# Adding high-dimensional data to mutivariate Cox model

I have a survival cancer clinical trials dataset from which I have generated Cox models using forward likelihood ratio testing within R. These models are based on 'traditional' cancer variables (eg. age, histology, metastasis etc).

I would like to extend the model using high dimensional data (where we have measured many thousands of genes - FWIW, this is DNA methylation data, which can range from zero to one, rather than gene expression). Several approaches have been suggested for investigating survival using high-dimensional data, but I am not aware of any approaches that fit my requirements, i.e. adding high-dimensional data to a base multi-variate model constructed using previously identified survival correlates.

As a first step, I am testing for bi-modality and reducing dimensionality by selecting the most bi-modal probes for further analysis. These probes would be the most amenable to testing and verification in the lab.

One approach would simply be to carry on with the forward LR testing, although this would leave me very prone to overfitting.

Another (more sensible, in my opinion) approach would be to aggregate collections of genes into (survival-related) metagenes and then trim the metagenes into a handful of testable genes, so that this could be a usable test clinically, although this may also be prone to overfitting.

The cancer I work on is rare and test/training cohorts are tricky. To put things into perspective, the clinical trials dataset is 135 cases, with a further 55 age-matched non-clinical-trials cases, which show no difference in survival to the clinical trials dataset.

So my question is, what sort of approaches should I be considering and is what I have done so far sensible?

Any advice from this rather rambling question is most appreciated.

Thanks for reading!

Ed

• I'm not sure if something like the "gene set enrichment analysis" can be used for DNA methylation as well, but if yes that may help you to aggregate collections of genes into metagenes. Apr 4, 2011 at 16:31
• Not sure whether you know her work, but Anne-Laure Boulesteix have some papers/reports on survival coupled to high-dimensional genetic data.
– chl
Apr 4, 2011 at 18:00
• @GaBorgulya +1, though from a quick Google and a v brief skim i like the look of this "simple alternative" (poss. more freely accessible preprint) Apr 4, 2011 at 18:19
• @chl, kudos for the Anne-Laure Boulesteix link - I was unaware of her work, but it seems to include answering the precise question that I have asked here.
– EdS
Apr 4, 2011 at 19:02

## 2 Answers

One approach would simply be to carry on with the forward LR testing, although this would leave me very prone to overfitting.

You could penalise model complexity to avoid overfitting. My favourite is the stepAIC function from the MASS package that uses AIC (can be configured to use BIC) as a goodness of fit.

• This will depend on the number of predictors, though. I'd favour L1/L2 penalties (or the elasticnet criteria). Furthermore, I think the issue here is that overfitting will result from selecting genes (or meta-genes) first, and then testing a model on this particular feature subspace. What do you think?
– chl
Apr 4, 2011 at 21:26
• Thanks to the links and thoughtful commentary provided, I've been led to Coxboost, a technique that enables me to include established covariates and add molecular information if it usefully extends the current model. It seems to do the trick, although I need to study it more to understand more fully what is going on with that approach.
– EdS
Apr 5, 2011 at 12:23
• @chl Thanks for your comment, I have to read and think about it! Apr 5, 2011 at 12:29
• @EdS I think this was what A-L Boulesteix used in a benchmark study (should find the notes I took during an informal talk she gave to my colleagues and me, though -- so let's take it for granted)
– chl
Apr 5, 2011 at 12:38

Edit: after the comment below from EdS my original answer was not meaningful any more. @EdS, thanks for the further information!

• thanks for the comments. The bimodality criterion is purely to ensure that any selected features are clinically relevant, since measuring DNA methylation is still fairly crude, and in a routine lab setting, the most sensitive you can hope for DNA methylation is unmethylated, hemi-methylated or methylated, so these extreme bimodal values are most useful
– EdS
Apr 4, 2011 at 19:03
• @Ga Please post comments like this as comments, not replies.
– whuber
Apr 5, 2011 at 15:51
• @whuber I did not want my original answer to stay, but neither wanted to delete it because that would have deleted the useful comment of EdS as well. If you suggest a better solution I'm happy to follow. Apr 5, 2011 at 17:46
• @Ga Oh, I see, you had an answer and then edited it. I'm always sorry when interesting answers are deleted, even when it turns out upon further clarification that they might be less relevant, but it sounds like you have hit on a reasonable solution here.
– whuber
Apr 5, 2011 at 17:55