What is the predicted "risk score" for cox models?

[zepedae]

I ran the following time-varying covariate cox model:

    model_int <- survival::coxph(Surv(tstart, tstop, status) ~  nat + dist + 
                                   sex + sf + popDens + medInc + 
                                  popDens*nat + popDens*dist + popDens*medInc, 
                                 data = model_df)

and I get the following summary

    Call:
    survival::coxph(formula = Surv(tstart, tstop, status) ~ nat + 
        dist + sex + sf + popDens + medInc + popDens * nat + popDens * 
        dist + popDens * medInc, data = model_df)
    
      n= 43846, number of events= 154 
       (251 observations deleted due to missingness)
    
                        coef exp(coef)  se(coef)      z Pr(>|z|)    
    nat            -0.121507  0.885585  0.124637 -0.975 0.329614    
    dist           -0.195417  0.822492  0.123732 -1.579 0.114255    
    sexm           -0.021949  0.978290  0.168305 -0.130 0.896240    
    sftransient     0.659347  1.933530  0.182534  3.612 0.000304 ***
    popDens         0.552056  1.736821  0.178899  3.086 0.002030 ** 
    medInc          0.006984  1.007008  0.074640  0.094 0.925454    
    nat:popDens     0.645145  1.906263  0.199470  3.234 0.001219 ** 
    dist:popDens    0.190398  1.209730  0.151516  1.257 0.208894    
    popDens:medInc  0.019754  1.019950  0.073993  0.267 0.789491    
    ---
    Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

I plotted the interaction effect by using plot_model to generate predicted values for 5 quantiles of nat across a range of popDens values (please ignore the title):

  sjPlot::plot_model(model_int, type = "emm", 
                      terms = c("popDens [-0.369923, 10]", "nat [-1.44193, -1.0567426, 0.0988196,0.9012933, 1.551297]"),
                      title = "Predicted Hazard Ratios",
                      legend.title = "Proportion Natural \nHabitat (quantiles)") + 
     scale_color_discrete(labels = c("0%", "25%", "50%", "75%", "100%")) + 
     theme_bw()

And I get the following plot:

So, how does plot_model generate risk scores? Is it the hazard ratio? If so is it the ratio of hazard rates between the new data and sample data? I haven't found anything definitive in the sjPlot or ggemeans documentation.

[strengejacke]

Do you have a reproducible example?

Maybe it's a bug in labelling the y-axis. You have three options for survival-models:
https://strengejacke.github.io/ggeffects/articles/introduction_plotmethod.html#survival-models

The above plot looks like that are indeed risk-scores, but it's strange that these vary between 0 and 1.