Does better screening lead to improvements in health outcomes? Conventional wisdom holds that this is always true. For instance, catching breast cancer at an early stage greatly improves survival probabilities. However, early screening can lead to a statistical anomaly where better screening appears to improve mortality rates even when treatments are entirely ineffective.
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 stage.
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 test.
Your post completely misses the point. “Statisticians may claim…”, right and I can say “The sky is falling”, but would it ever be published in a peer reviewed journal?
The real paradox of better screening is the challenge posed by type I vs type II errors. What is the cost of false positives (telling someone they have a disease when they really don’t), and false negatives (letting someone think they’re don’t have the condition when they do).
Why not write something meaningful on a real screening test of questionable value like PSA? Like this http://www.jamesgagne.com/PSAParadox.shtml
I don’t understand. Does stage 1 not lead to stage 2? Then if stage 1 is longer, and there’s no cure, how is it possible that half the cases are stage 1 and half stage 2? Should these be “type1” and “type2” instead?