Jason Shafrin, the Healthcare Economist, has a nice post explaining how a statistical illusion can make early screening for disease appear much more effective than it really is.
Here is an example using the dreaded disease economicitis. Let us
divide people into 3 groups.
- Healthy: You live forever.
- 1st stage economicitis is asymptomatic. Life
expectancy when 1st stage economicitis begins is 10 years. One half of
economicisits cases are 1st stage.
- 2nd stage economicitis appears when individuals
mysteriously grow a third or possibly fourth hand. Life expectancy with second
stage economicitis is 2 years. One half of economicitis cases
are 2nd stage.
Before any screening was developed, individuals would learn they had
economicitis when they started growing extra hands. Thus, documented
life expectancy for those with economicitis was 2 years, since all
individuals who were recorded as having economicitis were in the 2nd
Let us assume that a screening technique is now available. If the screening
device is able to detect 100% of stage 1 and stage 2 economicitis
cases, then we will see that life expectancy will increased to 6 years
(10/2+2/2=6). Statisticians looking at the data may claim the following: “The
economicitis screening test has increased life expectancy after
diagnosis from 2 to 6 years!”
This claim, however, is false since there is no effective treatment for
economicitis. The increase in average life expectancy is not due to
any improvement in health care, but only because the relatively healthier
individuals with 1st stage economicitis are now being detected by the
Many years ago, David Plotkin had a article in The Atlantic dealing with this issue and others with respect to breast cancer. The statistics are somewhat out of date but the article remains of real value.