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A classmate and I have been looking over some stats regarding a study looking at the (lets call it) survival rate of an item of food. He ran his analysis using coxph to generate a model to compare the survival of a piece of food on camouflaged vs non-camouflaged backgrounds. Reviewing the summary of this analysis he saw that the R squared returned a value of 0. Both of us are biology students with a very limited background in statistics, but it struck us as odd that the R squared could be 0, as surely there must be some marginal level of variance explained by the model. Reading up on this, I saw that R squared for coxph is not functionally equivalent to the R sq. returned by linear models etc.

So I guess my questions are: How should we interpret this information? Is there an equivalent measure for data variation?

I understand this is similar to a previous question asked about interpreting the R squared in coxph, but mine is more focused on a comparison of (or inability to compare) this value to one that might be returned in a linear model.

Many thanks.

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Skylar Lobdell
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  • The fact that your variable of interest is a dichotomous treatment variable is irrelevant. The nature of the $R^2$ used by `coxph()` is the same. This question is a duplicate. Also, when you post a question asking to interpret your output, it is helpful to paste in your output (& maybe some sample data, if possible). – gung - Reinstate Monica Apr 08 '15 at 16:17
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    In fairness, the OP had already examined the prior question and felt (I think correctly) that the answers did not directly address the relation of Cox $R^2$ to OLS $R^2$. – EdM Apr 08 '15 at 16:45
  • I agree that the prior question does not provide a satisfactory answer. The answer by EdM is good. – Seanosapien Nov 12 '17 at 19:36

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The $R^2$ values returned by Cox survival analyses (or by other analyses of binary-outcome data as in logistic regression) are sometimes called pseudo-$R^2$ because they aren't the same as the $R^2$ values returned in ordinary linear regression. This page has a description of several types of pseudo-$R^2$ values. The approach used in coxph bases its $R^2$ value on the improvement in likelihood between the fitted model and a model without predictor variables (null model).

That said, it sounds like camouflage did not have much of an effect on food "survival" in your study. If the overall survival analysis did not show significance, you shouldn't be examining $R^2$ values very closely in any event.

EdM
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