Here is an interesting study, that was not paid for by anybody with an agenda.
"This large population-based safety study found no evidence of increases in adverse neonatal events in infants born to individuals vaccinated against COVID-19 during pregnancy. In contrast, exposure to COVID-19 vaccination during pregnancy was associated with reduced rates of nontraumatic intracranial hemorrhage, hypoxic-ischemic encephalopathy, and neonatal mortality. The observed reduction in risk may reflect residual confounding rather than an actual protective effect of vaccination. However, these findings may provide reassurance to public health authorities, clinicians, pregnant individuals, and their families that infants are not at higher risk of adverse events due to COVID-19 vaccination during pregnancy."
"This study had findings concordant with smaller studies and had the advantage of evaluating specific neonatal diagnoses that were selected a priori as having biologically plausible links to COVID-19 vaccination. It also included information on BMI in pregnant individuals, a potentially important confounder.[sup]
20[/sup][sup],
21[/sup] A parallel study of 142 006 singleton infants (85 670 exposed) born in Ontario, Canada, found that infants of individuals vaccinated against COVID-19 during pregnancy had significantly lower risk of neonatal death than those born to unvaccinated individuals.[sup]
12[/sup] The Canadian study also reported that infants of vaccinated individuals had lower risk of severe neonatal morbidity, defined as a composite consisting of 7 neonatal procedures and 15 different diagnoses, including gestational age and birth weight.[sup]
12[/sup] Accordingly, the selective contributions of pregnancy outcomes and specific neonatal outcomes to the association with vaccination in pregnancy were unresolved."
"Thrombosis with thrombocytopenia and brain bleeding have been reported as rare but potentially fatal complications to COVID-19 vaccination. However, these adverse events have only been seen in association with use of adenovirus vector vaccines, which were not recommended or used in pregnancy in Sweden and Norway.[sup]
3[/sup][sup],
4,
19[/sup][sup],
22[/sup] The results of the current study were overall reassuring, with no indication of increased risks for cerebrovascular conditions in newborn infants after COVID-19 vaccination in pregnancy with mRNA vaccines. In addition, the present data do not suggest an increased risk of hypoxic-ischemic encephalopathy after vaccination during pregnancy, confirming previous findings from a smaller study."
"Pericarditis/myocarditis has been highlighted as a potential adverse effect of mRNA COVID-19 vaccines in young people, particularly in boys.[sup]
3[/sup][sup],
4,
19[/sup][sup],
23[/sup] Reassuringly and irrespective of mRNA vaccine manufacturer or trimester of administration, there were no cases of neonatal myocarditis among infants after maternal vaccination during pregnancy. In addition, no indications of an increased risk for other inflammatory neonatal diseases, such as respiratory distress syndrome or necrotizing enterocolitis, were observed."
"It is unlikely that mRNA COVID-19 vaccination during pregnancy directly reduces neonatal mortality, although others have suggested that such a protective effect is biologically plausible.[sup]
12[/sup] The vaccine does not seem to pass the placenta or induce placental inflammation, and could not be traced in cord blood.[sup]
25[/sup][sup],
26[/sup] The current study’s results could not elucidate the mechanisms that explain why infants of vaccinated individuals had lower risks of some outcomes including mortality. Unmeasured confounding due to vaccinated individuals being healthier may have contributed to the lower neonatal morbidity and mortality associated with COVID-19 vaccination during pregnancy."
Neonatal Outcomes After COVID-19 Vaccination in Pregnancy | Vaccination | JAMA | JAMA Network
"Conclusions
In this large population-based study, vaccination of pregnant individuals with mRNA COVID-19 vaccines was not associated with increased risks of neonatal adverse events in their infants."
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What's very interesting in that study is the mention of the mother's health, such as lifestyle factors, Body Mass Index was mentioned, fetal gestation period, etc.
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And yet another more recent study.
"Results
The findings indicated that vaccination against COVID-19 in pregnant women significantly increased the risk of neonatal jaundice (
P < 0.05). Conversely, the miscarriage rate among these women was significantly lower (
P < 0.05). No adverse outcomes were observed including hypertensive disorders, gestational diabetes, maternal hospitalization, maternal COVID-19 infection, preterm labor, premature rupture of membranes, perinatal mortality, admission to the neonatal intensive care unit, and low birth weight.
Conclusion
The results of this study indicate that the administration of inactivated COVID-19 vaccines does not lead to an increase in adverse maternal or neonatal outcomes. Notably, a reduction in miscarriage rates was observed exclusively within the vaccinated group regarding maternal outcomes, while mild neonatal jaundice without NICU admission was reported among neonatal outcomes. To validate these findings, additional studies with larger sample sizes and comparisons of different vaccine types are warranted. Consequently, it appears that COVID-19 vaccination is generally not associated with a significant increase in risks for mothers or newborns. Consistent with other research, these findings underscore the importance of recommending vaccination for pregnant women as a means to mitigate adverse maternal and neonatal outcomes."
https://bmcpregnancychildbirth.biomedce
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I think more of these types of studies should also focus on other factors, such as mother's lifestyle, BMI etc., that may or may not play a part in fetal death.