The SURVEYPHREG Procedure
- Overview
- Getting Started
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Syntax
PROC SURVEYPHREG Statement BY Statement CLASS Statement CLUSTER Statement DOMAIN Statement ESTIMATE Statement FREQ Statement LSMEANS Statement LSMESTIMATE Statement MODEL Statement NLOPTIONS Statement OUTPUT Statement Programming Statements REPWEIGHTS Statement SLICE Statement STORE Statement STRATA Statement TEST Statement WEIGHT Statement -
Details
Notation and Estimation Failure Time Distribution Time and CLASS Variables Usage Partial Likelihood Function for the Cox Model Specifying the Sample Design Missing Values Variance Estimation Domain Analysis Hypothesis Tests, Confidence Intervals, and Residuals Output Data Sets Displayed Output ODS Table Names ODS Graphics
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Examples
- References
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
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where 
. Let 
be the set of indices in the selected sample. Let
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and let 
be the identity matrix of appropriate dimension.
Let 
. The score residual for the 
th subject is
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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
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where 
is the observed information matrix and the 
matrix 
is defined as
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The observed residuals, their sums and means are defined as follows:
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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 
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.