Calculating the odds of undetected colorectal cancer

In a group of 200 adults aged 50 to 75, what are the chances of finding someone with undetected CRC?

Many take chances with their health, in particular CRC screening

Many take chances with their health, in particular CRC screening

The unscreened population for colorectal cancer is large. According to Exact Sciences (the manufacturer of the DNA + FIT test ‘Cologuard’) JP Morgan Healthcare Conference Presentation they estimate 85 Million Americans in the US as average risk and asymptomatic for colorectal cancer from the ages of 50 to 85, with an additional 19 Million ages 45 to 49. This totals 104 Million, almost a third of the population.

Using  67% (the percentage measured in 2017 per Reference 1) as up-to-date with their colorectal cancer screening, 0.33 x 85 Million = 28 Million Americans from the ages of 50 to 85 are not screened. As a Gastrointestinal physician once told me, “the worst conversation to have is to diagnose colorectal cancer in someone, and the first thing you think is ‘You should have seen me ten years ago.’ “

Rates of colorectal cancer incidence on the decline

Seer Statistics for Colorectal Cancer by age group over time

Seer Statistics for Colorectal Cancer by age group over time

The NCI maintains a resource called SEER (Surveillance, Epidemiology and End Results Program)  subtitled “An Authoritative Source for Cancer Statistics in the United States”. The chart above indicates the incidence and trend lines over the past 10 years, and makes the data available.

For example, to reproduce the chart above and access the raw data, here is the link to the variables I selected. For other cancers, for other ages, to select among ethnicities, you can also display by cancer stage. SEER is an extremely informative, and a valuable resource.

There is evidence that this decline is due to greater public awareness; in March of 2000, the television show host Katie Couric broadcast her colonoscopy, raising the rate of colonoscopies in a measurable and sustained manner. (Reference 2) Years later in 2016 she would reflect on her experiences as a cancer screening advocate, specifically for colorectal cancer. (Reference 3)

A geometric distribution math problem

In the 2014 pivotal study for Exact Sciences (Reference 4) out of 9,989 participants 65 (0.7%) had colorectal cancer. Using the same metric of 0.7%, with a given number of people (say 200), what are the odds that a person in that target group (ages 50 to 75, no familial or prior history of cancer) has colorectal cancer?

This is a geometric distribution problem and thanks to a colleague’s Excel skills with the POWER function came up with the following table. This is using a 0.7% probability, and the question is with a group of 100, 150, 200 people what is the chance that one of that group would have at least one person with undiagnosed disease.

Probability table with 0.7% occurance rate

Probability table with 0.7% occurance rate

The answer is 74%

With a group of 200 individuals ages 50-75, the chance of at least one person in that group having cancer is 74%; note that with 300 individuals the chance goes up to 87%, and at 400 it goes up to 93%.

It is something to think about when you put the 28 Million unscreened into that perspective – the risk for colorectal cancer is high, and early detection is a must.


  1. Siegel R.L. and Jemal A. et al 2017 Colorectal Cancer Statistics, 2017. PMID: 28248415
  2. Cram P. and Vijan S. et al Arch Intern Med. 2003 The impact of a celebrity promotional campaign on the use of colon cancer screening: the Katie Couric effect. PMID: 12860585
  3. Couric K. Am J Gastroenterol. 2016 An Unexpected Turn: My Life as a Cancer Advocate. PubMed PMID: 27021192.
  4. Imperiale T.F. and Berger B.M. et al. N Engl J Med. 2014 Multitarget stool DNA testing for colorectal-cancer screening. PMID: 24645800