Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Bailey’s Reanalysis Fails to Debunk, and Inadvertently Supports, Miller-Goldman’s Positive Correlation between Number of Vaccine Doses and Infant Mortality Rates

Version 1 : Received: 15 June 2022 / Approved: 16 June 2022 / Online: 16 June 2022 (11:00:46 CEST)

A peer-reviewed article of this Preprint also exists.

Goldman, G.S.; Miller, N.Z. Reaffirming a Positive Correlation Between Number of Vaccine Doses and Infant Mortality Rates: A Response to Critics. Cureus 2023, doi:10.7759/cureus.34566. Goldman, G.S.; Miller, N.Z. Reaffirming a Positive Correlation Between Number of Vaccine Doses and Infant Mortality Rates: A Response to Critics. Cureus 2023, doi:10.7759/cureus.34566.


Background—In 2011, Miller and Goldman published a study in Human and Experimental Toxicology that found a counterintuitive, positive correlation, r = 0.70 (r2 = 0.49, p < .0001), demonstrating that as nations require more vaccine doses for their infants, infant mortality rates (IMRs) tend to increase (worsen). The dataset (n = 30) included the United States, a nation that required the most vaccines for their infants, and all nations with better IMRs than the United States. Dr. E. Bailey, a professor at BYU, and her students, recently read the Miller-Goldman study and found it "troublesome that this manuscript is in the top 5% of all research outputs" and falsely claimed that its findings were due to "inappropriate data exclusion," i.e., failure to analyze the "full dataset" of all 185 nations. The "Bailey reanalysis," titled Infant vaccination does not predict increased infant mortality rate: correcting past misinformation, was posted to the medRxiv preprint server on September 10, 2021 (version 1) and October 5, 2021 (version 3) and Europe PMC preprint server on September 10, 2021. Objective—This present study examines the various claims postulated by the Bailey reanalysis and assesses the robustness of their methodology, analyses, and reported results and conclusions. Methods—Data discussed in this paper are based on the previously mentioned study by Miller and Goldman and the Bailey reanalysis. Results—Linear regression analysis of IMR and the number of vaccine doses for each country yield a statistically significant positive correlation of r = 0.70 (p < .0001) for the top nations (n = 30) chosen by Miller-Goldman and r = 0.16 (p < .04) for the "entire dataset" chosen by Bailey et al (n = 185). Bailey also conducted linear regression analyses (for the year 2019) of IMRs as a function of vaccination rates for each of eight different vaccines and reported statistically significant inverse correlations for 7 of 8 vaccines over the entire range of vaccination rates. However, Miller and Goldman reanalyzed the Bailey analyses for nations with vaccination rates below 60% and found no statistically significant correlation for six vaccines (DPT, Hib, hepatitis B, polio, rotavirus, and measles) and statistically significant positive correlations for tuberculosis (r = 0.8, p < .005) and pneumococcal (r = 0.6 p < .023) vaccines. Conclusions—Bailey’s reanalysis corroborates a statistically significant positive correlation originally reported by Miller and Goldman. However, Bailey’s reported correlation (r = +0.16, p < .04) is small, likely due to poor methodology (failing to account for covariates, i.e., disparities among numerous socioeconomic factors that add uncertainty to their conclusion). The r-value reported by the Bailey reanalysis demonstrates an effect size that is about one-fourth (0.16/0.70) that reported by Miller-Goldman—underscoring how critically important it is for Bailey's reanalysis to eliminate confounding variables. Moreover, Bailey’s linear regression analyses of IMR as a function of vaccination rates for each of eight different vaccines demonstrate that some countries with low vaccination rates have low IMRs, while other countries with high vaccination rates have high IMRs. Rather than supporting a strong inverse correlation, the Bailey reanalysis demonstrates high vaccination rates are neither necessary nor sufficient to cause low IMR.


artifacts; confounders; infant mortality rate; linear regression analysis; vaccination rates; vaccines; vaccine doses; hepatitis B vaccine


Biology and Life Sciences, Immunology and Microbiology

Comments (2)

Comment 1
Received: 17 May 2023
Commenter: John Calvin Jones, PhD
The commenter has declared there is no conflict of interests.
Comment: I oppose all vax, but Mssrs Miller and Goldman had many methodological problems. First, they do NOT have 30 data points in their regression. They collapsed the 30, into 5 categories, and averaged the IMF - with equal weights (ignoring the populations of individual nations)! Thus they created artifacts at TWO levels. Further, recommended shots are NOT administered shots. Lastly, the CIA factbook estimates of national IMF are erroneous. In statistical terms, the coefficients in their model are not valid. In social scientific terms, they knowingly omitted the most important factors for IMF - namely health and wealth of the mother, and access to clean water.
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Response 1 to Comment 1
Received: 19 May 2023
Commenter: (Click to see Publons profile: )
The commenter has declared there is no conflict of interests.
Comment: Mr. Jones communicated these same concerns nearly 10 years ago. We previously responded to these concerns to the satisfaction of journal editors who rejected his analysis. Our linear regression analysis DOES contain 30 data points and the positive correlation, r = 0.70 (p < .0001), demonstrated that among the most highly developed nations, those that require more vaccine doses for their infants tend to have higher infant mortality rates (IMRs).

Regarding the weighing of IMRs, presently 14 nations have populations greater than 100 million, 81 have populations greater than 10 million. If IMRs were to be weighted by the population of each nation, then any analysis of IMRs would be biased by the unusually large weight due to the populations of just two countries: India and China, each having a population of approximately 1.4 billion people and representing approximately 35% (2.8 billion/8 billion) of the world’s population. Miller and Goldman's un-weighted analysis was the most appropriate because why should the IMR of, for example, Iceland with a 0.39 million population be any less significant than the IMR of China with a 1,420 million population. When averaging the IMRs of these two nations, a weighted IMR would simply represent China (and not Iceland) since China’s population is >3,600 times that of Iceland. Likewise, a weighted analysis would mask any potential effect or influence that vaccines might have on IMR--especially among less populated nations that tend to have the best (lowest) IMRs.
Regarding recommended shots versus administered shots, most of the nations in our study had vaccine coverage rates of 90%–99% for the most commonly recommended vaccines. This was mentioned in our paper.

There is no evidence that CIA IMRs are not credible. They were specified to two decimal digits, unlike UNICEF estimates which were rounded to the nearest whole numbers.

By utilizing the more highly developed nations in the analysis, the reasonably good health and wealth of the mother and sufficient access to clean water are essentially a given. This allows for focusing on the effect of number of vaccinations on IMR in the relative absence of large discrepancies in socioeconomic factors.

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