# correct for multiple testing on correlated data with NaNs

First of all, I'm not a statistics expert, so I hope I can describe all relevant details of my problem:

I'm working with a dataset consisting of subject age (1st column), 13 ordinal scaled parameters (2nd-14nd columns) and observations for age and parameters (rows). The observations are incomplete and contain NaNs, for some parameters more than for others (the NaNs actually have a certain "pattern"). Additionally the parameters are pairwise correlated among each other with (Spearman) correlation coefficients ranging from about -0.7 to +0.7. (of course some of them are also uncorrelated)

I now want to test for each of those 13 parameters if they are significantly correlated with the subject age.

Therefore I now have to correct for multiple testing. Since the parameters are sometimes strongly correlated the general assumption for Bonferroni that the tests have to be independent, does not hold, therefore Bonferroni (or Sidak) would be too conservative.

Furthermore also the correlations between the 13 different parameters sometimes produces a more "valid" value (if. e.g. for 200 subjects both parameters were captured the correlation between them has a much narrower confidence interval than if only 20 parameters were captured)

My question now is: How can I correct for multiple comparisons factoring in the dependencies of the parameters?

• Regarding the differing number of valid values, the hypothesis test p-value will account for that already. A variable with only 20 valid values will require a comparatively stronger correlation to be deemed significant than a variable with 200 valid values. Although you may want to consider that NaN may in fact be a useful value, since you point out that your data is not missing at random - in that case NaN isn't just a value that happens to be missing, it can actually contain information about the sample. – Nuclear Wang Jul 1 at 15:21
• The pattern of missing values is semi-random, since there are some coherences like "if the value of parameter A is missing the value of parameter B is missing almost certainly, but not otherwise". But Parameter A itself is missing at random. Are there standard approaches to be able to make some claims as "this parameetr is correlated with subject age but this one not"? – user252456 Jul 4 at 12:09