Residual Carrier Risk Calculator
Residual Carrier Risk Calculator
The Bayesian posterior after a negative carrier screen, from the prior carrier frequency and the panel’s detection rate — because a negative screen lowers the risk and never removes it.
Residual Carrier Risk
Prior, detection rate → residual riskA prior carrier frequency of 1 in 25 and a panel detection rate of 90%, after a negative result
Bayes after a negative screen
P(negative screen | carrier) = 1 − DR
P(negative screen | non-carrier) = 1
residual risk = [ (1/N) × (1 − DR) ] ÷ [ (1/N) × (1 − DR) + (1 − 1/N) ]
equivalently, residual risk = 1 in [ 1 + (N − 1) ÷ (1 − DR) ]
- 1 / N
- the prior carrier probability, before the test — the carrier frequency in this person’s population. Where it is not published directly it can be derived from disease prevalence under Hardy-Weinberg
- DR
- the detection rate: the proportion of carriers the panel would identify. So 1 − DR is the proportion of carriers a negative result fails to exclude, and it is this quantity that the whole calculation turns on
- the numerator
- the probability of being a carrier AND screening negative — a missed carrier. This is the only route by which a person with a negative result is still a carrier
- the denominator
- the total probability of a negative result: missed carriers plus everyone who is not a carrier. Non-carriers screen negative with probability 1, which is why the second term is simply 1 − 1/N
- the reciprocal form
- a check on the algebra worth doing. Dividing through gives 1/residual = 1 + (N − 1)/(1 − DR), so a prior of 1 in 25 with a 90% detection rate is exactly 1 + 24/0.1 = 241 — a residual risk of exactly 1 in 241, not an approximation
- what it assumes
- that the detection rate quoted applies to this person’s population, and that the prior is right for them. Both are ancestry-dependent, and both are more uncertain than the three decimal places of the output suggest
Worked example
A prior carrier frequency of 1 in 25 and a panel detection rate of 90%, after a negative result
Prior carrier probability = 1 ÷ 25 = 0.04, and the probability a carrier screens negative = 1 − 0.90 = 0.10
Numerator, carrier AND negative = 0.04 × 0.10 = 0.004
Denominator, negative by any route = 0.004 + (1 − 0.04) = 0.004 + 0.96 = 0.964
Residual risk = 0.004 ÷ 0.964 = 0.0041494, i.e. 0.415%
As a reciprocal that is exactly 1 in 241, which the algebraic shortcut confirms: 1 + (25 − 1) ÷ (1 − 0.90) = 1 + 240 = 241
The prior risk was 1 in 25. The negative screen has reduced it about tenfold, to 1 in 241 — it has not removed it, and the size of the reduction is set entirely by the detection rate
Drop the detection rate to 80% and the same negative result leaves 1 in 121, a residual risk more than twice as high. Raise it to 99% and it leaves 1 in 2,401
The same negative result at different detection rates, prior 1 in 25
| Detection rate | Residual risk | As 1 in |
|---|---|---|
| 0% (no test) | 4.000% | 1 in 25 — the prior, unchanged |
| 50% | 2.041% | 1 in 49 |
| 80% | 0.826% | 1 in 121 |
| 90% | 0.415% | 1 in 241 |
| 95% | 0.208% | 1 in 481 |
| 99% | 0.042% | 1 in 2,401 |
The same 90% detection rate at different priors
| Prior carrier frequency | Residual risk | As 1 in |
|---|---|---|
| 1 in 25 | 0.415% | 1 in 241 |
| 1 in 50 | 0.204% | 1 in 491 |
| 1 in 100 | 0.101% | 1 in 991 |
A negative screen lowers the risk; it does not remove it
Carrier screening looks for specific variants, or sequences specific genes, and reports whether any were found. A negative result is often received as though it were an exclusion. It is not. It is evidence, and its strength is exactly quantifiable: a person who was a carrier before the test had a 1 − DR chance of screening negative anyway, where DR is the panel’s detection rate, and that is the only route left by which a person with a negative result is still a carrier. Bayes’ theorem turns that into a posterior — divide the probability of being a missed carrier by the total probability of a negative result — and the answer is the residual risk.
The arithmetic simplifies into a form worth remembering. The reciprocal of the residual risk is 1 plus (N − 1) divided by (1 − DR). A prior of 1 in 25 with a 90% detection rate therefore leaves exactly 1 in 241: the test has reduced the risk roughly tenfold, because a tenth of carriers are missed. More generally the reduction factor is about 1/(1 − DR), which makes the dependence on detection rate immediate. A 99% panel divides the risk by about a hundred; an 80% panel divides it by five.
That dependence is the reason a negative carrier screen cannot be interpreted without knowing which panel produced it. The same negative result on the same person leaves 1 in 121 at an 80% detection rate and 1 in 2,401 at 99% — a twentyfold difference in residual risk arising from the test, not from the person. Reporting a negative carrier screen without its detection rate withholds the information needed to read it.
And detection rates are ancestry-specific. This is not a caveat but a structural feature of how carrier panels were built: they were assembled from the variants found to be common in the populations studied first and most thoroughly, so they capture a high proportion of carriers in those populations and a lower proportion elsewhere. A panel with an excellent published detection rate can perform substantially worse in a person whose ancestry is not well represented in the variant sets it was derived from, and using the headline figure for such a person understates the residual risk — systematically, and in the direction of false reassurance. Where ancestry is mixed or unknown, the conservative detection rate is the honest input. Full-gene sequencing raises the detection rate for everyone, at the cost of returning variants of uncertain significance, and for couple risk, testing the partner reduces the joint risk far more than repeating the same test on one person ever could.
Frequently asked questions
How do you calculate residual carrier risk after a negative screen?
Residual risk = [(1/N) × (1 − DR)] ÷ [(1/N) × (1 − DR) + (1 − 1/N)], where 1/N is the prior carrier frequency and DR the detection rate. For a prior of 1 in 25 and a 90% detection rate: 0.004 ÷ 0.964 = 0.415%, or exactly 1 in 241.
Does a negative carrier screen mean I am not a carrier?
No. It means the variants the panel tests for were not found. A carrier had a 1 − DR chance of screening negative anyway, so a residual risk always remains — 1 in 241 in the worked example above, down from a prior of 1 in 25. The screen reduces the risk substantially without eliminating it.
Why does the detection rate matter so much?
Because it sets the size of the reduction. The residual risk falls by roughly a factor of 1/(1 − DR), so a 99% panel divides the prior risk by about a hundred while an 80% panel divides it by five. The same negative result leaves 1 in 2,401 or 1 in 121 depending only on the panel used.
Do carrier screening detection rates differ by ancestry?
Yes, and substantially. Panels were built from variants found to be common in the populations studied first and most, so they detect a high proportion of carriers in those populations and a lower proportion in others. Using a headline detection rate for a person whose ancestry is not well represented understates the residual risk.
Where does the prior carrier frequency come from?
From published population carrier frequencies where they exist, or from disease prevalence under Hardy-Weinberg where they do not — the carrier frequency calculator does that conversion. The prior should be the one for the person’s own population, since it varies as much as the detection rate does.
Related calculators
References
- Gregg AR, Aarabi M, Klugman S, et al. Screening for autosomal recessive and X-linked conditions during pregnancy and preconception: an ACMG practice resource. Genet Med. 2021;23(10):1793–1806.
- Edwards JG, Feldman G, Goldberg J, et al. Expanded carrier screening in reproductive medicine — points to consider. Obstet Gynecol. 2015;125(3):653–662.
- Ogino S, Wilson RB. Bayesian analysis and risk assessment in genetic counseling and testing. J Mol Diagn. 2004;6(1):1–9.
- Grody WW, Thompson BH, Gregg AR, et al. ACMG position statement on prenatal/preconception expanded carrier screening. Genet Med. 2013;15(6):482–483.
Medical Disclaimer: The tools and content provided here are for educational and reference purposes only. They are not intended to substitute for professional medical advice, diagnosis, or treatment. Clinical decisions should always be based on the comprehensive assessment of a qualified healthcare professional.