Incomplete-trio transmission-selection bias

If one parent is heterozygous and the other parent's genotype is missing, a homozygous child reveals the observed parent's transmitted allele, whereas a heterozygous child need not. Selecting only revealed transmissions can therefore bias the transmission disequilibrium test. For allele-1 frequency $p$ under random mating and fair transmission, the probabilities of an allele-1 or allele-2 homozygous child from an observed heterozygous parent are $p/2$ and $(1-p)/2$. Among selected homozygous children, the observed allele-1 transmission probability is $p$, not generally $1/2$. A complete-trio analysis avoids this reconstruction rule; methods retaining missing-parent families need an explicit likelihood function or a valid conditional adjustment. Family-based association tests using genotype data with uncertainty discusses this bias.