[R] Problem in anova with coxph object

[Matthias Gondan]

Dear R users,

I noticed a problem in the anova command when applied on
a single coxph object if there are missing observations in
the data:

This example code was run on R-2.6.1:

 > library(survival)
 > data(colon)
 > colondeath = colon[colon$etype==2, ]
 > m = coxph(Surv(time, status) ~ rx + sex + age + perfor, data=colondeath)
 > m
Call:
coxph(formula = Surv(time, status) ~ rx + sex + age + perfor,
    data = colondeath)

               coef exp(coef) se(coef)      z      p
rxLev     -0.028895     0.972  0.11037 -0.262 0.7900
rxLev+5FU -0.374286     0.688  0.11885 -3.149 0.0016
sex       -0.000754     0.999  0.09431 -0.008 0.9900
age        0.002442     1.002  0.00405  0.603 0.5500
perfor     0.155695     1.168  0.26286  0.592 0.5500

Likelihood ratio test=12.8  on 5 df, p=0.0251  n= 929

 > anova(m, test='Chisq')
Analysis of Deviance Table
 Cox model: response is Surv(time, status)
Terms added sequentially (first to last)

        Df  Deviance Resid. Df Resid. Dev P(>|Chi|)
NULL                       929     5860.4         
rx       2      12.1       927     5848.2 2.302e-03
sex      1 2.054e-05       926     5848.2       1.0
age      1       0.3       925     5847.9       0.6
perfor   1       0.3       924     5847.6       0.6

Now I include nodes which has some missing data:

 > m = coxph(Surv(time, status) ~ rx + sex + age + perfor + nodes, 
data=colondeath)
 > m
Call:
coxph(formula = Surv(time, status) ~ rx + sex + age + perfor +
    nodes, data = colondeath)

              coef exp(coef) se(coef)      z       p
rxLev     -0.08245     0.921  0.11168 -0.738 0.46000
rxLev+5FU -0.40310     0.668  0.12054 -3.344 0.00083
sex       -0.02854     0.972  0.09573 -0.298 0.77000
age        0.00547     1.005  0.00405  1.350 0.18000
perfor     0.19040     1.210  0.26335  0.723 0.47000
nodes      0.09296     1.097  0.00889 10.460 0.00000

Likelihood ratio test=88.3  on 6 df, p=1.11e-16  n=911 (18 observations 
deleted due to missingness)

 > anova(m, test='Chisq')
Analysis of Deviance Table
 Cox model: response is Surv(time, status)
Terms added sequentially (first to last)

        Df  Deviance Resid. Df Resid. Dev P(>|Chi|)
NULL                       911     5700.6         
rx       2       0.0       909     5848.2       1.0
sex      1 2.054e-05       908     5848.2       1.0
age      1       0.3       907     5847.9       0.6
perfor   1       0.3       906     5847.6       0.6
nodes    1     235.3       905     5612.3 4.253e-53

The strange thing is that rx is not significant anymore.

In the documentation for anova.coxph, there is a warning that

> The comparison between two or more models by |anova| or will only be 
> valid if they are fitted to the same dataset. This may be a problem if 
> there are missing values.
>
However, I inserted a single object to be analyzed sequentially. Is
this a bug in R, or is it covered by the warning?

Best wishes,

Matthias