Author: Alboukadel Kassambara, Przemyslaw Biecek

# ggforest: How to Show Interactions Hazard Ratio

#### Alboukadel Kassambara, Przemyslaw Biecek

# Introduction

In general case it may be tricky to automatically extract interactions or variable transformations from model objects. A suggestion would be to create manually new variables that capture desired effects of interactions and add them to the model in an explicit way. This article describe an example of how to do this.

# Load required R packages

    library(survminer)
    library(survival)

# Compute a Cox model with interaction terms

    res.cox <- coxph(Surv(time, status) ~ ph.karno * age, data=lung)
    summary(res.cox, conf.int = FALSE)

    Call:
    coxph(formula = Surv(time, status) ~ ph.karno * age, data = lung)

      n= 227, number of events= 164
       (1 observation deleted due to missingness)

                       coef  exp(coef)   se(coef)      z Pr(>|z|)
    ph.karno     -0.1211782  0.8858761  0.0486092 -2.493   0.0127 *
    age          -0.1206758  0.8863212  0.0610426 -1.977   0.0481 *
    ph.karno:age  0.0016586  1.0016600  0.0007525  2.204   0.0275 *
    ---
    Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

    Concordance= 0.598  (se = 0.025 )
    Likelihood ratio test= 14.52  on 3 df,   p=0.002
    Wald test            = 13.42  on 3 df,   p=0.004
    Score (logrank) test = 13.44  on 3 df,   p=0.004

Visualization of the hazard ratios using the function `ggforest()`.

    ggforest(res.cox, data = lung)

On the plot above, it can be seen that `ggforest()` ignores the interaction term `ph.karno:age`.

To fix this, a solution is to create manually the variable that handles the interaction:

    lung$ph.karno_age <- lung$ph.karno * lung$age

and now you can fit an additive model and the `ggforest()` function will include it in the plot:

    res.cox2 <- coxph(Surv(time, status) ~ ph.karno + age + ph.karno_age, data = lung)
    summary(res.cox2 , conf.int = FALSE)

    Call:
    coxph(formula = Surv(time, status) ~ ph.karno + age + ph.karno_age,
        data = lung)

      n= 227, number of events= 164
       (1 observation deleted due to missingness)

                       coef  exp(coef)   se(coef)      z Pr(>|z|)
    ph.karno     -0.1211782  0.8858761  0.0486092 -2.493   0.0127 *
    age          -0.1206758  0.8863212  0.0610426 -1.977   0.0481 *
    ph.karno_age  0.0016586  1.0016600  0.0007525  2.204   0.0275 *
    ---
    Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

    Concordance= 0.598  (se = 0.025 )
    Likelihood ratio test= 14.52  on 3 df,   p=0.002
    Wald test            = 13.42  on 3 df,   p=0.004
    Score (logrank) test = 13.44  on 3 df,   p=0.004

    ggforest(res.cox2, data=lung)