Rejoinder to Román, Gich, and Soriano (2015)

It is good to see that Roman, Gich, and Soriano (2015) appear to distance themselves from the suggestion that the Moon can somehow influence the rate of hospital admissions at their bleeding unit. The title and body of the article by Roman, Soriano, Fuentes, Galvez, and Fernandez (2004; “The influence of the full moon on the number of admissions related to gastrointestinal bleeding”) clearly implied a causal relationship. Their description of a specific mechanism implicating the Moon as the causal agent, no matter how speculative, reinforced the allegation that the Moon had some influence on the number of hospital admissions. As the authors’ data show, the Moon is innocent. Greater-than-expected admission rates are observed on Days 9, 12, 13, 27, and 29 of the “lunar cycle” (Roman et al.’s [2004] definition), but only one of these days is associated with the full moon. Establishing an association with the full moon would require, at the very least, a demonstration that the number of hospital admissions near full moon differs from the number of admissions in equivalent time intervals at other times during the lunar cycle. One cannot simply ignore, as Roman et al. (2004) have done, admission rates on certain days of the lunar cycle. Regarding the third item in Roman et al.’s (2015) rebuttal, I wish to emphasize that I am not responsible for the statement that a difference in dispersion or shape of two distributions invalidates the statistical test known as Mann–Whitney. This fact was established by statisticians (Hollander & Wolfe, 1999). Statisticians also generally agree that one should not trust results of statistical tests when test assumptions are violated. The authors’ attempt to clarify the assignment of hospital admissions to so-called “full moon days” and “non-full moon days” confirms that their procedure introduced a bias. Although they acknowledge that there were 13 instances in which the full moon fell on Day 30 of the calendar, they still insist on labeling Day 29 as the “full moon day. ” Remarkably, the authors write in their rebuttal that “there were no admissions on these 13 extra non-full moon days. ” Let us examine the probability of such an event. There were 447 hospital admissions in the 738-day study, corresponding to an average rate of admissions of 0.61 per day. The probability that there was no hospital admission on the first Day-30 instance is given by the Poisson distribution, specifically exp(−.61) = . 55. The probability that there was no hospital admission on any of the 13 Day-30 instances, as Roman et al. (2015) claim, is exp(−.61*13) = . 00038, or 1 chance in 2628. In other words, if one conducted 2628 studies similar to that of Roman et al. (2004), only one of these studies would yield such an exceptional outcome. Are we expected to believe that their study happens to be the one study among 2628 that fortuitously escaped the annoying consequences of the fact that the duration of the lunar cycle is variable? There is a 0.038% chance that their statement is true and a 99.962% chance that a more mundane explanation is true. Could it be that the authors selected a posteriori which day they would label “Day 30” (presumably a day with no hospital admissions), thereby hopelessly biasing the data by shifting the number of hospital admissions around on 13 separate occasions? Could it be that another day of the lunar cycle would have garnered the largest number of admissions with the proper accounting? This supposition, as well as other claims in their article, must regrettably remain unconfirmed because the raw data are not available. In this context, the authors’ call for additional studies is not warranted. The data as presented are sufficient to refute the hypothesis. With proper analysis of the raw data, one would most likely be in a position to exonerate the Moon with a higher level of confidence. Because I am not a health professional, I am not in a position to directly improve healthcare, and I am genuinely grateful to all those who devote their careers to the health professions. I trust that it is possible to improve healthcare while remaining committed to evidence-based reasoning. I understand that some health professionals are under the impression that the Moon influences hospital admission rates or birth rates. However, careful examination of the data reveals that these beliefs are unfounded. For a lucid and compelling explanation of the cognitive biases that shape our questionable beliefs, see Gilovich (1993).