The SURVEYPHREG Procedure
Taylor Series Linearization
The Taylor series linearization method is the default variance estimation method used by PROC SURVEYPHREG. See the section Notation and Estimation for definitions of the notation used in this section. Let
where 
. Let A be the set of indices in the selected sample. Let
and let 
be the identity matrix of appropriate dimension.
Let 
. The score residual for the 
subject is
For TIES=EFRON, the computation of the score residuals is modified to comply with the Efron partial likelihood. See the section Residuals for more information.
The Taylor series estimate of the covariance matrix of 
is
where 
is the observed information matrix and the 
matrix 
is defined as
The observed residuals, their sums and means are defined as follows:
The factor 
in the computation of the matrix reduces the small sample bias that is associated with using the estimated function to calculate deviations (Fuller et al. (1989), pp. 77–81). For simple random sampling, this factor contributes to the degrees of freedom correction applied to the residual mean square for ordinary least squares in which p parameters are estimated. By default, the procedure uses this adjustment in the variance estimation. If you do not want to use this multiplier in the variance estimator, then specify the VADJUST=NONE option in the MODEL statement.