Risk and Screening.
Hi. I'm Dr Nic
and I'm going to tell you about risk,
particularly applied to screening.
Risk is another word for probability but with a bad outcome.
We tend to say, "the risk of getting caught..."
or, "the risk of getting a disease..."
but we don't usually say, "the risk of winning a million dollars..."
Risk is important to understand
when we consider screening tests for diseases.
Because the screening tests are not totally accurate,
we need to know what the chances are of different outcomes.
We will use an imaginary disease for this video,
but the principles apply to all sorts of screening,
including cancer, infectious diseases,
mental illness, lie detection
and recruitment decisions.
"Earpox" is a hypothetical disease that affects a small percentage
of the population,
namely, 2.5%.
The proportion affected is called "prevalence".
If earpox is caught in the early stages,
before there are any visible signs,
it can be treated and cured by applying a therapeutic tattoo.
Left untreated, earpox causes loss of the external ear.
The screening test for earpox is fairly accurate.
It correctly diagnoses 88% of all cases of earpox.
The value, 88%, is called the sensitivity.
However, the earpox screening test also indicates the presence of earpox
in 8% of people who don't actually have it.
This means that 92% of people who don't have earpox
will be correctly identified.
This value, 92%,
is called the specificity.
There are four different outcomes in this instance.
A person can have earpox.
The test identifies that they do have earpox,
they can choose to be treated and cured.
A person can earpox,
the test does not identify that they have earpox,
they are not treated,
and suffer the effects of earpox.
This is called a false negative.
A person does not have earpox,
and the test correctly identifies that they do not have earpox.
A person does not have earpox,
and the test incorrectly indicates that they do have earpox,
and they are treated unnecessarily.
This is called a false positive.
We will show this scenario first as an icon diagram,
and then as a table.
We want to know,
what are the probabilities of each of the four possible outcomes.
We also want to know what the relative probabilities are,
such as the probability of not having earpox,
even though the test indicates that we do.
It is easy to underestimate the number of false positives.
Icon diagram or spot chart.
This diagram represents 1000 people as spots.
Of the 1000,
2.5%-- or 25--
have earpox.
We show these 25 people with earpox
as yellow spots.
People without earpox,
are shown as green spots.
We screen all 1000 people.
The screening test correctly identifies 88% of the 25 cases,
so there are 22 people who are identified, treated and cured.
A blue border
indicates that the person gets a positive result
from the screening test.
There are 3 people with earpox who are not detected,
and their earpox becomes incurable.
The screening test also falsely detects earpox
in 8% of the 975 people who do not have earpox.
That is 78 people!
These people are shown as green dots with blue borders.
The other 897 people are fine--
they do not have earpox,
and the test has indicated that,
so they are not treated.
So altogether,
78 + 22-- which equals 100 people--
are indicated as having earpox.
Phoebe is told her test result is positive for earpox.
What is the probability that she is actually okay
and does not need to be treated?
There are 78 out of 100 people who have tested positive
but are okay.
That means that there is a 78% chance that Phoebe is okay
and does not need to be treated.
However, the test shows that she does need to be treated
and she may choose to have therapeutic tattoos unnecessarily.
For many diseases, the prevalence in the population is quite low,
which means that the number of false positives
may be considerably greater than correct positives,
even with a good test.
This scenario can also be shown as figures on a table.
The trick to creating one of these tables
is always to make the rows what is the reality,
and the columns, the test result.
I find it helpful to indicate
which are the correct results
with little ticks.
We choose a number for the total number of people.
In this case, 1000 is a good number to use
as it avoids having fractional values in the table.
Next we work out what proportion of people will and won't have the disease
from the prevalence data.
2.5% of 1000 is 25.
Everyone else does not have earpox.
Now we look at the sensitivity of the test
which is 88%.
88% of the 25 people who do have earpox
will be correctly identified as having earpox.
88% of 25 is 22.
25 minus 22 equals 3.
Three people who do have earpox
will not be correctly identified.
They will have a false negative result.
Next we look at the specificity of the test which is 92%.
92% of the 975 people who do not have earpox
will be correctly identified as not having earpox.
92% times 975 equals 897 people.
This leaves 975 minus 897--
which equals 78 people--
who do not have earpox,
but whom the test identified as having earpox.
We add up the columns to complete the table.
This table is then used to answer questions such as:
What proportion of people who are screened
receive a positive result--
meaning that the test says that they have the disease?
We can see that this is 100 divided by 1000, or 10%.
Looking at those who are tested positive,
the probability of actually having earpox
is 22 out of 100, or 22%.
Answer the following questions using the table.
The answers will be given after the credits.
1. What is the probability that a given person who is screened
gets a negative result--
that is, that the test does not say that they have earpox?
and 2. If the test says they do not have earpox,
what is the probability that they really do?
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