[R] Predictions from a Cox model - understanding centering of binary/categorical variables

[Bonnett, Laura]

Dear all,

I am using R 3.4.3 on Windows 10.  I am preparing some teaching materials and I'm having trouble matching the by-hand version with the R code.

I have fitted a Cox model - let's use the ovarian data as an example:
library(survival)
data(ovarian)
ova_mod <- coxph(Surv(futime,fustat)~age+rx,data=ovarian)

If I want to make predict survival for a new set of individuals at 100 days then that is trivial using predict.coxph e.g.:
newdata <- data.frame(futime=rep(100,5),fustat=rep(1,5),age=c(45,50,55,60,65),rx=c(1,2,1,2,1))
preds <- predict(ova_mod,newdata,type="expected")
survpreds <- exp(-1*preds)
survpreds
[1] 0.9967635 0.9969739 0.9859543 0.9868629 0.9401437

However, due to centering I believe, I am finding this a bit difficult to replicate by hand.

To replicate the analysis I need the baseline survival at 100 days, the regression coefficients, and the mean/proportions.
Baseline survival at 100 days: summary(survfit(ova_mod),time=100)$surv = 0.9888
Regression coefficient: ova_mod$coef = 0.1473 (age) & -0.8040
Mean age: mean(ovarian$age) = 56.1654
Proportions with rx: prop.table(table(ovarian$rx)) = 0.5 0.5

So, to recreate the predicted survival probability I would work out the linear predictor for my first individual:
LP1 = ((45-56.1654)*0.1437)+((1*0.5)*-0.8040) = -2.0470
However, predict(ova_mod,newdata,type="lp") suggests that it should be -1.2430.  Therefore have I misinterpreted the centering?  I.e that we take off the mean value from continuous variables, and multiply by the proportion with that response for binary/categorical variables?

Then, assuming the I have the correct LP of -1.2430, I need to raise the baseline survival estimate at 100 days to the exp(LP1).  This gives 0.9968 which is almost the predicted value of 0.9968 of above.  However, I need to get the linear predictors to agree with the output first!

Many thanks for your help with this.

Kind regards,
Laura

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