The Efficacy of the Moderna Vaccine¶

Approximate analysis.

False assumptions:

all subjects on trial for the same amount of time
subjects "independent" (e.g., aren't co-workers working in an office, or paramedics riding together in an ambulance)
randomization was not stratified
ignore anybody who was "lost": treat final number as if it were initial number

See the FDA Briefing Document for Moderna at the Vaccines and Related Biological Products Advisory Committee Meeting, December 17, 2020.

In [5]:

import math
import numpy as np
import scipy as sp
from scipy.optimize import brentq  # Brent's root-finding algorithm
# from scipy.stats import binom as sp.binom      # the Binomial distribution
from scipy.special import binom 

In [6]:

N_v, N_u = 13934, 13993  # vaccinated, unvaccinated
x_v, x_u = 11, 185       # infected among vax, unvax
r_v = x_v/N_v            # risk
r_u = x_u/N_u
rr = r_v/r_u

In [7]:

1 - rr

Out[7]:

0.9402887744928795

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