The Combined Paternity Index (CPI) is a likelihood ratio that measures how much more likely a set of DNA results is to occur if a tested man is the biological father of a child, compared to an unrelated, random man from the relevant population.
It is calculated by multiplying the individual Paternity Index (PI) obtained at each tested genetic locus.
What Is a Paternity Index (PI)?
At a single STR (short tandem repeat) locus, the Paternity Index compares two explanations for the child's paternal allele: that it came from the tested man, versus that it came by chance from a random, unrelated man in the population. The PI at each locus depends on whether the alleged father is homozygous or heterozygous at that locus, and on the frequency of the relevant allele in the reference population database used.
How the CPI Is Calculated
The CPI is the product of the PI values obtained at every genetic locus tested:
CPI = PI(locus 1) × PI(locus 2) × PI(locus 3) × ... × PI(locus n)
Because STR loci are inherited independently, multiplying the per-locus values is statistically valid and produces a combined measure of the overall strength of the genetic evidence across the full tested profile. A typical modern STR panel tests 20 or more autosomal loci, so a strong, fully consistent paternity result commonly produces a CPI in the trillions or higher.
From CPI to Probability of Paternity
The CPI itself is a likelihood ratio, not a probability. To express the result as a probability of paternity (commonly denoted W), the CPI is combined with a prior probability — an assumed starting probability of paternity before considering the DNA evidence, conventionally set at 0.5 (50%) unless case-specific information justifies a different value:
W = (CPI × prior) / [(CPI × prior) + (1 − prior)]
With a very high CPI, W approaches 100% even though it can mathematically never reach it exactly. This is why properly written paternity reports state the probability as "greater than" a stated threshold (for example, >99.99%) rather than exactly 100%, and explicitly note that the result is conditional on the stated prior assumption.
What a High CPI Does and Doesn't Mean
- A high CPI reflects strong statistical support for paternity given the tested loci — it is not, by itself, legal proof of paternity.
- The result is conditional on the population allele-frequency database used for the calculation, which should be documented in the report.
- CPI calculations assume the mother's profile is available and correctly attributed (a duo calculation, without a maternal sample, generally produces a lower CPI than a trio calculation with one, since fewer alleles can be conclusively attributed to the father).
- A single incompatible locus does not automatically exclude a tested man — established mutation rates mean a single-step allele difference at one locus is sometimes still consistent with paternity, and validated software should apply a documented mutation model rather than an automatic exclusion.
Frequently Asked Questions
Is a CPI of over 1 million considered conclusive?
There's no single universal legal threshold, but many laboratories and courts treat a CPI in the millions or higher, combined with a probability of paternity above 99.9%, as very strong support for paternity. The exact interpretation language used should follow the laboratory's own validated reporting standard.
Why do two labs sometimes report slightly different CPI values for the same case?
Differences usually come from using different population allele-frequency databases, different theta (population substructure) correction values, or differences in which loci were usable in each analysis — not from an error in the underlying math.
Can a CPI be calculated without the mother's DNA sample?
Yes — this is called a duo (or motherless) paternity test. It generally produces a lower CPI than a trio test with the mother's sample, because fewer alleles can be conclusively attributed to the father alone.
AlleleSight automates CPI, RMP, and Likelihood Ratio calculations directly from genotyped STR data, using a documented population database and theta correction, and withholds a statistical result whenever the underlying profile can't reliably support one.
Learn more about AlleleSight's statistical engine