To treat or not to treat

Probability Level pending

Pancreatic Cancer is a rare, but lethal type of cancer. On an average, 12 in 100,000 people get affected by the disease and over 90% of the affected people die within 5 years.

A new radical treatment has been developed to treat pancreatic cancer. However, it has serious side effects and should therefore be administered only when the probability of the patient having pancreatic cancer is greater than 90%.

The current diagnostic test is 99% reliable. (i.e., the result is correct 99% of the time).

Should a more reliable test be designed to meet the requirements of the treatment? Answer 99000 if a new test is NOT required. If a new test with a minimum reliability of p % p\% is required, type your answer as ⌊ 1000 p ⌋ \lfloor 1000p\rfloor .

Disclaimer : The figures quoted are just for the mathematics involved and they may be far from reality.


The answer is 99998.

Janardhanan Sivaramakrishnan by Janardhanan Sivaramakris… , 42

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Let e e denote the incidence of the cancer and r r denote the reliability of the diagnostic test.

Chances of a person being sick and being diagnosed as sick = e r er .

Chances of a person being normal, but being diagnosed as sick = ( 1 − e ) ( 1 − r ) (1-e)(1-r) .

We want,

e r ≥ 9 ( 1 − e ) ( 1 − r ) er \ge 9(1-e)(1-r)

This gives,

r > ( 1 − e ) ( 1 − 8 9 e ) r > \frac{(1-e)}{(1-\frac{8}{9}e)}

Substituting e = 12 100000 e=\frac{12}{100000} , we would have r > 0.999987 ⟹ p > 99.9987 % r>0.999987\implies p>99.9987\% .

Thus the required answer would be ⌊ p ∗ 1000 ⌋ = 99998 \lfloor p*1000\rfloor=\boxed{99998}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...