## Child Body Identification Trick

- The problem
Given DNA profiles for Mother (M), Father (F), and a body (C) suspected to be their
child, what is the likelihood ratio LR supporting relationship versus unrelated?

- Strategy
Solve the problem in terms of two related problems.
- Compute the trio paternity index PI for the M-C-F trio,
as if F were an alleged father.
- Compute the duo maternity index MI relating M-C as parent-child or unrelated
- The desired LR=PI•MI

- Why does it work?
Consider these 3 hypotheses:
- H
_{0}: M and F are the parents of C.
- H
_{1}: M is the mother of C, F is unrelated to C.
- H
_{2}: All three are unrelated.

In terms of these hypotheses, note that
- LR compares H
_{0} vs. H_{2}
- PI compares H
_{0} vs. H_{1}
- MI compares H
_{1} vs. H_{2}

or in formulas:
- LR = Pr(DNA data | H
_{0}) / Pr(DNA data | H_{2})
- PI = Pr(DNA data | H
_{0}) / Pr(DNA data | H_{1})
- MI = Pr(DNA data | H
_{1}) / Pr(DNA data | H_{2})

from which obviously LR=PI•MI as claimed.

- What good is it?
In DNA•VIEW you can of course directly compute the
body ID LR using the Automatic Kinship Case
program. However, for an irregular
suitation involving possible mutation or null alleles, the kinship calculation is
not as sophisticated and accurate as the calculation done by the special-purpose
Paternity Case calculation. Therefore it can be advantageous to do the
body ID calculation in two steps using Paternity Case.