Dear Statisticians
   
  In Martin Bland’s interesting article to the BMJ, ‘Multiple significance tests: the Bonferroni method', he appears to highlight two scenarios when a Bonferroni-type adjustment could be appropriate - namely, a) when a variable is represented by several independent categories and multiple comparisons are carried out over these categories in order to find an effect and b) when an attempt is made to find an association between a particular factor and multiple outcome variables, where the measures represented by the outcomes variables are not independent.
   
  I am trying to relate the second of these two scenarios to a study I am considering at the moment. I suspect (although that I am currently verifying this with a neurologist) that presence of any one of the genotypes in an individual may not be biologically independent of that of presence of at least some of the other genotypes. The outcome variable for the study is presence or absence of disease. As well as testing for multiple main effects over genotypes (and many other factors), multiple gene-gene interactive effects and multiple gene-environment interactive effects are also of interest. 
   
  I would greatly value and appreciate advice on how to respond to the results of such a study if a binary logistic regression analysis produced a p-value of 0.03, say, for a single gene-environment interaction when no other tests for main gene or environmental effects, gene-gene or gene-environmental effects proving to be significant. Would you consider this lonely significant p-value to constitute good evidence for the existence of such an interaction or (if occurrences of the genotypes were not biologically independent) would there be a need to correct for multiple comparisons in respect of this single ‘effect’, thus undermining the existence of a true interactive effect? In particular, I am unclear about the validity of the above p-value as a final p-value on the basis of the many genetic factors which would require to have been entered into the logistic regression analysis to test both for main and interactive effects. Please would you kindly assist me to improve my
 understanding in this area. (By way of explanation, I should stress that the value of 0.03 has been chosen as a p-value, above to illustrate a case where a result have been shown to be signficant at the 5% but not the 1% signficance level, as this is typical of the type of result relevant to the above study.)
   
  Further, I understand that it is not so appropriate to carry out Bonferroni-type corrections when carrying out tests for association between a given factor and multiple outcome measures if the multiple outcomes measures are independent. If I am correct in my understanding here, would this remove the need to correct the above p-value for multiple testing were it to be the case that the genetic factors were found to be biologically independent? 
   
  On a separate note, it may well be the case that binary logistic regression is not an optimal statistical procedure to perform for the above sort of study, in which case I would also welcome suggestions for improvement.
   
  Thank you so much for your interest and assistance. I should be happy to clarify any details if appropriate.
   
   
  Best wishes
   
  Margaret
   

 		
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