let us adopt the following notation: Tj and Sj are random variables that refer to the true and the surrogate endpoints of a patient j, respectively. Zj is a binary indicator for treatment. The present book focuses on multiple-trial surrogate evaluation methods. These methods assume that information regarding the endpoints is available from multiple clinical trials (or from multiple other relevant units in which the patients are clustered, such as the investigators who treated the patients or the countries where patients live in). When the multiple-trial surrogate validation methods are considered, the (T, S, Z) notation is supplemented with an index i = 1, ..., N that refers to the ith clinical trial, in the ith of which there are j = 1, ..., n* study participants. Thus in the multiple-trial setting, Tj and Sj are random variables that denote the true and the surrogate endpoints for patient j in trial i, respectively. Zj is the binary treatment indicator for patient j in trial i. When S and/or T are repeatedly measured over time, an additional index t = 1, ..., k is used to indicate the time t at which a measurement took place. For example, when S is repeatedly measured over time, Sjt refers to the surrogate endpoint for patient j in trial i at time t.

 
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