Given a new vector of covariates , the linear predictor is computed as , where is the maximum likelihood estimate of . The variance of is estimated by

where denotes the estimated covariance matrix for .

Suppose the estimated baseline hazard is . Given , the cumulative hazard function can be predicted by

Denote the vector of parameters that is used for obtaining as . It is apparent that . The vector of parameters that need to be estimated can be represented as .

The variance of can be estimated by applying the delta method:

where

and denotes the estimated covariance matrix for .

Given , the predicted survival function is estimated by

The standard error of can be conveniently estimated by an application of the delta method:

By default, a natural log transformation is applied to obtain the pointwise confidence limits for and . You can use the CLTYPE= option to specify a different transformation for .