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n the fall and early winter of 2015, a startling number of infants in northeastern Brazil were born with abnormally small heads. Mounting global concern gave rise to theories about what was responsible. And while public health authorities fairly quickly fingered the Zika virus as the culprit, a couple of other theories established deep roots on social media platforms.

But the just-published final report of a study conducted in Brazil discounts those two theories. The work, by Brazilian scientists, suggested there is no link between the cases of microcephaly and exposure to the insecticide pyriproxyfen, nor to maternal vaccination during pregnancy.

The Brazilian government had begun treating drinking water sources with pyriproxyfen in 2014 to control Aedes aegypti, the main mosquito species that transmits Zika, dengue, and other viruses. And in late November of that year, it also started offering pregnant women a vaccine to protect against tetanus, diphtheria, and pertussis.

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The Tdap vaccine, as it is called, is widely given elsewhere during pregnancy. The Centers for Disease Control and Prevention, for instance, recommends pregnant women get the shot during each pregnancy to protect their newborns against pertussis — whooping cough.

Pertussis infection in infants can be life-threatening, but because of the way their immune systems work, babies do not begin to get vaccinated against the bacterium until they are 2 months old. Antibodies from their mothers protect them in their first weeks of life.

The Brazilian researchers conducted a case-control study in Recife, a northeast city hard-hit by microcephaly. They compared the pregnancies of women who gave birth to babies with microcephaly to women who gave birth at the same time to babies without the condition.

The case-control study gathered reams of information about the gestation of the cases — 82 babies and nine affected fetuses that were stillborn — and those of 173 healthy babies that served as the “controls.” By comparing a multitude of factors — things like smoking or vaccination rates — between the two groups of mothers, qualities that differentiated the two groups come into focus.

This kind of study cannot prove that Exposure X caused Condition Y. But it can indicate where there seem to be links or “associations” between an exposure and an illness — and where no such association exists.

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“Importantly, this article provides the first evidence that exposure to the insecticide pyriproxyfen and vaccines administered during pregnancy were not associated with an increased risk of microcephaly,” Federico Costa and Albert Ko wrote in a commentary that accompanied the study, published in the journal Lancet Infectious Diseases. Costa, who is with Brazil’s Oswaldo Cruz Institute, and Ko, from Yale University’s School of Public Health, said the biological plausibility of these two rumored causes was always weak.

By contrast, the association between Zika infection during pregnancy and microcephaly was “extremely strong,” the study authors reported.

The study also found that a high proportion of the mothers of the control babies had antibodies to Zika virus, illustrating how widespread infection was in northeastern Brazil.

Ko and Costa noted that neither this study, nor several others that have been done, can explain why only a small portion of women infected with the virus gave birth to severely affected infants. Answers may come, they wrote, from larger studies that look at things such as how prior dengue infection affects infection with Zika.

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