III.
Multinomial probabilities for genotype combinations in case/mother duos
| 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|
| Cell (row) index | Genotypesagmgc | P(gm, gc|dis)b |
P(gm, gc|dis)b with reparameterization  = R1Ip = R2 γ12 = S1 = S2γ21 = Im/Ip = γ11 = γ22/γ12γ21
|
P(gm, gf, gc|dis)bcd assuming random mating and HWE (and with reparameterization from column 4) |
| 1 | 22 22 | R2S2ImIpγ22(µ1+µ2) |
 (µ1+µ2) |
 /Σ |
| 2 | 22 12 | R1S2Imγ21(µ2+µ3) |
 (µ2+µ3) |
 /Σ |
| 3 | 12 22 | R2S1ImIpγ12(µ2+µ4) |
 (µ2+µ4) |
 /Σ |
| 4 | 12 12 | R1S1γ11(Im(µ4+µ5)+Ip(µ2+µ4)) |
 ( (µ4+µ5)+µ2+µ4) |
 /Σ |
| 5 | 12 11 | S1(µ4+µ5) |
 (µ4+µ5) |
 /Σ |
| 6 | 11 12 | R1Ip(µ3+µ5) |
 (µ3+µ5) |
 /Σ |
| 7 | 11 11 | µ5+µ6 | µ5+µ6 |
 /Σ |
a
gm refers to the unordered alleles in the mother. gc refers to the unordered alleles in the child.
b
dis indicates the event that the child is affected with disease.
c
A1 and A2 are the allele frequencies of allele 1 and 2, respectively.
d
Formula for Σ is given in the Appendix.