On 2017 Jan 26, Janet Kern commented:

Bonferroni is a 'multiple comparisons adjustment' for reducing the risk of false-positive findings when engaging in statistical 'fishing expeditions' among many unrelated associations. It is appropriate only when any of the following are true: 1. those associations are equally important, likely, and expected to be zero (absent) based on external (a priori) considerations; 2. the cost of any false negative is minor compared to the cost of any false positive; and 3. the associations are independent (unrelated) to one another. In return for the reduce risk of false positives, multiple comparison adjustments, like Bonferroni, dramatically increase the risk of missing real associations (false negatives). So, even if there were no other objections, Bonferroni as used by the authors (with N = 8) is simply erroneous. Using Bonferroni in this study was wrong for several other reasons: First, the authors specifically wanted to test if influenza vaccination during pregnancy was a risk factor for ASD—this was not a 'fishing expedition" as assumed by Bonferroni (violating '1' above). Second, the overall association of influenza vaccination anytime during pregnancy depends completely on the associations within each trimester, so violates the Bonferroni assumption of independence (violates '3' above). Third, the first trimester is expected to be the period of greatest vulnerability for the developing fetus, and so is a pre-specified hypothesis. (In other words, before the study, the stakeholders expected (a priori) an association, which also violates '1') Finally, we need to be confident that vaccines are safe: the costs of wrongly concluding that the influenza vaccine is safe rivals the costs of wrongly concluding that it causes harm, which violates the Bonferroni assumption ('2') that wrongly concluding harm is more costly than wrongly concluding safety.

On 2017 Jan 26, Janet Kern commented:

Bonferroni is a 'multiple comparisons adjustment' for reducing the risk of false-positive findings when engaging in statistical 'fishing expeditions' among many unrelated associations. It is appropriate only when any of the following are true: 1. those associations are equally important, likely, and expected to be zero (absent) based on external (a priori) considerations; 2. the cost of any false negative is minor compared to the cost of any false positive; and 3. the associations are independent (unrelated) to one another. In return for the reduce risk of false positives, multiple comparison adjustments, like Bonferroni, dramatically increase the risk of missing real associations (false negatives). So, even if there were no other objections, Bonferroni as used by the authors (with N = 8) is simply erroneous. Using Bonferroni in this study was wrong for several other reasons: First, the authors specifically wanted to test if influenza vaccination during pregnancy was a risk factor for ASD—this was not a 'fishing expedition" as assumed by Bonferroni (violating '1' above). Second, the overall association of influenza vaccination anytime during pregnancy depends completely on the associations within each trimester, so violates the Bonferroni assumption of independence (violates '3' above). Third, the first trimester is expected to be the period of greatest vulnerability for the developing fetus, and so is a pre-specified hypothesis. (In other words, before the study, the stakeholders expected (a priori) an association, which also violates '1') Finally, we need to be confident that vaccines are safe: the costs of wrongly concluding that the influenza vaccine is safe rivals the costs of wrongly concluding that it causes harm, which violates the Bonferroni assumption ('2') that wrongly concluding harm is more costly than wrongly concluding safety.