Referee 3's Review:

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N.B. These are the comments made by the referee when reviewing an earlier version of this paper. Prior to publication the manuscript has been revised in light of these comments and to address other editorial requirements.
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This is quite an interesting and well-written paper that uses an information theoretic approach to analyze the relationships between a single nucleotide polymorphism in the promoter of the MDM2 oncogene, gender, and age of cancer onset in patients harboring a germline inactivating P53 mutation. I recommend several changes in the methodology and presentation before accepting the paper for publication.

On page 6, right before the methods section, I do not see how the last sentence starting with "Thus the measured mutual information..." follows from what was stated previously. Mutual information is a quantity that is estimated from the data, but it is unclear what penalty for overfitting the authors are referring to -- this sounds like the minimal description length (MDL) principle.

On page 7, on line 11 from the bottom, what is meant by "the optimal measure of statistical dependency"? this implies some criterion of optimality. The authors should explain or remove the word optimal.

Since H(X) is defined, H(X,Y) should be defined also, as should H(X|Y)

Page 8: I am concerned about the manner in which the number of optimal bins was chosen. This is very heuristic and, since this is an important parameter, I would recommend a more principled way to select it. There are also a number of other approaches for estimating entropy and mutual information other than using the histogram-based methods (i.e. binning). For example, one approach is to estimate the density using a kernel density estimation approach (the bandwidth or smoothness parameter can be chosen automatically in a data dependent way) and compute entropy from the estimated densities.

I(X,Y; Z) should be defined explicitly.

Page 9, in the statistical analysis section: the authors state that the null hypothesis was that no correlation existed between a single variable and age of diagnosis. Do the authors specifically mean no correlation? Also, in the next sentence where the null hypothesis is that no correlation exists between two variables and age of diagnosis -- what exactly is meant by this statement? This needs to be made precise.

In the results section, the authors refer to the average age difference, but report the Mann Whitney test, in several places. There is nothing wrong with that, but it's a bit confusing, since the Mann Whitney test is not designed for testing the difference between two means.

Minor comments:
on page 5, line 6 from the top, "germline"

Mathematical variables needs to be italicized, e.g. on page 7.

Line 1 of statistical analysis section: "how to accurately interpret"