# Adjusted Survival Curves Strata Specification with Continuous Predictor

I have a continuous predictor in a multivariate Cox regression. I have chosen to present the hazard ratio per standard deviation difference (and subsequently done the same for all continuous covariates to ease comparisons).

I prefer to create a figure to illustrate these results as well. I have chosen to present adjusted survival curves from the Cox model. I do not know how I should specify the strata in this case. My first inclination is to do a median-split of the predictor of interest (which is continuous) and then show the curves for "High" and "Low" groups -- is such an approach acceptable; any improvements? A previous answer suggested to use the "covariate at means method" and plot predicted survival curves for 20th and 80th percentile.

• What tool are you using for this? Sep 1, 2019 at 2:20
• R: survival library and survminer library. I think ggadjustecurves() function is my best bet because there are options for conditional and marginal approaches (which may be more valid than averaging at covariates) Sep 1, 2019 at 2:24

If I've understood you correctly, you have standardized your continuous covariates (subtract the mean, divide by standard deviation) so that your hazard ratios are interpreted as the change in the log hazard per standard deviation change in the predictor.

Plotting adjusted survival curves sounds like a good idea to me. You could do something like $$-2\sigma$$, $$-1\sigma$$, $$0\sigma$$, $$1\sigma$$, and $$2\sigma$$ for your covariate of choice. This would give you 5 survival curves (though if you show confidence intervals, it could get a bit busy).

Personally, I would avoid arbitrary splits. "High/Low" is a bit nebulous just looking at the viz, so I would have to go hunting for wherever you defined what those groups mean. The $$\sigma$$ approach would be clear to anyone familiar with statistical modelling.

• Good points, I will try and pursue this. As a follow-up, why must the hazard ratio be interpreted as the change in the log hazard per standard deviation change. Is this true even though I have not taken the log of my covariates? What if I did transform my covariate? Let's say A, B, C are all continuous predictors. What is the interpretation if I standardize these covariates and take the log? Additionally, is it possible to just take the log of A and B and not C (but all three remain standardized)? Sep 1, 2019 at 4:11
• The cox model is expresses the log hazard ratio as a linear combo of covariates. $\log(HR) = \beta_0 + \sum_i \beta_i x_i$. When you run summary on a coxph model, you will see the table returns coef and exp(coef). coef is the log hazard ratio (i.e. the $\beta$ in the model) and thus exp(coef) is the hazard ratio. No need to transform any covariates, you can leave them as they are. Sep 1, 2019 at 15:40
• There might be reason to transform the covariates given a positive skew to remove influence of extremes, correct? If I was to log10 transform, would the hazard ratios be interpreted as the change in the log hazard per standard deviation change in log10 predictor? Sep 1, 2019 at 16:00
• Yes, that's the correct interpretation. Sep 1, 2019 at 16:21
• Thanks for your input. This is getting away from the main question but I'd like your expertise on the matter. I am standardizing all my continuous covariates (and transforming them if needed), however I would like to express the change in the log hazard per 10 year change for my covariate "Age" as standard deviation does not make much sense for this. Just like any other regression model, this is okay to do as long as I specify this, correct? Sep 1, 2019 at 17:11

You could use the contsurvplot package to create some plots that were designed specifically for the purpose that you are talking about, as described in an answer to this post: Converting survival analysis by a continuous variable to categorical so as to find level of most significant difference