What About The Data on Efficacy of the Vaccine Against Infection?
While not the primary endpoint of the study, data was presented on the efficacy of the vaccine as defined by comparing the number of cases of Covid-19 occurring more than 7 days after the second dose in the vaccinated group with that of the placebo group. They found an over 90% reduction in risk among the vaccinated group for getting Covid-19 during the study. If you look at the data, you will see 3 cases in the vaccinated and 16 in the placebo. You have to take into account there are more children in the vaccinated arm of the study when comparing risk (1450 vs 736 that completed trial). Based on the size of the study and the alpha value selected, the real reduction may be has high as 98% or as low as 68% (this is your “confidence interval”). If the vaccine is safe, a 68% reduction of risk as a worst case scenario would still be a nice result. Refer to page 60 of the release if hunting to look at these numbers.
As before, if you were curious as to whether the sample size was appropriate for the measurement, it comes down to retrospectively creating expectations since we already know the data. The percentage of children in the placebo control group who became infected with Covid-19 was 2.174% (16 of 736). The percentage of children in the vaccinated group who became infected was 0.2% (3 of 1450). Plugging those numbers into the calculator (two independent study groups, dichotomous endpoint, alpha of 0.05, and power of 80%, enrollment ratio of 2) shows that you would only require a sample size of 936 (312 placebo and 624 vaccinated). This aspect of the Pfizer trial had significantly more children than required in each group. The sample size selected was therefore sufficiently selected for its purpose.
What Study Size Would I Use to Assess Halving the Rates of Hospitalizations and Deaths?
As aforementioned, hospitalizations and deaths in children are far rarer occurrences, and therefore will require larger studies to demonstrate. How large? While in some ways a masochist, I had zero desire to do these calculations long hand. Again, here is the link to the online calculator used to arrive at the numbers to be presented. For these calculations, select the “One study group” option with “Dichotomous” endpoints. I used the 0.05 alpha level and 80% power. Again feel free to mess around with these as it pertains to your comfort level.
Without further ado, let’s run some numbers to get a grasp of how large a sample size is required to assess rates of hospitalization. At present there have been roughly 70,000 hospitalizations of children due to Covid-19. There are roughly 75 million children in the country. Using those numbers, 0.093% of children in this country have been hospitalized due to Covid-19. To run a necessary sample size, we need to make an estimate of how well we expect the vaccine to work. If for example, we anticipate that it will only protect against half the infections (i.e.: 0.0465% of vaccinated children would still become infected with Covid-19), a trial of 28,056 children is required. If, however, we anticipate it to work as it has in other age bands, anticipating a 90% reduction in cases (0.0093%) may be a better number to plug in. In that case, only 6,753 children need to be enrolled to assess whether the vaccine worked as expected. In a nutshell, the better you expect the vaccine to work, the smaller the trial needed to assess, but this study is not of sufficient size to assess the endpoint of hospitalizations.
To assess vaccine efficacy at preventing death in children would, by extension of what we saw above, require far larger studies still. Using similar anticipated benefits, if only a 50% reduction in risk of death is expected, just over three million children would need to be enrolled in the study. This is clearly not a realistic study to conduct. That number remains unreasonable for a trial even at 90% anticipated benefit in risk reduction as that would still require 720,000 children be enrolled.
What Study Size Would I Use to Assess Ensuring Myocarditis is Not Occurring More Frequently Among The Youngin’s?
As the young children are not at high inherent risk from infection, it is critical to ensure their risk reward ratio remains favorable to take the vaccine when accounting for side effects. Using similar strategy as before, let’s apply our “plugging and chugging” skills as it pertains to assessing for side effects.
Since myocarditis was the most concerning of the side effects noted to date in the adolescent population, we will perform some sample calculations to decide how large a study would be needed to ensure we are not increasing the risk in the younger population as we compare them with the adolescents. You can then use this same strategy to go have fun with any side effect that is of concern to you as you calculate your own levels of tolerance. For these calculations, use the “One study group” design with “dichotomous” endpoint (I left the alpha at 0.05 and power at 80%).
Currently about 1 in 50,000 adolescents develop myocarditis after receiving the Pfizer vaccine. That is 0.002% of the vaccinated population. If one wants to ensure that that rate is less than 1 in 25,000 children (i.e.: more frequent than adolescents by a factor of 2), one would need to enroll 496,173 children in the study. If one wanted to ensure that the rate was less than 1 in 10,000 (i.e.: more frequent than adolescents by a factor of 5), one needs to enroll a more manageable 46,123 children to address the concern.
Working backwards, if you wanted to know what the current study was able to detect based on its size, the answer is a 1 in 1428 risk of myocarditis (or 0.07% of children receiving the vaccine). While Pfizer trial reported no cases of myocarditis among the 5 to 11 year children, it was not designed to assess for this outcome.