Chapter 8 – Theoretical Biophysics  387

January 2021, it was estimated that up to 1 in 40 people in England was infected with

COVID-​19, while by February 2021 this estimate was more like 1 in 115. If this LFT was used

by someone in England, what is the probability that if they appeared to test positive on the

LFT then they actually were infected with COVID-​19

a At the height of the pandemic?

b A month later?

c Comment on these results.

Answers

This question is all about using the principle of Bayes theorem in that the probability

of an event occurring, more fully known as the posterior probability, is determined not

only by the general likelihood of the event happening but also by the probability of

one or more other events also having occurred (known at the prior probabilities, or

priors). In this case, the posterior is the probability that the LFT gives a positive result

given the prior occurrence that the person is actually infected by COVID-​19.

a If, for simplicity, we consider 100,000 people, then at the height of the pandemic, 1

in 40 is equivalent to 2500 people infected with COVID-​19, so the remaining 97,500

are not infected. But if the LFT sensitivity and specificity are 85% and 99%, respect­

ively, this means that 85% of the 2500 (i.e. 1955 people) and 1% of the 97,500 (i.e.

975 people) would expect to have a positive LFT results (or 2930 people in total)

of whom 2500 would actually have a COVID-​19 infection. So, using Bayes theorem,

the posterior probability of someone with a positive LFT who also is infected with

COVID-​19 is 2,500/​2,930 or ~85%.

b By a similar argument, 1 in 115 people is 870 people out of 100,000 infected with

COVID-​19, while 99,200 people are not; 85% of the 870 (i.e. 740 people) and 1% of

the 99,200 (i.e. 992 people) would expect to have a positive LFT results (or 1732

people in total) of whom 740 would actually have a COVID-​19 infection. So, the

probably of someone with a positive LFT having COVID-​19 is 2740/​1732 or ~42%.

c When the community level of COVID-​19 infection is relatively high, the LFT shows

reasonably high probability of given a true positive result—​it is accurate and reli­

able. However, once community infection levels of COVID-​19 are significantly

lower, the true positive level may reach a stage of being potentially unreliable

(e.g. <50%). This is an example of the base rate paradox in Bayesian analysis: even

though most LFTs are in themselves very sensitive and specific, if the probability

of someone having COVID-​19 is small then false-​positives will make up most of

the positive LFT results. Note, these estimates were predicated using only indi­

cative sensitivity and specificity levels reported during the pandemic in the UK,

and the answers to the questions above will vary widely depending on the actual

values used. For example, sensitivity and specificity levels measured for LFTs from

different studies taken from a systematic review published in August 2021 ranged

from 37.7–​99.2%, whereas the specificity ranged from 92.4–​100% (Misty et al.,

2021).

8.7  SUMMARY POINTS

◾Molecular simulations use Newton’s second law of motion with varying degrees

of approximations of atomic energy potentials to predict the motions of atoms

as a function of time over a scale from hundreds of picoseconds for ab initio QM

simulations to tens of nanoseconds for classical MD and tens of microseconds for

CG approaches.