Colorectal screening with FIT, by the numbers

Written and reviewed by a practicing emergency physician · Updated August 2026

A fecal immunochemical test costs a few dollars, arrives in the mail, and asks for nothing but a sample and a stamp. It is also, by the arithmetic below, wrong about eleven times out of twelve when it raises an alarm. Both facts are true at once, and the interesting thing about FIT is that the second fact barely matters — because of what the test is for. FIT is the cleanest example in common use of a triage test: a cheap, repeatable first pass whose job is not to diagnose cancer but to decide who needs the expensive, definitive look.

Three numbers, and where they come from

• Sensitivity ≈ 79% — of people who truly have colorectal cancer, about 79 in 100 have a positive FIT on a single round. A meta-analysis of nineteen studies by Lee and colleagues puts the pooled figure at 79%, with individual studies ranging widely around it.
• Specificity ≈ 94% — about 94 of every 100 people without cancer are correctly cleared; roughly 6 in 100 are flagged anyway, most often from bleeding that has nothing to do with cancer.
• Prevalence ≈ 0.7% — in the large screening study by Imperiale and colleagues, 65 of 9,989 average-risk adults undergoing screening colonoscopy — about 0.7% — turned out to have colorectal cancer. That is the base rate a first screening round faces.

The same head-to-head study is a useful cross-check on the meta-analysis: in it, FIT ran at 73.8% sensitivity and 94.9% specificity for cancer — a little lower on both counts than the pooled figures, and close enough that the story below doesn't change whichever pair you use.

The 2×2, worked by hand

Send FIT kits to 1,000 average-risk adults and have every one returned. First split the population by the truth: 1,000 × 0.007 = 7 people with colorectal cancer, and 993 without.

Now apply the test. Of the 7 with cancer, 7 × 0.79 ≈ 6 are flagged (true positives) and about 1 is missed this round (a false negative). Of the 993 without cancer, 993 × 0.06 ≈ 60 are flagged anyway (false positives) and about 933 are correctly cleared (true negatives).

Follow the positive column. About 66 people get a letter saying their test was abnormal, and only about 6 of them have cancer. The positive predictive value:

PPV = (0.79 × 0.007) ÷ [(0.79 × 0.007) + (0.06 × 0.993)] = 0.00553 ÷ 0.06511 ≈ 0.085 — about 1 in 12.

Computed from exact rates that is 8.5%; dividing the rounded people, 6 ÷ 66, gives 9.1% — the same answer to the precision that matters. Eleven of every twelve positive FITs are false alarms, for the reason every rare-disease screen shares: the cancer-free crowd the false positives come from is more than a hundred times larger than the group with cancer. That mechanism has its own guide.

Why a 1-in-12 positive is fine here

A PPV of 8.5% would be alarming if a positive FIT led straight to surgery. It doesn't. It leads to a colonoscopy — a test that can actually look at the colon, remove what it finds, and settle the question. The whole design leans on that second step: FIT trades away predictive value to stay cheap, easy, and repeatable, precisely because a definitive follow-up exists to absorb its false alarms.

That follow-up is not free, which is where the harm side of the ledger lives. The U.S. Preventive Services Task Force's 2021 evidence review puts serious colonoscopy complications — major bleeding or a perforation — at roughly one per 565 procedures. Run the cascade: of our 66 positives, all are referred for colonoscopy, so a screening round of 1,000 people buys about 66 scopes to find 6 cancers, and roughly one serious complication for every eight or nine such rounds. Whether that trade is worth it is exactly the kind of ledger screening harms and biases teaches you to read — and for colorectal cancer, where removing precursor polyps genuinely prevents disease, guideline bodies have consistently judged that it is: the USPSTF recommends screening from age 45 to 75 (Grade A for ages 50–75, Grade B for 45–49).

A negative is genuinely reassuring — this round

Now the negative column. 934 people are cleared, and 933 of them are truly cancer-free — a negative predictive value above 99.8%. Before the test, a person's chance of harboring colorectal cancer was 0.7%; after a negative FIT it is about 0.16%. In likelihood-ratio terms the test earns its keep in both directions: LR+ = 0.79 ÷ 0.06 ≈ 13, a solidly useful positive, and LR− = 0.21 ÷ 0.94 ≈ 0.22, a real (if not decisive) push toward health. How those ratios move a probability is its own guide.

The catch is the phrase this round. One in five cancers slips past a single FIT, which is why the programs that use it repeat it every year. Repetition patches the sensitivity problem — a cancer missed this year gets another chance to bleed next year — but it compounds the false-alarm problem: at 94% specificity, ten annual rounds give a person nearly a one-in-two chance of at least one false positive along the way (1 − 0.94¹⁰ ≈ 46%, an idealized upper bound that assumes each round errs independently). That accumulation, and what the real-world data show it does, is worked through in repeated screening and false positives.

The test you return beats the test you don't

One more number decides more than any of the others, and it never appears in an accuracy table: the fraction of people who actually do the test. A colonoscopy-first strategy has higher single-shot sensitivity, but it asks for a day off work, a bowel prep, and sedation; mailed FIT asks for almost nothing. In the Imperiale study the newer multitarget stool-DNA test beat FIT on sensitivity (92.3% versus 73.8%) at the cost of specificity (86.6% versus 94.9%) — and every such comparison is moot for the person who returns neither kit. The calculator's uptake slider exists for exactly this reason: set it below 100% and watch missed cancers pile up in the "never tested" column no matter how good the test is. A mediocre test completed reliably outperforms an excellent test skipped.

What generalizes

FIT is the friendly extreme of the screening map: a test whose low positive predictive value is a design choice rather than a flaw, because a definitive, therapeutic follow-up exists and the test is cheap enough to repeat. Compare it with PSA, where the follow-up is itself contested; with mammography, where the follow-up work-up is the main population-level harm; and with NIPT, where the confirmatory test carries real risk. Same arithmetic every time — what changes is what a positive costs.