Can someone explain my Cox model to me in plain English?
I fitted the following Cox regression model to all of my data using the cph
function. My data are saved in an object called Data
. The variables w
, x
, and y
are continuous; z
is a factor of two levels. Time is measured in months. Some of my patients are missing data for variable z
(NB: I have duly noted Dr. Harrell's suggestion, below, that I impute these values so as to avoid biasing my model, and will do so in the future).
> fit <- cph(formula = Surv(time, event) ~ w + x + y + z, data = Data, x = T, y = T, surv = T, time.inc = 12)
Cox Proportional Hazards Model
Frequencies of Missing Values Due to Each Variable
Surv(time, event) w x y z
0 0 0 0 14
Model Tests Discrimination
Indexes
Obs 152 LR chi2 8.33 R2 0.054
Events 64 d.f. 4 g 0.437
Center 0.7261 Pr(> chi2) 0.0803 gr 1.548
Score chi2 8.07
Pr(> chi2) 0.0891
Coef S.E. Wald Z Pr(>|Z|)
w -0.0133 0.0503 -0.26 0.7914
x -0.0388 0.0351 -1.11 0.2679
y -0.0363 0.0491 -0.74 0.4600
z=1 0.3208 0.2540 1.26 0.2067
I also tried to test the assumption of proportional hazards by using the cox.zph
command, below, but do not know how to interpret its results. Putting plot()
around the command gives an error message.
cox.zph(fit, transform="km", global=TRUE)
rho chisq p
w -0.1125 1.312 0.2520
x 0.0402 0.179 0.6725
y 0.2349 4.527 0.0334
z=1 0.0906 0.512 0.4742
GLOBAL NA 5.558 0.2347
First Problem
- Can someone explain the results of the above output to me in plain English? I have a medical background and no formal training in statistics.
Second Problem
As suggested by Dr. Harrell, I would like to internally validate my model by performing 100 iterations of 10-fold cross-validation using the
rms
package (from what I understand, this would entail building100 * 10 = 1000
different models and then asking them to predict the survival times of patients that they had never seen).I tried using the
validate
function, as shown.> v1 <- validate(fit, method="crossvalidation", B = 10, dxy=T) > v1 index.orig training test optimism index.corrected n Dxy -0.2542 -0.2578 -0.1356 -0.1223 -0.1320 10 R2 0.0543 0.0565 0.1372 -0.0806 0.1350 10 Slope 1.0000 1.0000 0.9107 0.0893 0.9107 10 D 0.0122 0.0128 0.0404 -0.0276 0.0397 10 U -0.0033 -0.0038 0.0873 -0.0911 0.0878 10 Q 0.0155 0.0166 -0.0470 0.0636 -0.0481 10 g 0.4369 0.4424 0.6754 -0.2331 0.6700 10
How do you perform the 100x resampling? I think my above code only performs the cross-validation once.
I then wanted to know how good my model was at prediction. I tried the following:
> c_index <- abs(v1[1,5])/2 + 0.5 > c_index [1] 0.565984
Does this mean that my model is only very slightly better than flipping a coin?
Third Problem
Dr. Harrell points out that I have assumed linearity for the covariate effects, and that the number of events in my sample is just barely large enough to fit a reliable model if all covariate effects happen to be linear.
- Does this mean that I should include some sort of interaction term in my model? If so, any advice as to what to put?
cph
output to me in plain English, or point me to a reference that would do so. Dr. Harrell, thanks so much for your help so far! $\endgroup$