Data and Methods
Ip, et al., (“Ip”) conducted a longitudinal study of health records from 45.7 million adults in England [
1]. These researchers studied various indicators for cardiovascular health for the first 26 weeks after vaccination. In comparison to the unvaccinated, the AstraZeneca ChadOx1 COVID-19 vaccine (“AstraZeneca Product”) posed a statistically significant hazard for intracranial venous thrombosis and thrombocytopenia. The mRNA vaccines, including the Pfizer-BioNTech BNT162b2 COVID-19 mRNA product (“Pfizer Product”) were statistically significant for myocarditis and pericarditis. The authors state that “[t]hese findings support the wide uptake of future COVID-19 vaccination programs” and “[t]his England-wide study offers reassurance regarding the cardiovascular safety of COVID-19 vaccines … [w]e hope this evidence addresses public concerns, supporting continued trust and participation in vaccination programs and adherence to public health guidelines.”
Whiteley, et al., (“Whiteley”) was an earlier publication by largely the same research group that published Ip [
2]. Whiteley conducted a similar analysis utilizing the same data, however limiting outcomes to the first 28 days post vaccination, with similar outcomes. Whiteley did address mortality, which Ip subsequently and inexplicably omitted.
By comparison, Horne et al. (“Horne”), with 7.6 million subjects [
3], Parker et al. (“Parker”), with 427,000 subjects [
4], and Hulme et al. (“Hulme”) with 2.7 million, all assessed mortality between the AstraZeneca Product and the Pfizer Product [
5].
Ip conducted a longitudinal study of health records from 45.7 million adults in England between December 2020 and January 2022 [
1].
Supplementary Tables S8–S10 include hazard ratios that were fully adjusted (“for a wide range of comorbidities, age, sex, and prior COVID-19”) and 95% confidence intervals for 13 classifications of cardiovascular, arterial, and venous thrombotic events in six time windows (week 1, week 2, weeks 3-4, weeks 5-12, weeks 13-24, and weeks 25-26) since first dose vaccination with the AstraZeneca Product, Pfizer Product, and the Moderna mRNA-1273 (“Moderna Product”) respectively.
Whiteley previously had analyzed 13 vascular events in addition to lower limb fracture and death.
Tables S4 and S5 contain hazard ratios for the AstraZeneca Product and Pfizer Product respectively [
2]. Sub-groupings include younger than 70 years old and greater or equal to 70 years old; and events that occur in the first 28 days and after 28 days.
Horne compared eligible adult recipients of two doses of the Pfizer Product (n=1,951,866) or the AstraZeneca Product (n=3,219,349) with the unvaccinated (n=2,422,980) [
3]. Supplemental
Table S7 compares the adjusted non-COVID-19 death hazard ratio of the Pfizer Product vs. the AstraZeneca Product.
Parker compared two-dose AstraZeneca Product (n=257,580) recipients and two-dose Pfizer Product (n=169,205) recipients cohort analysis, additionally 130,765 are matched for analysis [
4]. Supplemental
Table S8 includes an AstraZeneca Product vs. Pfizer Product hazard ratio for non-COVID-19 death.
Hulme analyzed 1,406,637 individuals vaccinated with the Pfizer Product and 1,249,425 individuals vaccinated with the AstraZeneca Product. Supplemental
Table S2 shows the hazard ratios of death in seven different time windows in the first 70 days after first dose [
5].
Ratio of Hazard Ratios
Logarithm parameters μ and σ are used in the equations for hazard ratio (HR) and 95% confidence interval CI.
The Ip et al. article does not make available μ or σ, as such we derive them from the stated hazard ratios.
For example from Ip, et al., the week 1 arterial composite for AstraZeneca aHR is 0.84 (0.80,0.87) and for Pfizer is 0.73 (0.69,0.76). Using Equation 1 we can calculate mu as the natural log of the stated hazard ratios (AstraZeneca: μ = -0.174, and Pfizer: μ = -0.315).
Because the confidence intervals are rounded to two significant figures, we subtract 0.005 from the lower bound and add 0.005 to the upper bound to evaluate the maximum possible 3-significant figure confidence interval to extrapolate σ. With each end of the 95% confidence interval, we solve for σ and use the maximum value, allowing again for the greatest possible interpretation of error (AstraZeneca σ =max(0.0281, 0.0208), and Pfizer σ=max(0.032, 0.0239)).
The ratio of two independent logarithmic normal distributions is itself a logarithmic normal distribution. The ratio of hazard ratios (RHR) for two hazard ratios (a and b) and corresponding ratio of confidence intervals (RCI) are represented here:
Ratio of hazard ratios in data science is a secondary analysis, used when one does not have access to the primary data. Pursuant to the data availability statement, on the day of publication of Ip, Jablonowski contacted the British Heart Foundation Data Science Centre requesting the data utilized. As of this writing, they have not responded to the request.
The original study authors presented their hazard ratios and confidence intervals to only two decimal places. Secondary analysis of such low precision reporting is limited, and must consider the widest possible confidence interval. We lowered the reported lower confidence interval by 0.005 and raised the upper confidence interval by the same value to assess the largest possible interval pre-rounding. We solve for σ from both upper and lower intervals, and only entertain the maximum value of σ.
Accordingly, we can calculate the ratio of hazard ratios (AstraZeneca/Pfizer) by Equation 3 exp(μ[AstraZeneca]-μ[Pfizer]) yielding 1.151. The confidence interval may then be calculated by Equation 4 yielding (1.058, 1.252). A statistically significant ratio of hazard ratios showing AstraZeneca is positively associated with arterial composite disease.