S6 Ep. 3: One in ten, part 3 (Statistics)

Deep Breaths

Today, we share our third discussion in our four part series about statistics with Dr Shannon Morrison.
In this episode, we discuss the following topics:

• sensitivity and specificity
• positive predictive values (PPV) and negative predictive values (NPV)
• risk ratios
• odds ratios
• number needed to treat (NNT) and number needed to harm (NNH)

And here are the calculations for Shannon's working example of sensitivity, specificity, PPV and NPV (looking at diagnostic tests for the covid-19 pandemic):
Part 1 - PCR tests for Covid-19 (2020):
Let’s say that the prevalence of COVID was 1 in 100,000 people. PCR testing has (roughly) sensitivity of 90% and specificity of 99%.
That means, if you took 1,000,000 people and did a PCR test for COVID:

• 10 people actually had COVID
• 9 of those 10 people would test positive (sensitivity 90%) - and that means 1 of those 10 people would test negative
• 999,990 people did not have COVID
• 989,990 of those people would correctly test negative (sensitivity 99%)
• So that means 10,000 people would incorrectly test positive

From those numbers:
10,009 people tested positive
9/10,009 correctly tested positive - so the PPV is 0.09%
And:
989991 people tested negative
989990/989991 correctly tested negative - so the NPV is 99.99%
Part 2 - PCR tests for Covid-19 (2022):

Now let’s say that 1 in 100 people have COVID. Let’s say we do a PCR test on one million people again.
Now:

• 10,000 people have COVID, and 9,000 of them test positive (so 1,000 of them test negative)
• 990,000 people do not have COVID - 980,100 of them test negative (and 9,900 test positive)
• PPV = 9000/(9000+9900) = 47.6%
• NPV = 99.89%

The test hasn’t changed - but now if you get a positive result, there is a 47.6% chance of it being true.
So for the same test: as the prevalence increases, the PPV increases (0.09% ⇒ 47.6%) and the NPV decreases (99.99% → 99.89%).
Part 3 - RAT tests for Covid-19:
Let’s just accept an overall sensitivity of 60% and specificity of 99%.
We’re going to test a million people again.
10,000 people have COVID
6000 will correctly test positive (sensitivity 60%)
That means 4000 incorrectly test negative
990,000 people do not have COVID
980,100 of them will correctly test negative (99% specificity)
9,900 will incorrectly test positive
As the sensitivity decreases, the number of false positives don’t change, but the number of false negatives increases - in this case, from 1000 to 4000.
And (you can take my word for this one!) - as the specificity decreases, the number of false negatives doesn’t change but the number of false positives increases.
Resources for today's episode:
Zedstatistics (youtube channel) - short videos explaining various concepts in statistics from an Australian Statistician
Johns Hopkins Coursera Short Course - Biostatistics in Public Health (this course has free enrolment and takes approx 4 months to complete - it commenced on January 30th)
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