The R Book

Cox's Proportional Hazards

The median age at death was one week later in the October cohort, but look at the width of the confidence intervals: 3 to 9 versus 2 to 7. Clearly there is no significant effect of cohort on time of death. What about gap size? We start with a full analysis of covariance using coxph rather than survfit.

model1<-coxph(Surv(death,status)~strata(cohort)*gapsize)
summary(model1)

Call:
coxph(formula = Surv(death, status) - strata(cohort) * gapsize)
   n= 60

coef   exp(coef)   se(coef)         z       p
gapsize                -1.19       0.305      0.621    -1.910   0.056
gapsize:strata(cohort)  0.58       1.785      0.826     0.701   0.480
cohort=September
                       exp(coef)   exp(-coef)   lower .95   upper .95
gapsize                    0.305         3.27      0.0904        1.03
gapsize:strata(cohort)     1.785         0.56      0.3534        9.02
cohort=September

Rsquare= 0.076 (max possible= 0.993 )
Likelihood ratio test= 4.73 on 2 df, p=0.0937
Wald test            = 4.89 on 2 df, p=0.0868
Score (logrank) test = 5.04 on 2 df, p=0.0805

There is no evidence of any interaction (p = 0.480) and the main effect of gap size is not quite significant in this model (p = 0.056). We fit the simpler model with no interaction:

model2<-coxph(Surv(death,status)~strata(cohort)+gapsize)
anova(model1,model2)

Analysis of Deviance Table

Model 1: Surv(death, status)~ strata(cohort) * gapsize
Model 2: Surv(death, status)~ strata(cohort) + gapsize
   Resid. Df   Resid. Dev   Df  Deviance
1         58     293.898
2         59     294.392    -1   -0.494

There is no significant difference in explanatory power, so we accept the simpler model without an interaction term. ...