Applied Survival Analysis Using R by Dirk F. Moore

Author:Dirk F. Moore
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Note that the first part of this residual is the Schoenfeld residual given in Eq. 7.2.1. We formulate a quantity C defined by

We define a cluster-adjusted variance by and a cluster-adjusted standard error for by

If there are q covariates, then is a vector, and the covariance matrix for from the Cox model is given by V, and the standard errors (based on the standard Cox model assuming independent subjects) is the square root of the diagonal elements of V, i.e. .

The score residuals are matrices, the quantity C is now a q by q matrix given by and the cluster-adjusted covariance matrix is given by . Since the empirical covariance matrix C is sandwiched between two copies of , this estimate is often referred to as the “sandwich” estimator. The adjusted standard errors of the parameter estimate is given by . Summaries of the theory may be found in Klein and Moeschberger [36] and in Hosmer, Lemeshow and May [32].

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