Reporting System (VAERS) that tracked outcomes in about 200 million individuals, and similar systems are in place in numerous other countries, in particular the United Kingdom and Israel. Using information from this large database, it was quickly recognized that there was a low, but consistent rate of patients presenting with post‐vaccination myocarditis and/or pericarditis. For example, data obtained from VAERS have shown that the incidence peaks in young males of 15–17 years with 105.9 cases per million doses administered and identified the second dose as the highest risk compared to the first dose.

A recent population study investigated the risk for myocarditis in 12–15‐year‐old adolescents after receiving BNT162b2. Data for the incidence of hospitalization for myocarditis between June and October 2021 were collected by the Israeli Ministry of Health (IMoH). The risk estimates of myocarditis after the second dose among male recipients were 8.09 cases/100 000 and among female recipients 0.69 cases/100 000. The risk of myocarditis after receipt of the second vaccine among 12–15‐year‐old male adolescents was estimated to be 1/12 361, but 1/144 439 among female adolescents. 28 ​​​​​​​

The study also noted that the small population size made it less likely to see a “rare event such as sudden cardiac death” among the age group.

Epidemiologic studies often must cope with sparse-data problems due to small sample sizes or to reduction in effective sample size due to the study of very uncommon (or common) exposures1 or highly correlated variables.2 However, determining the presence and impact of sparse data in a given study is not as clear as one might believe. In studies with only a few categorical variables, the researcher may be able to identify the presence of sparse data by observing the sample size within cells of contingency tables.3However, as data become more complex, this approach becomes untenable. In a regression model with a large number of covariates, researchers should be concerned about the potential impact of data sparseness

Male Decedents

Among the 925 male decedents, no death certificate listed vaccination either as the immediate or as a contributing cause of death. Overall, 17 (2%) deaths among males were attributed to COVID-19. Death certificates cited noncardiac causes of death or other conditions contributing to death for 842 (91%) of the male decedents. Among the remaining 66 (7%) male decedents, excluding a cardiac cause of death based on the death certificate was not possible. Among these 66 decedents, IIS vaccination records were available for 58 (88%); receipt of at least one mRNA COVID-19 vaccination was recorded for 24 (41%).

Among the 24 male decedents with an mRNA COVID-19 vaccination record in IIS, two (8%) died within 100 days of having received the vaccine. The first death was recorded as having occurred in a natural manner 21 days after COVID-19 vaccination. The immediate cause of death noted on the death certificate was congestive heart failure attributed to hypertension; other significant conditions included morbid obesity, type 2 diabetes, and obstructive sleep apnea. The second decedent had received a COVID-19 vaccine dose 45 days before the date of death; the cause of death was recorded as “undetermined natural cause.” Toxicology results were negative for alcohol, cannabinoids, methamphetamine, and opiates; aripiprazole, ritalinic acid, and trazodone were detected. Follow-up with the medical examiner could neither confirm nor exclude a vaccine-associated adverse event as a cause of death for this decedent.

About This Calculator

This calculator uses a number of different equations to determine the minimum number of subjects that need to be enrolled in a study in order to have sufficient statistical power to detect a treatment effect.1

Before a study is conducted, investigators need to determine how many subjects should be included. By enrolling too few subjects, a study may not have enough statistical power to detect a difference (type II error). Enrolling too many patients can be unnecessarily costly or time-consuming.

Generally speaking, statistical power is determined by the following variables:

• Baseline Incidence: If an outcome occurs infrequently, many more patients are needed in order to detect a difference.
• Population Variance: The higher the variance (standard deviation), the more patients are needed to demonstrate a difference.
• Treatment Effect Size: If the difference between two treatments is small, more patients will be required to detect a difference.
• Alpha: The probability of a type-I error -- finding a difference when a difference does not exist. Most medical literature uses an alpha cut-off of 5% (0.05) -- indicating a 5% chance that a significant difference is actually due to chance and is not a true difference.
• Beta: The probability of a type-II error -- not detecting a difference when one actually exists. Beta is directly related to study power (Power = 1 - β). Most medical literature uses a beta cut-off of 20% (0.2) -- indicating a 20% chance that a significant difference is missed.