Along with teaching and research most academics have an obligation to perform ‘service’ to their university, community and discipline.  This includes editorial and committee work, administrative work and reviewing articles for publication.  Peer-review is an important part of the academic system, and while sometimes reading and critiquing a strangers manuscript is educational, it is often a burden, and time-consuming.

So, how many articles can the average academic expect to review each year?

Number of journal articles published per year: 1,500,000 (Björk et al., 2008)

Proportion of articles submitted to journal for publication that get reviewed: 50% (Nature Materials Editorial 2015)

Proportion of these that get accepted 33%  (Nature Materials Editorial 2015)

Number of articles reviewed every year: (1.5 million x 1/.5 x 1/.33 = 9,000,000)

Average number of reviewers per-paper: 5 (based on personal experience, includes re-reviews)

Number of reviews required each year: 45,000,000

Number of University professors worldwide.  Using Statistics Canada data, I took the proportion of population employed as professors in Canada (0.12%) and multiplied that by the global population of 7.1 billion, giving a total of 9,000,000 university professors around the world.

Average number of manuscripts reviewed each year: 5

This excludes the review of grants, book chapters, books, manuscripts that aren’t submitted for peer review, etc.  It also ignores that some fields publish more than others, and, some academics are asked to peer review more papers than others, and that the success rate varies considerably by discipline.  However, it also does not account for reviews done by post-docs, graduate students and scholars employed in non-university settings.  I suspect this number is low, probably but probably fairly close to the average value across all fields.

*This analysis was not ‘peer reviewed’

I have compiled data on West Nile virus infections in humans for Canadian (excluding the maritime) provinces .

West Nile virus incidence in Canadian provinces, 2003 – 2015
Year	Canada	BC	AB	SK	MB	ON	PQ
2002	414					395	19
2003	1481	0	275	947	143	94	17
2004	25	0	1	10	3	14	1
2005	225	0	10	58	58	101	7
2006	151	0	40	19	51	43	0
2007	2215	0	320	1397	582	18	1
2008	36	0	1	13	12	9	1
2009	13	2	2	0	2	4	0
2010	5	1	1	0	0	9	0
2011	101	0	0	0	0	64	37
2012	428	0	9	9	39	249	126
2013	115	1	21	9	3	53	28
2014	21	0	0	0	5	10	6
2015	78	0	0	0	5	33	40

The list of sources I used for the table is here

• http://www.healthycanadians.gc.ca/diseases-conditions-maladies-affections/disease-maladie/west-nile-nil-occidental/surveillance-eng.php
• http://www.bccdc.ca/health-info/diseases-conditions/west-nile-virus-wnv/surveillance
• http://www.health.alberta.ca/health-info/WNv-evidence.html
• http://www.gov.mb.ca/health/wnv/stats2014.html
• https://www.publichealthontario.ca
• http://www.cbc.ca/news2/background/westnile/
• http://www.health.alberta.ca/documents/WNv-Infection-Rate-Report-09.pdf
• http://www.phac-aspc.gc.ca/wnv-vwn/nsr-rns_2012/w43/index-eng.php
• http://www.phac-aspc.gc.ca/wnv-vwn/nsr-rns_2013/final/index-eng.php
• http://healthycanadians.gc.ca/publications/diseases-conditions-maladies-affections/west-nile-2014-nil-occidental/index-eng.php
• http://healthycanadians.gc.ca/diseases-conditions-maladies-affections/disease-maladie/west-nile-nil-occidental/surveillance-eng.php

Not all these sources are authoritative (for example, the CBC was the only source I could find for some of the numbers).  Also, not all these data sources clearly distinguished between travel-related and non travel-related infections.  Finally, the actual counts can change over time based on the laboratory tests, and for other reasons, so the final numbers are always a little mushy.  But you get the general idea.

Scientists may soon identify a clear connection between Zika and microcephaly, but I want to assess the publicly available data to determine whether or not it lends support to the Zika-microcephaly theory.  My focus is on the epidemiology rather than the pathology, which means I am using data on the incidence of infection and microcephaly to determine whether or not there is a statistical association between the two.

Taken at face value, the data would suggest a very powerful association between Zika and microcephaly.  Here are the reported number of microcephaly cases in Brazil for 2014 & 2015

2014: 147
2015 (based on information as of February, 2016): 4443 (suspected and confirmed)

Assuming a constant birth rate between years, and that Zika appeared in 2015, that’s more than a 30 times difference in absolute risk between 2014 and 2015, and 4296 microcephaly cases attributable to infection with Zika virus. That’s stronger than the association between smoking and lung cancer.

Are the microcephaly data to be believed?

There is good reason to think that Brazil’s surveillance of congenital anomalies may not be particularly accurate. Based on work by Dolk (2010), the rate of microcephaly in Europe is 2.9 per 10,000 live births. If we assumed the same absolute risk for Brazil, we would expect almost 9,000 cases of microcephaly per year. Using the same math, there should be about 350 cases in Pernambuco State, the region of Brazil where much of the early concern was concentrated.  The most recent numbers I can find suggest as many as 1,500 cases of microcephaly in that region, though apparently many of these cases are not confirmed.

The discrepancy in cases is not surprising given the difficulty of diagnosing microcephaly, which at least initially, relies on measurements of head circumference against a population average, then followed up with brain imaging for confirmation.  In a paper recently published in The Lancet, the authors suggest that given the risks associated with diagnostic brain imaging used to confirm cases, it may be important to reduce the number of false-positive clinical diagnoses by changing the standards of measurement currently used.  This is particularly true given the potential stigma of diagnosis and absence of any specific treatment once a diagnosis is made.  In short, the evidence suggesting a recent spike in microcephaly is contested, and it may be some time before reliable data emerge.

Association between Zika incidence and microcephaly

If we were to assume the microcephaly data were representative, what is the connection between microcephaly and exposure to Zika?

Around 71,000 (2015-2016) Zika cases have been confirmed in Brazil as of February 2016.  However, like other flaviviruses, Zika may often be sub-clinical, so let’s multiply this number by 10, giving us 710,000 infections in Brazil over this period.  I estimate that the prevalence of pregnancy in Brazil is roughly equal to the birth rate (15 per 1000) which means that around 10,650 of these 710,000 infected people were pregnant women. The current concern is exposure in the first trimester, but to be conservative, I’ll just divide 10,065 by two, which gives us 5,325 women exposed to Zika at a time that would increase risk of microcephaly.

Now, if the difference in incidence between 2014 and 2015 is to be believed, then that means 4,296 cases of microcephaly among these 5,325 women would be explained by Zika, which gives an Zika incidence rate of 0.81, meaning that 81% of pregnant women exposed to the Zika virus will have a child diagnosed with microcephaly. To put this in context, pregnant women standing within 1200 metres of the atomic explosion at Hiroshima had 55% chance of giving birth to a child with microcephaly (Plummer 1952). The incidence rate ratio of Zika exposed mothers to baseline rates of microcephaly (0.81 divided by 0.00029) is over 250, which is as strong a causal association as you will find.

Based on these data, the causal relationship between Zika and microcephaly is so striking as to be implausible.  After all, Zika has appeared in human populations before without evidence of microcephaly; if the association between cause and effect was as clear as the evidence here suggests, the association would have been seen before.

Conclusion

It is hard to find reliable data that would help determine whether or not there are more microcephaly cases in Brazil in recent years than in years prior to the discovery of the ZIka virus in the western hemisphere.  So to some degree, the answer to the question I posed in the title remains unclear.  Under these circumstances, the public health response may be entirely appropriate; when uncertain, it is often wise to play it safe.

Nevertheless, the number of Brazilian microcephaly cases being used by news sources and social media are probably not accurate enough to deserve reporting without considerable qualification, and certainly should not be used as primary evidence demonstrating the relationship between Zika and microcephaly.  There is good reason to think that awareness and fear of disease can cause apparent (but imprecise and/or inaccurate) trends in disease to emerge from time to time.  Back in 2006 my colleagues and I observed this very problem with estimating incidence of West Nile virus following the pathogen’s emergence in Western Canada.

 

Consider the following graphic:

This graphic is a representation of the costs and benefits of gun ownership as a function of environment and ability.  Costs and benefits are simplified to ‘probability of causing my death’ and ‘probability of preventing my death’, respectively.  This does not account for all (or even most) of the costs and benefits of gun ownership, and the values on the axes on the graph are for illustration, and do not accurately represent probabilities of harm specifically or generally.  Nevertheless, the graph can be used to understand the circumstances in which gun possession could be considered rational and irrational.  This is done by dividing the probability on the y-axis by the probability on the x-axis; if the resultant ratio is above 1, then gun ownership is rational.  Otherwise it is not.

As one would expect, for a child, gun ownership is usually a bad idea since their lack of skill and maturity is more likely to result in them harming themselves than using the firearm for self protection. At the other extreme, trained soldiers in war zones are probably more likely to survive when in possession of a firearm.  Nevertheless, an untrained soldier is still worse off than a trained soldier since the probability of accidentally dying at the hands of his own gun is higher than his trained contemporaries.

The more general question for the public is where am I on this graph?  Am I more likely to die or prevent death when in possession of a gun?  To some degree, this question can be answered with a little bit of data and some trivial arithmetic.

Let’s start with the annual homicide rate in the US.  It’s somewhere around 5 per 100,000 per year.  One of the arguments in favour of firearm ownership is that individual risk of homicide is lowered by possessing a firearm (moving up the y-axis of my graph).  It is hard to know what value to assign this reduction in homicide risk, but John Lott has suggested that concealed handgun laws reduce murders by 8%.  This seems a reasonable number to start with, but I’ll be generous and round it up to 10%, and use that as a working value.  So I am assuming that by possessing a firearm, one can reduce their risk of homicide by 0.5 per 100,000.

Next, we must determine the rate of accidental death from a firearm, the rate of firearm suicide, and the rate of firearms being turned on the person wielding them.  There are between 500 and 700 accidental gun deaths per year in the US, which gives us a rate of between 0.16 and 0.22 per 100,000.  I’ll choose the lower of these two values to work with.  The rate of firearm suicide is roughly 6 per 100 000.  However we can’t use this rate in our calculation since in the absence of a gun, people may commit suicide using other means.  So I am going to arbitrarily drop this value to 0.6 per 100,000—this is an estimate of firearm suicide that wouldn’t have otherwise occurred even if firearms weren’t available.  Even harder is to know the rate of deaths in which a person’s firearm is turned on them in a confrontation.  I don’t have an estimate of the rate of death from this type, so let’s just call this value an unknown, X.  We do know that X can’t exceed 5 (since this is the homicide rate) and that X it is probably a fairly small value.

So the ratio of probabilities, r,  is calculated as

r = 0.5 / (0.16 + 0.6 + X).

This formula tells us whether or not the gun ownership is rational in a population over the long term.  The numerator is the net survival benefit of firearm ownership (y-axis).  The denominator is the net cost (x-axis).  The formula might have been very different if we were to include externalized costs of gun ownership on survival, but let’s keep it simple.  If r is above 1, then owning a firearm is rational, if below 1, owning a firearm is irrational.

Given the assumptions thus far, owning a gun does not seem rational for the population as a whole.   Even if we set X=0, r is still less than 1.  But this does not take into account variations in environments and contexts of gun ownership, which seem to explain important differences in suicide and homicide rates.  The suicide and homicide rates in the US vary considerably with ethnicity.  Based on US Department of Justice Statistics, the homicide rate for white Americans is around 3 per 100,000, and for African Americans around 17 per 100,000.  Suicide rates in the white population are about double that of the African American population.  So now we have two additional ratios to consider:

r_whites = 0.3 / (0.16 + 0.7 + X), and

r_{African Americans} = 1.7 / (0.16 + 0.35 + X).

Based on these data gun ownership is probably not rational in the white population (r_whites is less than 1).  On the other hand, for African Americans it may be very rational to own a gun (r_{African Americans} is greater than 1).

If we stratify suicide rates and homicide rates by gender, the results are also interesting:

r_women= 0.2 / (0.16 + 0.3 + X), and

r_men = 0.68 / (0.16 + 0.9 + X).

From these calculations, gun ownership is probably irrational for women and men, but more irrational for women than men.  I suspect if we stratified by income, race and sex simultaneously, an even clearer picture would result: gun ownership is clearly irrational rich white women, and clearly rational for poor African American men.

If this all seems rather cynical, well it should.  While I’ve framed this thought experiment in terms of a simple calculation of rationality, it merely adopts the controversial logic behind the argument that firearms reduce an individual’s risk of being a victim of violence.  This is the kind of statement that can be analyzed empirically, and given the data available to me, the logic does not seem to hold universally, but is very much dependent on circumstance, and in particular, the social environment in which one lives.

Even if some of the parameters I’ve used  are imprecise, there are some important things to take away from this exercise.

First, as the homicide rate goes down, it becomes less and less rational to own a gun, and in many US states (and in most OECD countries) gun ownership is probably universally irrational when it comes to self-preservation.  People own guns for reasons other than defense against murder, and that has not been taken into account here, but nor has the fact that gun ownership promotes a culture that many people find distasteful, and creates negative social externalities that can have wide reaching effects. In any case, in a debate on the question of survival alone, gun-control advocates may be able to make the superior appeal to logic and common sense.  Second, the demographic inequalities in the US suggest a perverse race paradox in gun ownership.  White people in the U.S. are more likely to own guns than African Americans, yet are less likely to be killed in a homicide whether or not they own a gun.

I am not so naive to think that any evidence I present will change the minds of the pro-gun advocates, or even that what I’ve written here is really new.  However, I do favour trying to understand decisions by examining whether or not they are logically coherent and rational, since at least we can then better understand the true motives for favouring one position over another.  In this case, one has to question the real motives of gun advocates–if guns don’t make most of us safer, then why frame them as a tool of self defense?

Acknowledgement

Thanks to William Bland, who pointed out the importance of stratifying suicide rates by gender and ethnicity.