Quality and Reliability Methods - SAS

Chapter 20 Reliability and Survival Analysis II 393
Proportional Hazards Model
Whole Model, Parameter Estimates, and Effect Likelihood Ratio Tests Tables
• The Whole Model table shows the negative of the natural log of the likelihood function
(–LogLikelihood) for the model with and without the covariates. Twice the positive difference between
them gives a chi-square test of the hypothesis that there is no difference in survival time among the
effects. The degrees of freedom (DF) are equal to the change in the number of parameters between the
full and reduced models. The low Prob>Chisq value (ChiSq values indicate
that KPS and at least one of the levels of Cell Type are significant, while Treatment, Prior, Age, and Diag
Time effects are not significant.
Calculating Risk Ratios for Multiple Effects and Multiple Levels
The Risk Ratios option is available from the red-triangle menu of the Proportional Hazards Fit title bar of
the report and shows the risk ratios for the effects. Figure 20.20 shows the Risk Ratios for the continuous
effects (Age, Diag Time, KPS) and the nominal effects (Cell Type, Treatment, Prior). Of particular interest
in this section, for illustration, is the continuous effect, Age, and the nominal effect with four levels (Cell
Type) for the VA Lung Cancer.jmp sample data.
For continuous columns, unit risk ratios and range risk ratios are calculated. The Unit Risk Ratio is
Exp(estimate) and the Range Risk Ratio is Exp[estimate(x Max – x Min )]. The Unit Risk Ratio shows the risk
change over one unit of the regressor, and the Range Risk Ratio shows the change over the whole range of
the regressor. For example, for the continuous effect, Age, in the VA Lung Cancer.jmp sample data, the risk
ratios are calculated as
Unit Risk Ratios
exp(β) = exp(-0.0085494) = 0.991487
Range Risk Ratios
exp[β(xmax - xmin)] = exp(-0.0085494 * 47) = 0.669099
Risk Ratios for Cell Type
For categorical columns, risk ratios are shown in separate tables for each effect. For the nominal effect, Cell
Type, all pairs of levels are calculated and are shown in the Risk Ratios for Cell Type table. Note that for a
categorical variable with k levels, only k -1 design variables, or levels, are used. In the Parameter Estimates
table, parameter estimates are shown for only three of the four levels for Cell Type (Adeno, Large, and