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The PHREG Procedure |
Residuals are used
to investigate the lack of fit of
a model to a given subject. You can obtain
martingale and deviance residuals for the
Cox proportional
hazards regression analysis by requesting that they be
included in the OUTPUT data set. You can plot these
statistics and look for outliers.
Consider the stepwise regression analysis performed
in Example 49.1. The final model included variables
LogBUN
and HGB. You can generate residual statistics for this
analysis by refitting the model containing those variables
and including an OUTPUT statement.
The keywords XBETA, RESMART, and RESDEV
identify new variables that
contain the linear predictor
scores
,martingale residuals, and
deviance residuals.
These variables are xb, mart, and
dev, respectively.
proc phreg data=Myeloma noprint; model Time*Vstatus(0)=LogBUN HGB; output out=Outp xbeta=xb resmart=mart resdev=dev; run;
The following statements plot the residuals against the linear predictor scores:
proc gplot data=Outp; plot (mart dev)*xb / vref=0 cframe=ligr; symbol1 value=circle c=blue; run;
The resulting plots are shown in Output 49.7.1 and Output 49.7.2. The martingale residuals are skewed because of the single event setting of the Cox model. The martingale residual plot shows an isolation point (with linear predictor score 1.09 and martingale residual -3.37), but this observation is no longer distinguishable in the deviance residual plot. In conclusion, there is no indication of a lack of fit of the model to individual observations.
Output 49.7.1: Martingale Residual Plot
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