INTRODUCTION

Influenza pandemics have occurred at irregular intervals throughout human history, causing widespread morbidity and mortality. Pandemic influenza viruses are known to be re-assorted human/animal strains of the virus to which humans have little prior immunity, but the mechanisms are poorly understood that make one re-assorted strain cause a pandemic, while countless others do not ref. [Reference Nicholls1].

The paper that first claimed a connection between solar activity and influenza was published by Hope-Simpson in 1978 [Reference Hope-Simpson2]. Hope-Simpson long espoused the view that influenza is not a contagious disease, but rather associated with human responses to solar phenomenon [Reference Hope-Simpson3]. His 1978 paper purported, without any reference to literature to support the claim, that six influenza ‘pandemics’ occurred between 1918 and 1971, and the timing of each were all within ±1 year of a maximum in the sunspot cycle. However, in reality, only three pandemics are generally agreed upon to have occurred during that time period [Reference Morens and Taubenberger4–Reference Patterson13]. It is true that of these three (1918, 1957, and 1968), all in fact occurred within ±1 year of the solar cycle peaks. However, a trivial statistical analysis shows that this is not extraordinary; the Binomial 95% confidence interval for the estimated probability of observing a pandemic within ±1 year of a peak when three out of three have actually been observed is [0·29, 1·0] [Reference Clopper and Pearson14], but of all years during that time period, 16 out of 54 (30%) were within ±1 year of peak. This null hypothesis value of 30% is at the lower end of the Binomial 95% confidence interval of the observed, but within it.

However, as straightforward as this analysis is, it is based on only three events. Normally, in a paper one would never consider presenting a statistical analysis based on so few samples, because when sample sizes are very small the probability of a Type II error when testing the null hypothesis is very high [Reference Suen and Ary15], and model validation is impossible [Reference Chatfield16, Reference Casella and Berger17]. It is interesting to note that the Hope-Simpson paper was not in fact peer-reviewed, but rather correspondence to the editors of Nature. Had the paper been peer-reviewed by experts in influenza and/or statistics, it likely would have been pointed out that (a) half of the purported pandemics never actually occurred, and (b) the sample sizes were far too small for general inference.

In 1978, two astronomers, Hoyle and Wickramasinghe, espoused a theory that many diseases hitherto assumed to be infectious were actually seeded into the population from extraterrestrial origin [Reference Wickramasinghe and Wickramasinghe18]. As a ‘test’ of this theory, they attempted to explain the patterns of spread of influenza in day schools local to their university. They claimed that the only plausible explanation for the patterns they observed was that influenza was spreading in the population not via contact between people in the population, but through viruses arriving from outer space [Reference Wickramasinghe and Wickramasinghe18]. They announced their work in a paper in a news publication, New Scientist [Reference Hoyle and Wickramasinghe19], which is not peer-reviewed.

Hoyle and Wickramasinghe subsequently published a note in 1990 that claimed that the sunspot/pandemic link purported by Hope-Simpson also occurred during the ‘1978–79’ pandemic, and that their theory of extraterrestrial influenza explained this phenomenon [Reference Hoyle and Wickramasinghe20]. In reality however, the pandemic was in 1977, which was further from a solar maximum than 1978. Like the Hope-Simpson paper before it, the Hoyle and Wickramasinghe note was also a letter to the editors of Nature. Once again, had the paper been peer-reviewed by experts, it likely would have been pointed out that they got the date of the 1977 pandemic wrong, and that a statistical analysis to support their hypothesis of the purported relationships of sunspot cycles to additional pandemics prior to 1900 was entirely lacking. Indeed, it was pointed out by Lyons and Murphy in a subsequent letter to Nature that cause must necessarily precede effect, and several of the pandemics discussed by Hoyle and Wickramasinghe preceded the solar maximum [Reference Lyons and Murphy21]. They also took issue with the definition of the pandemics used, as did von Alvensleben [Reference Von Alvensleben22]. Von Alvensleben also pointed out that the pandemics listed by Hoyle and Wickramasinghe were in fact apparently randomly distributed within the periodic solar cycle.

Despite the questionable basis of these early, non peer-reviewed claims of an association between sunspots and influenza pandemics, it is now often talked about as an established ‘fact’ in the literature. Some, however, have put forward more biologically plausible explanations for the purported phenomena, including suggesting that vitamin D levels may depend on the variation in solar radiation during the sunspot cycle [Reference Hayes23], and that the migration patterns of birds that spread the influenza may be sensitive to geomagnetic changes [Reference Fuhrmann24].

Sunspot data are readily available from the Royal Observatory of Belgium in Brussels (currently available at http://www.sidc.be/silso/datafiles, accessed September 2016). Using these data, other researchers have attempted statistical analyses to verify the purported association between influenza pandemics and sunspots. This analysis examines the work of researchers that claim to verify the sunspot/pandemic effect; Ertel, Tapping et al., and Yeung [Reference Ertel25–Reference Yeung27]. Two of the analyses claim that maxima in sunspot activity are associated with influenza pandemics [Reference Tapping, Mathias and Surkan26, Reference Yeung27], while another claims that both maxima and minima in sunspot activity are associated with pandemics [Reference Ertel25]. A brief synopsis of each analysis is given below, and each is described fully in Appendix A.

Before describing each analysis, however, some things should be noted about the general problems with these analyses, primarily related to issues of robustness to analysis assumptions, and problems with data mis-transcription from sources in the literature:

• If an analysis used a particular formulation of a ‘distance’ statistic to assess how far a particular year lies from a maximum or minimum in sunspot activity, the conclusion of the analysis should not depend on the exact formulation of distance statistic used, when other similar and equally valid distance statistics might be employed.

• Identifying pandemics, particularly prior to the 19th century, is a highly subjective process, and there is disagreement in the literature on the list of pandemics prior to the early 1800s. Analyses of the potential of a connection between sunspot number and influenza activity should be robust when using different, equally plausible lists of pandemics.

• Similarly, when using multiple citations to sources of lists of pandemic years, the analysis may involve assessing pandemic years by only taking years for which k out of the n sources agree; in which case, the analysis conclusions should be robust to different assumptions of k.

• There are two alternate specifications of sunspot activity, the Wolf (or ‘Zürich’, or ‘International’) and Group sunspot numbers; it has been noted in the literature that the latter is likely more accurate prior to the modern era, while the former is more accurate for characterising recent ongoing levels of sunspot activity [Reference Hoyt and Schatten28–Reference Clette, Balogh, Hudson, Petrovay and von Steiger31]. Ertel, Tapping et al., and Yeung [Reference Ertel25–Reference Yeung27] all used the Wolf sunspot numbers, even though for the two latter analyses the Group sunspot numbers were also available. Analysis conclusions should be robust to different specifications of the sunspot activity.

• In general, analysis conclusions should be robust to changes in any of the arbitrary selections used in the analysis.

• Analyses should also be robust under alternate choices of the statistical analysis methodology used, particularly when a particular analysis method makes maximal use of the information in the data. Thus, an analysis that simply compared something like the mean of a ‘distance’ statistic for pandemic years to the average distance statistic for all years should be robust if a more powerful, non-parametric statistical test, such as the Kolmogorov–Smirnov or Anderson–Darling tests [Reference Richardson32], is used to compare the shape of the two distributions from which the means are calculated. Two distributions, for instance, can have similar means, but very different shapes. And, particularly for small samples, one outlier in a distribution of just a few events may dramatically effect the mean, yet overall the distribution is consistent with being drawn from the larger distribution.

• Many of the different compilations of lists of past pandemics were actually derivative of the same historical sources. This is noted in Yeung [Reference Yeung27], for example. The various references also cited each other frequently. Thus, lists of pandemics presented in the literature as being independent compilations, were not.

• Note here that the Ertel, Tapping et al., and Yeung [Reference Ertel25–Reference Yeung27] analyses all made transcription mistakes in the dates of influenza pandemics cited from the literature.

The following sections give brief synopses of the Ertel, Tapping et al., and Yeung [Reference Ertel25–Reference Yeung27] analyses, followed by a presentation of our own analysis of the available data. The robustness of the analysis to the assumption of various different, yet equally valid, ‘distance’ statistics, was assessed. For completeness, the analysis was performed using 10 different compiled lists of purported pandemics between 1700 and 1977, and also subsets of purported pandemics mutually agreed upon by k (where k goes from 1 to 10) of the reviews in refs [Reference Morens and Taubenberger4–Reference Patterson13]Footnote 1 (all of which were published after the 1977 pandemic, and cover the period from 1700 onwards). The pandemic year 2009 was added to the lists. Additionally, the robustness of the analysis to using the Wolf and Group sunspot numbers was assessed.

No statistically significant evidence that solar activity is related to influenza activity was found.

Ertel [ Reference Ertel 25] analysis In 1994, Ertel, a parapsychologist, performed an analysis claiming to verify that influenza pandemics occurred near both sunspot minima and maxima. He also published a later analysis claiming a link between sunspots and human creativity [Reference Ertel and Nyborg36]. Using lists of influenza epidemics (many of which were not pandemics) between 1700 and 1985 from nine different sources in the literature [Reference Hope-Simpson2, Reference Pyle12, Reference Patterson13, Reference Hoyle and Wickramasinghe19, Reference Creighton33, Reference Assaad, Bektimirov, Ljungars-Esteves and Stuart-Harris37–Reference Burnet40] and an encyclopaedia entry from 1970, Ertel arbitrarily defined a ‘pandemic’ to be an epidemic that at least three of the sources agreed upon. Ertel included in these sources several cited sources that were actually derivative of other cited sources (thus the 10 sources were not independent). Ertel also mis-transcribed data from several sources, and used some older references even when more up to date reviews were made available by some authors (for instance the list of epidemics in Beveridge et al. [Reference Beveridge38] was updated in Beveridge [Reference Beveridge10]). To determine whether or not epidemics appeared to be clustered around the times of maxima and minima in sunspot activity, Ertel defined a metric based on the unsigned distance, D, in years of an epidemic from a sunspot maximum. He then transformed D into a new statistic, Q, which was −1 if D was the maximal possible distance between sunspot maxima, or +1 if it was at the minimum possible distance: (1) $$Q = 1 - 2D/D_{{\rm max}}{\rm,} $$ where D max is the maximum value of D during a solar cycle (where each solar cycle begins at the solar minimum). While this statistic might, on the face of it, seem reasonable, it lacks sensitivity to whether or not an event occurs near a solar cycle minimum (the solar cycle is highly asymmetric in its periodicity, with maxima often occurring just a few years after a minimum, thus midway between two maxima usually does not correspond to the minimum, and the minimum in Q also thus does not generally correspond to the minimum in the solar cycle). Additionally, the Q statistic is not sensitive to whether the epidemic comes before or after the sunspot peak, and has only limited sensitivity to whether the epidemic is near a minimum in sunspot activity, despite the fact that Ertel was attempting to show that influenza epidemics occur near both maxima and minima in sunspot activity. Cross-checking the analysis, as described in Appendix A, revealed that the results are highly sensitive to Ertel's choice of distance statistic and statistical analysis methodology. Correcting Ertel's mis-transcription of the data, and removing derivative lists of epidemics also negate Ertel's claims of significance. Thus, largely because of the choice of distance measure and mis-transcriptions of data, Ertel concludes that sunspot activity is significantly associated with influenza activity. In addition to these problems with the analysis, Ertel concluded that during the 1700s the influenza pandemics appeared to significantly occur around the sunspot minima, but after that there was no significant clustering. Ertel came up with an explanation for the decrease in significance by stating that it must have something to do with long-term changes in sunspot activity. This is an excellent example of ‘cherry-picking’ data, where it is claimed that the results testing the null hypothesis are significant… except where they aren't [Reference Dienes41, Reference Morse42].

Tapping et al. [ Reference Tapping, Mathias and Surkan 26] analysis Tapping et al. [Reference Tapping, Mathias and Surkan26] performed an analysis where they examined the distance, in years, of influenza pandemics to the nearest sunspot maximum. The sunspot cycle periodicity is not constant and has varied since 1700 between 9 and 14 years. Tapping et al. [Reference Tapping, Mathias and Surkan26] thus expressed the distance of pandemics to sunspot maxima as fractions of the period of the sunspot cycle at that point in time (i.e. as a phase), defined as (2) $$\phi = \displaystyle{{{\rm signed}\;{\rm distance}\;{\rm to}\;{\rm nearest}\;{\rm maximum}} \over \matrix{({\rm year}\;{\rm of}\;{\rm next}\;{\rm minimum}) \cr\qquad- ({\rm year}\;{\rm of}\;{\rm previous}\;{\rm minimum})} }.$$ Using this metric, they attempted to determine if maxima in solar activity have been associated with subsequent increased incidence of influenza pandemics. As described in Appendix A, the analysis of the data in the Tapping et al. [Reference Tapping, Mathias and Surkan26] paper appears to have multiple issues, and their analysis results were not reproducible.