Brian S. Everitt A Handbook of Statistical Analyses using SPSS

Display 10.12 Saving results from a Cox regression.
assumption is expected to hold for each of the covariates included in the
model. For example, for the binary covariate group, the assumption states
that the hazard ratio of completing the task between a child in the row
group and one in the corner group is constant over time. For continuous
covariates such as EFT, the assumption states that proportionality of hazard
functions holds for any two levels of the covariate. In addition, accommodating
continuous covariates requires the linearity assumption. This
states that their effect is linear on the log-hazard scale.
Schoenfeld residuals (Schoenfeld, 1982) can be employed to check for
proportional hazards. The residuals can be constructed for each covariate
and contain values for subjects with uncensored survival times. Under the
proportional hazard assumption for the respective covariate, a scatterplot
of Schoenfeld residuals against event times (or log-times) is expected to
scatter in a nonsystematic way about the zero line, and the polygon
connecting the values of the smoothed residuals should have approximately
a zero slope and cross the zero line several times (for more on
residual diagnostics, see Hosmer and Lemeshow, 1999).
SPSS refers to the Schoenfeld residuals as “partial residuals” and supplies
them via the Save… button on the Cox Regression dialogue box. The resulting
sub-dialogue box is shown in Display 10.12. It allows saving information
regarding the predicted survival probability at the covariate values of each
case and three types of residual diagnostics. We opt for the Schoenfeld
residuals. This results in the inclusion of three new variables, labeled pr1_1
(“partial” residual for eft), pr2_1 (residual for age), and pr3_1 (residual for
group) in our Data View spreadsheet. We then proceed to plot these residuals
against task completion times (time). The resulting scatterplots become
more useful if we include a Lowess curve of the residuals and a horizontal
reference line that crosses the y-axis at its origin.
The resulting residual plots are shown in Display 10.13. The residual
plot for EFT indicates no evidence of a departure from the proportional
hazards assumption for this covariate. As expected, the Lowess curve
varies around the zero reference line in a nonsystematic way
(Display 10.13a). For covariates age and group, the situation is less clear.
© 2004 by Chapman & Hall/CRC Press LLC