# [R] hazard ratio of interaction Cox model

Frank E Harrell Jr f.harrell at vanderbilt.edu
Tue Dec 18 13:41:18 CET 2007

```Giulia Barbati wrote:
> Dear Forum,
> I have a question about interaction estimate in the Cox model:
> why the hazard ratio of the interaction is not produced in the summary of the model?
> (Instead, the estimate of the coefficient is given in the print of the model.)

The 'hazard ratio of the interaction' is not well defined.  Decide what
hazard ratio you want to estimate, then ask summary to compute that, e.g.

summary(modINT, XX_PR=c(1,3), XX_DISF=2)

will estimate the 3:1 XX_PR hazard ratio at XX_DISF=2

Frank Harrell

>
>
> # Example:
>
> modINT <-cph( Surv(T_BASE, T_FIN,STATUS)~ NYHA + ASINI + RFP + FE_REC + XX_PR*XX_DISF)
>
> print(modINT)
>
>
>                   coef se(coef)     z        p
> NYHA=2       1.254    0.584  2.15 0.031767
> ASINI           0.665    0.409  1.62 0.104247
> RFP=2            0.725    0.704  1.03 0.302578
> FE_REC=2        -1.637    0.810 -2.02 0.043331
> XX_PR            2.189    0.649  3.37 0.000748
> XX_DISF          3.233    1.000  3.23 0.001222
> XX_PR * XX_DISF -2.852    1.280 -2.23 0.025852
>
> summary(modINT)
>
>  Effects              Response : Surv(T_BASE, T_FIN, STATUS)
>
>  Factor         Low    High Diff.  Effect S.E. Lower 0.95 Upper 0.95
>  ASINI         2.0725 2.85 0.7775  0.52  0.32 -0.11        1.14
>   Hazard Ratio  2.0725 2.85 0.7775  1.68    NA  0.90        3.13
>  XX_PR          0.0000 1.00 1.0000  2.19  0.65  0.92        3.46
>   Hazard Ratio  0.0000 1.00 1.0000  8.92    NA  2.50       31.86
>  XX_DISF        0.0000 1.00 1.0000  3.23  1.00  1.27        5.19
>   Hazard Ratio  0.0000 1.00 1.0000 25.35    NA  3.57      179.88
>  NYHA - 2:1 1.0000 2.00     NA  1.25  0.58  0.11        2.40
>   Hazard Ratio  1.0000 2.00     NA  3.50    NA  1.12       11.00
>  RFP - 2:1      1.0000 2.00     NA  0.73  0.70 -0.65        2.10
>   Hazard Ratio  1.0000 2.00     NA  2.07    NA  0.52        8.20
>  FE_REC - 2:1   1.0000 2.00     NA -1.64  0.81 -3.23       -0.05
>   Hazard Ratio  1.0000 2.00     NA  0.19    NA  0.04        0.95
>
>
>
>
>
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