[R] Cox Proportional Hazards

[David Winsemius]

On Aug 21, 2012, at 3:40 AM, Nanthinee Jeevanandam wrote:

> I have run this model for my data set on insect survival time for
> different temperature treatments in R. I understand the Wald statistic
> reports on whether the variable
> makes a difference to the model but there is also a p-value so i am
> not sure whther to report the Wald statistic. I have pasted a copy of
> my result below. Humidity is categorical (a & b) while temperature is
> continuous.
>
> coxph(formula = Surv(time, death) ~ Humidity + temp)
> n= 1504, number of events= 1504
>
>               coef   exp(coef) se(coef)          z    Pr(>|z|)
> Hum.b -0.03023   0.97022  0.05695   -0.531    0.595
> temp   1.19094   3.29017  0.03360   35.444   <2e-16 ***
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
>          exp(coef) exp(-coef) lower .95 upper .95
> Humb    0.9702     1.0307    0.8678     1.085
> temp      3.2902     0.3039    3.0805     3.514
>
> Concordance= 0.918  (se = 0.013 )
> Rsquare= 0.742   (max possible= 1 )
> Likelihood ratio test= 2036  on 2 df,   p=0
> Wald test            = 1281  on 2 df,   p=0
> Score (logrank) test = 1948  on 2 df,   p=0
>
>
> How do I interpret the Wald test in this case?  Really appreciate  
> the help.

The inferential tests are all in agreement. (Saying p < 2e-16 is  
equivalent to saying p = 0 when dealing with the limitations of  
floating point numbers.)  I would think you would separately interpret  
the humidity effect, possibly saying that the differences in the two  
humidity conditions appears to have little influence on survival with  
the humidity level "b" having only a slightly lower survival rate that  
was not statistically significant, but that the temperature effects  
were (highly) significantly different than zero with the point  
estimate suggesting a tripling of the death rates for a one unit  
increase in temperature.

(I find such an effect biologically unlikely assuming the temperature  
is measured in any of the usual temperature scales, and wonder if you  
have made a coding error some place. I would need to see a much better  
description of the data before proceeding. Did you incorrectly create  
a numeric variable from factor levels? )


-- 
David Winsemius, MD
Alameda, CA, USA