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I'm doing a survival analysis on a dataset. considering "DV" as outcome var, "T" as time to event or censor, V1 - V6 independent variables.
I want to use conventional Coxph analysis as rouine statistic method, and also i want to do a machine learning method on my dataset (say as sensitivity analysis).

COXPH ANALYSIS
By coxph i found for example, variables V1 and V5 have significant contribution to my outcome "DV" after multivariable coxph.
Random forest for survival analysis
I also perform random forest survival analysis(Using randomForestSRC of R). At the end of process, i used VIMP function for variable importance finding.
It revealed 3 variables as most important.(eg. consider V1, V5, V3)

Now my question:
Is it correct to conclude from the variable importance result of randomforestSRC, that variables V1, V5 And V3 had significat contribution to the outcome, (say confirming my previous coxph analysis). Or it just tells that for OOB data, these variable had most contribution for true split points of nodes and it does not representative of whole dataset?

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In the Cox proportional hazards model, you can make a statistical statement about which variables have statistically significant impact (coefficients that are different from zero). In the random forest model, you can say that those three variables are the most important according to the importance heuristic, but you can't make a statistical statement about it.

So my answer is that no, it is not correct to conclude that variable importance from the random forest tells you that V1, 3, 5 have a significant contribution. If you need to make a statement about the relationship between the variables, stick with the Cox proportional hazard model. If you want additional accuracy and possibly additional robustness, the random forest might be better. The variable importance of the random forest helps you understand the results and the model, but it doesn't do the statistical work.

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  • $\begingroup$ Please correct me if i'm wrong: based on your answer, Is the following plan for analysis of my data correct? : I will conduct a random forest on my dataset, and find variables ranked by their importance, then i run univariable coxph for each variable to find positive or negative effect of the variables on the outcome var. (Or is there a method to find correlation of the independent var with outcome var in random forest). $\endgroup$
    – Behnam Hedayat
    Commented Feb 8, 2021 at 11:41
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    $\begingroup$ I was suggesting that you run the multivariate Cox proportional hazard model to find which variables are statistically significant or significant contributors. I was suggesting that you run the random forest model if you want to try to get more accurate predictions. I'm not suggesting that you mix the models in any way. Pick your objective, then pick the right model for your objective. $\endgroup$
    – R Carnell
    Commented Feb 8, 2021 at 14:24
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    $\begingroup$ @Behhed univariable coxph is not a good idea. Besides the usual problems in univariable analyses when predictors are correlated or some predictor values might affect the influence of others on outcome, there is an inherent bias in Cox models, as in logistic regression, if any predictor associated with outcome is omitted from the model. The suggestions made in this answer (+1) are on point. $\endgroup$
    – EdM
    Commented Feb 8, 2021 at 16:10
  • $\begingroup$ @Carnel i'm sorry if i misconcepted your answer. To be honest i'm newbie in machine learning. Actually in addition to knowing variables importance by random forest, i want to know the relation of variables to the target var(somthing like HR or OR). Now for this purpose do you suggest "partial dependence plot and analysis" in random forest? as i know it gives correlation of variables with target var. $\endgroup$
    – Behnam Hedayat
    Commented Feb 8, 2021 at 18:15
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    $\begingroup$ @Behhed. Yes, the partial dependence plot will give you an idea of the functional relationship between the independent and dependent variable. The advantage of these plots is that they are clear and simple to explain. The disadvantage is that there is no way to determine the "significance" of the effect and it does not account for the distribution of the underlying variable. In theory, the Cox proportional hazards model also helps you understand the functional form if your fit meets all the model assumptions and fit diagnostics. $\endgroup$
    – R Carnell
    Commented Feb 8, 2021 at 19:56

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