Laura Bonnett
2010-Jul-21 12:37 UTC
[R] Fractional Polynomials - Hazard Ratios and Relative Hazard Plots
Dear All, I am using Windows and R version 2.9.2 with libraries cmprsk, mfp and Design. I have a dataset with approximately 1700 patients (1 row per patient) and I have 12 outcomes, three of which are continuous. I have performed univariate analyses to see if any factors are associated with a higher likelihood of the event of interest (achieving 12 month remission from epileptic seizures) and also an analysis adjusted for multiple variables. I have tried log and fractional polynomial (FP) transformations of each continuous variable. In the case of age, used for the example below, the FP transformation led to the best model fit according to the AIC. I have therefore applied this transformation for all analyses. To begin with I have fitted a Cox model stratified by randomisation period, rpa, (either before or after a certain date). fit1 <- mfp(Surv(Remtime,Rcens) ~ fp(age) + strata(rpa), family=cox, data=nearma, select=0.05, verbose=TRUE) I would like two things from this model, hazard ratios and and an associated hazard ratio plot. I am aware that the hazard ratios produced from a fractional polynomial transformation are not to be used directly (i.e. those obtained from summary(coxfitf1)). Instead the derived functional form of the variable should be used to estimate hazard ratios post hoc. I have attached a word document explaining how hazard ratios and confidence interval can be derived and given a worked example for the variable, age. The univariate results are: Age (years) ?10 (10 to 25] (25 to 37] (37 to 50] (50 to 71]>711.00 1.00 (1.00 to 1.00) 0.99 (0.99 to 1.00) 0.99 (0.99 to 0.99) 0.99 (0.98 to 0.99) 0.98 (0.97 to 0.99) To create a plot of the relative hazard I have used the code: plot(nearma$age,predict(fit1,type="risk"),xlab="Age",ylab="Relative Hazard") The produced plot is attached. As you can clearly see, the hazard ratios above and the relative hazard plot do not agree. This is also the case for the other two continuous variables that have been transformed via the FP approach. The hazard ratios for age using the model adjusted for multiple variables are as follows, which do coincide with the plot: Age (years) ?10 (10 to 25] (25 to 37] (37 to 50] (50 to 71]>711.00 0.86 (0.77 to 0.95) 0.78 (0.65 to 0.94) 0.80 (0.64 to 1.00) 1.01 (0.81 to 1.25) 1.61 (1.27 to 2.05) Can anyone therefore explain why the univariate hazard ratios do not coincide with the relative hazard plot and yet the hazard ratios from the multivariable model do? I know that the calculations are correct for both sets of hazard ratios. Thank you for any help you can provide as I am at a loss to explain the difference in the plot fo the calculations - they should, after all, be saying the same thing! Thank you, Laura