Our first iteration of the analysis uses the case control methodology to adjust for the risk of the outcome. This showed acetaminophen was protective again central apnea. The model was spoiled by a nasty interaction in a small cell of infants who had both fever and had received acetaminophen. This could be thought of as artifactual relating to a small numbers in that cell; however the link test strongly suggested misspecification in the model. Our next iteration used propensity score matching to control the baseline risk of receiving acetaminophen or ibuprofen. We worked with various models from the simplest, taking only history of fever, very complicated descriptive ones, and finally settled on the model reported which behaves well both as a propensity score tool and as a relatively parsimonious model in general.* This again showed the same result of the previous model with a similar inconvenient interaction. Again, the link test suggested misspecification.

Finally, we combined these approaches adjusting for both the underlying probability of central apnea and of receiving acetaminophen.  Again acetaminophen was protective against central apnea, moreover the interaction disappeared.

And so there you have it. Some positive press for acetaminophen. Acetaminophen was indeed protective against central apnea. The number of infants receiving ibuprofen was too low to allow for further analysis; although we did notice that no infant who received both subsequently developed apnea. This is a provocative finding although it is likely much less surprising to readers of the animal literature than clinicians. The next step is to find limits of the hypothesis and then to test that refined hypothesis prospectively.

*(This is a minority philosophy in propensity scoring but both we and reviewers favor this approach  and in any event the results were the same regardless of the propensity score model used.)