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Two Time-to-Event Endpoints

In the Surrogate package, the function SurvSurv() can be used to evaluate the appropriateness of a candidate surrogate when both the surrogate and the true endpoints are time-to-event (Survival time) endpoints.

The function SurvSurv() implements the information-theoretic approach to estimate individual-level surrogacy (see Section 10). Trial-level surrogacy (Rrial) is estimated using a two-stage approach proposed by Buyse et al. (2011). In particular, the following trial-specific Cox proportional hazard models are fitted in Stage 1:

where Si0(t), Ti0(t) are the trial-specific baseline hazard functions, Zj is the treatment indicator for subject j in trial i, and а*, в* are the trial-specific treatment effects on S and T, respectively. In Stage 2, the following model is fitted:

where the parameter estimates for в* and a* are based on the model that was fitted in Stage 1. The classical coefficient of determination of the fitted Stage 2 model provides an estimate of Rrial.

Main function arguments

The function SurvSurv() requires the following arguments:

  • • Dataset=, Surr=, True=, Trial.ID=, Pat.ID=: The name of the dataset and the names of the variables in the dataset that contain the surrogate and true endpoint values, the trial indicator, and the patient indicator, respectively.
  • • SurrCens=, TrueCens=: The names of the variables in the dataset that contain the censoring indicators for the surrogate and the true endpoints, respectively. These censoring indicators should be coded as 1 = event and 0 = censored.
  • • Weighted=: A logical argument. If TRUE, then a weighted regression analysis is conducted at Stage 2 of the two-stage approach. If FALSE, then an unweighted regression analysis is conducted at Stage 2. Default Weighted=TRUE.
  • • Alpha=: The а-level that is used to determine the confidence intervals around Rtrial, LRF, and LRFa. Default Alpha=0.05.
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