Your Mammogram Came Back Positive: What Are the Odds You Actually Have Cancer?
If you receive a positive mammogram result, there's only around a 1.7% chance that you actually have breast cancer for average-risk women. Learn why this counter-intuitive result happens and what Bayes' Theorem teaches us about medical screening.
Imagine receiving a call from your doctor's office. Your routine mammogram came back abnormal. They need you to come in for additional testing. Your heart races. Your mind immediately jumps to the worst-case scenario. You start googling survival rates and treatment options.
But here's a question most people never think to ask: If your mammogram is positive, what are the actual odds that you have breast cancer?
The answer might surprise you. In fact, it surprises most doctors too. This is where Bayes' Theorem—a mathematical formula for updating beliefs based on new evidence—reveals something deeply counter-intuitive about medical screening.
The Surprising Truth About Positive Mammograms
📊 The Most Important Number in This Article:
If you receive a positive mammogram result, there's only around a 1.7% chance that you actually have breast cancer for average-risk women (though this varies based on individual risk factors).
Read that again. Even with an abnormal mammogram, the probability that you have cancer is somewhere between 1 in 60 and 1 in 15. Put another way, 93% to 98% of positive mammograms are false positives—they look suspicious but turn out to be benign.
This isn't a criticism of mammography. Screening mammograms are highly effective at detecting breast cancer early, with a sensitivity of about 87%, meaning that they catch about 87% of cases.[3] The issue is that most people—including many healthcare providers—don't understand how to interpret a positive result when the underlying disease is relatively rare.
This is a textbook case of base rate neglect, one of the most common errors in probabilistic reasoning. And Bayes' Theorem is the tool that helps us think clearly about it.
Understanding the Numbers
Before we dive into the Bayesian analysis, let's establish the key statistics from authoritative medical sources.
Breast Cancer Prevalence
Breast cancer is the most common cancer among women in the United States. According to the National Cancer Institute's SEER program, approximately 13% of women will be diagnosed with breast cancer at some point during their lifetime.[4] This is often expressed as "1 in 8 women."
⚠️Lifetime Risk vs. Screening Risk
Lifetime risk is very different from the probability of having undetected cancer at any single screening. At a routine mammogram for a 50-year-old woman with no symptoms, the probability of currently having breast cancer is only about 0.2% (2 in 1,000 women).
This low "base rate" or "prior probability" is the key to understanding why positive results are so often false alarms.
Mammogram Accuracy
Screening mammography has well-documented accuracy metrics:
| Metric | Value |
|---|---|
| Sensitivity | 87% – Correctly identifies 87% of women who have cancer[3] |
| Specificity | 89-90% – About 89-90% of women without cancer receive a negative result[2][5] |
| False Positive Rate | 10% – About 10% of mammograms lead to a callback[1][2] |
Important: After 10 annual mammograms, 50-60% of women will experience at least one false positive result.[3] This is not a flaw—it's an inevitable consequence of trying to catch every possible cancer while screening millions of healthy women.
| Screening Outcome | Percentage (per 1,000 women) |
|---|---|
| True Negative (correctly identified as cancer-free) | ~89% (~890) |
| False Positive (incorrectly flagged as suspicious) | ~10% (~100) |
| True Positive (correctly identified as having cancer) | ~0.17% (~1.7) |
| False Negative (cancer missed) | ~0.03% (~0.3) |
The Bayesian Calculation
Now let's use Bayes' Theorem to answer our original question: If a mammogram is positive, what's the probability of actually having cancer?
Bayes' Theorem
P(Cancer | Positive Test) = [P(Positive Test | Cancer) × P(Cancer)] / P(Positive Test)
P(Cancer | Positive Test) = Probability of having cancer given a positive mammogram (what we want to find)
P(Positive Test | Cancer) = Sensitivity = 87% = 0.87
P(Cancer) = Base rate = 0.2% = 0.002
P(Positive Test) = Overall probability of a positive test
Step 1: Calculate P(Positive Test)
The overall probability of a positive test comes from two sources: true positives and false positives.
P(Positive Test) = P(Positive | Cancer) × P(Cancer) + P(Positive | No Cancer) × P(No Cancer)
P(Positive Test) = (0.87 × 0.002) + (0.10 × 0.998)
P(Positive Test) = 0.00174 + 0.0998
P(Positive Test) = 0.10154
About 10.2% of women will receive a positive result.
Step 2: Calculate P(Cancer | Positive)
Now we can calculate the probability of cancer given a positive test:
P(Cancer | Positive) = (0.87 × 0.002) / 0.10154
P(Cancer | Positive) = 0.00174 / 0.10154
P(Cancer | Positive) = 0.0171
P(Cancer | Positive) ≈ 1.7%
🎯 The Answer: Even with a positive mammogram, there's only a 1.7% chance of actually having breast cancer. The other 98.3% of positive results are false alarms.
Why This Happens: The Base Rate Matters
The counter-intuitive result comes from the low base rate of breast cancer at screening. Even though mammography is quite accurate (87% sensitivity), breast cancer is relatively uncommon at any single screening (0.2% prevalence).
Think of it this way: In a group of 1,000 women getting screened:
🔴 2 women actually have breast cancer
→ Mammography will correctly identify about 1.7 of them (87% sensitivity)
🟢 998 women do not have cancer
→ Mammography will incorrectly flag about 100 of them as suspicious (10% false positive rate)
Result: Out of roughly 102 positive results, only 1.7 are true positives
That's where the 1.7% comes from: 1.7 / 102 ≈ 0.017
The false positives vastly outnumber the true positives because there are so many more healthy women than women with cancer in the screening population.
What Happens After a Positive Result?
When a mammogram shows an abnormality, radiologists use the BI-RADS (Breast Imaging Reporting and Data System) scoring system to categorize findings:[1]
| BI-RADS Score | Meaning | Recommended Follow-Up |
|---|---|---|
| 0 | Incomplete/unclear result | Follow-up mammogram within a few weeks |
| 3 | Probably benign | Mammogram in 6 months |
| 4 | Suspicious abnormality | May require breast biopsy |
| 5 | Highly suggestive of cancer | Breast biopsy |
Of the women who are called back for additional testing, only about 7% will ultimately be diagnosed with cancer.[1] The rest—93%—will go through additional imaging, and sometimes biopsies, only to learn that the suspicious finding was benign.
The Psychological Impact
Research shows that false positive results can cause significant anxiety and worry, with some women experiencing these feelings for years afterward.[3]
However, it's important to remember that this is an inherent part of effective screening. The alternative—missing actual cancers—would be far worse.
Does This Mean Mammograms Aren't Worth It?
Absolutely not.
Despite the high false positive rate, mammography remains the gold standard for breast cancer screening. Here's why:
✅ Early detection saves lives
The 5-year relative survival rate for breast cancer is 91.7% overall, but this varies dramatically by stage at diagnosis.[4] Cancers detected early through screening are far more treatable than those found after symptoms appear.
✅ The math still favors screening
Yes, many women will experience the stress of a false positive. But the alternative—not screening and missing early cancers—leads to worse outcomes. The U.S. Preventive Services Task Force recommends that women be screened for breast cancer every other year starting at age 40 and continuing through age 74.[1]
✅ Understanding the statistics empowers better decisions
Knowing that a positive result is most likely a false alarm doesn't mean you should skip follow-up testing. It means you can approach that testing with a more calibrated sense of risk, reducing unnecessary anxiety while still taking the appropriate medical steps.
Who Is at Higher Risk for False Positives?
False positive mammogram results are more common among certain groups:[1][3]
👩 Younger women
Especially those under 50
🔬 Women with dense breasts
Breast density makes it harder to distinguish abnormalities
🩺 Women with previous biopsies
Prior biopsies can create scar tissue
👨👩👧 Family history of breast cancer
Genetic predisposition increases screening sensitivity
If you fall into one of these categories, you're more likely to experience a callback for additional testing. This doesn't mean mammography is less valuable for you—it just means the test characteristics are slightly different, and you should be prepared for the possibility of follow-up.
The Broader Lesson: Base Rates Matter
The mammogram example illustrates a fundamental principle that applies far beyond medical screening: base rates matter enormously when interpreting test results.
This same pattern appears in:
• Drug testing – Most positive drug tests in low-prevalence populations are false positives
• Disease screening – Rare diseases produce many false positives even with accurate tests
• Security screening – Most "suspicious" behaviors flagged by security systems are innocent
• Spam filters – Most emails flagged as spam in low-spam environments are legitimate
Whenever you're evaluating evidence—whether it's a medical test, a news headline, or a personal judgment—ask yourself: What's the base rate? How common is the thing I'm trying to detect? A highly accurate test for a rare condition will still produce mostly false positives.
Conclusion: Think Like a Bayesian
If you receive a positive mammogram, here's what you should remember:
1. Don't panic
The odds are strongly in your favor—there's about a 98% chance it's a false alarm.
2. Do follow up
That remaining 2% is why additional testing exists. Follow-up imaging and, if necessary, a biopsy will provide much more definitive information.
3. Update your beliefs with new evidence
If additional tests also come back suspicious, the probability of cancer increases significantly. Bayes' Theorem isn't just for the initial screening—it applies at every step as you gather more evidence.
4. Keep screening
False positives are an unavoidable part of effective screening. The alternative—missing early cancers—is far worse.
Bayesian reasoning teaches us to think probabilistically, to weigh evidence carefully, and to update our beliefs as new information arrives. In the case of mammography, it reveals that a positive result is far less alarming than most people assume—but still important enough to investigate thoroughly.
The next time you face an uncertain situation with incomplete information, remember the mammogram paradox. Ask yourself: What's the base rate? How accurate is my evidence? And what's the actual probability once I account for both?
That's thinking like a Bayesian.
Share This Post
About the Author
Written by Avi Turetsky. Questions or feedback? Connect with me on LinkedIn.
Medical Disclaimer: The author is not a physician, and this article is for educational purposes only. It should not be taken as medical advice. The information presented here is based on published medical research and statistical analysis, but individual medical decisions should always be made in consultation with qualified healthcare professionals who can consider your personal medical history, risk factors, and circumstances. If you have questions about mammography screening or any medical test results, please consult with your doctor.
References
[1] National Cancer Institute. (2024). "Mammogram False Positives Affect Future Screening Behavior." Cancer Currents Blog. https://www.cancer.gov/news-events/cancer-currents-blog/2024/mammogram-false-positives-affect-future-screening
[2] Breast Cancer Surveillance Consortium. (2017). "Screening Performance Benchmarks: Sensitivity, Specificity, False Negative Rate for Mammography." https://www.bcsc-research.org/statistics/screening-performance-benchmarks
[3] Susan G. Komen Foundation. (2025). "Accuracy of Mammograms." https://www.komen.org/breast-cancer/screening/mammography/accuracy/
[4] National Cancer Institute SEER Program. (2025). "Cancer Stat Facts: Female Breast Cancer." https://seer.cancer.gov/statfacts/html/breast.html
[5] UC Davis Health. (2024). "False-positive mammogram results discourage some women from future screenings." https://health.ucdavis.edu/news/headlines/false-positive-mammograms-discourage-some-women-from-future-screenings/2024/08
Get New Posts via Email
Subscribe to receive updates when we publish new Bayesian analysis articles.