The RMSTREG Procedure

Pseudovalue regression is a generic method of fitting generalized linear models to time-to-event data (Andersen, Klein, and Rosthøj 2003). This section describes how the method works and how you can apply it to analyze models of the RMST.

Let be independent and identically distributed quantities that might be random variables or vectors of variables. Let for some function . Suppose is an unbiased estimator of .

Let be independent and identically distributed samples of covariates, and define the conditional expectation of given by as

The ith pseudo-observation of is computed as

where is the jackknife leave-one-out estimator for based on .

The generalized linear model (Nelder and Wedderburn 1972) for assumes

where is a suitable link function. Note that an additional column can be added to for an intercept effect.

Using pseudo-observations, you can estimate the regression parameters by solving the following estimating equations

where is a working covariance matrix.

Let be a solution of the estimating equations. You can use a sandwich estimator to estimate the variance of . It takes the form

is the model-based estimator of and is given by

is the empirical estimator of and is computed as

Andersen, Hansen, and Klein (2004) proposed using pseudovalue regression to analyze the RMST models. Assume is a prespecified time point of interest. Let be the time-to-event variable for the ith subject. The RMST models can be fitted using pseudovalue regression by letting

Because the nonparametric estimator is unbiased, it can be used in place of in the estimation process.