Score and deviance residuals based on the full likelihood approach in survival analysis

Abstract

Assuming the proportional hazards model and non-informative censoring, the full likelihood approach is used to obtain two new residuals. The first residual is based on the ideas used in obtaining score-type residuals similar to the partial likelihood approach. The second type of residual is based on the concept of deviance residuals. Extensive simulations are conducted to compare the performance of the residuals from the full likelihood-based approach with those of the partial likelihood method. We demonstrate through simulation studies that the full likelihood-based residuals are more efficient than their partial likelihood counterpart in identifying potential outliers when the censoring proportion is high. The graphical techniques are used to illustrate the applications of these residuals using some examples.

Keywords: deviance residuals; full likelihood; non-informative censoring; partial likelihood; proportional hazards; score-type residuals.

Figure 1.

Plot summarizing the AUC levels for the score residuals computed using the full and partial likelihood functions involving the covariate $X_{.3}$

Figure 2.

Plot summarizing the AUC levels for the score residuals computed using the full and partial likelihood functions involving the covariate $X_{.2}$

Figures 3A-3C.

Plots of the full likelihood and partial likelihood score residuals against age, albumin, and bilirubin values in PBC data

Figure 4.

Plot of full likelihood deviance residual against risk score (linear predictor) of age, albumin, and bilirubin values in PBC data

Figures 5A-5C

Plots of full likelihood and partial likelihood score residuals for age, progesterone receptor, and estrogen receptor levels in the German breast cancer study