4. The following data are the results from the Pfizer Covid 19 vaccine trials. Placebo (N=21,686) No. of participants Surveillance time Efficacy End-Point Subgroup BNT16262, 30 µg (N=21,669) No. of...

1. 
   

   What is a 90% confidence interval for the proportion of people receiving the first vaccine  becoming infected with Covid 19?

   
   


2. The placebo group consisted of persons not receiving the vaccine. 21686 individuals were in  the placebo group in this trial and 275 were eventually infected by Covid 19. What is the  probability of becoming infected with Covid 19 if you were in the placebo group and not  receiving the Pfizer vaccine? This isP(infected placebo group)
   

Extracted text: 4. The following data are the results from the Pfizer Covid 19 vaccine trials. Placebo (N=21,686) No. of participants Surveillance time Efficacy End-Point Subgroup BNT16262, 30 µg (N=21,669) No. of participants Surveillance time person-yr (no. at risk) person-yr (no. at risk) Covid-19 occurrence After dose 1 After dose 1 to before dose 2 50 4.015 (21,314) 275 82 3.982 (21,258) 39 Dose 2 to 7 days after dose 2 27 Days after dose 2 21 172 a) 21669 individuals were given the vaccine in this trial and 50 were infected after they received the first vaccine. What is the probability of becoming infected with Covid 19 after receiving 1 dose of the Pfizer vaccine? This is P(infected vaccinated group) b) What is a 90% confidence interval for the proportion of people receiving the first vaccine becoming infected with Covid 19? c) The placebo group consisted of persons not receiving the vaccine. 21686 individuals were in the placebo group in this trial and 275 were eventually infected by Covid 19. What is the probability of becoming infected with Covid 19 if you were in the placebo group and not receiving the Pfizer vaccine? This is P(infected placebo group) d) Efficacy is defined as E = (P(infected placebo group)- P(infected vaccinated group)) Use your P(infected placebo group) answers for parts a and c to find the efficacy for a single dose of the Pfizer vaccine. Note the Pfizer vaccine requires 2 doses for maximum efficacy. We do not consider that case here.


Extracted text: 4a) P(infected vaccinated group) = 4b) lower bound for probability =. 4b) upper bound for probability=. 4c) P(infected placebo group)= ( P(infected placebo group)- P(infected vaccinated group) 4d) efficacy for single dose = P(infected placebo group) Efficacy = .