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Discrete TDT calculation

Discrete TDT calculation. Calculate probability of parental mating type given affected offspring Calculate probability of offspring genotype given parental mating type and affected Calculate overall probability of heterozygous parents transmitting allele A as opposed to a

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Discrete TDT calculation

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  1. Discrete TDT calculation • Calculate probability of parental mating type given affected offspring • Calculate probability of offspring genotype given parental mating type and affected • Calculate overall probability of heterozygous parents transmitting allele A as opposed to a • Calculate TDT test statistic, power

  2. Step 1 : P(GP|D) • P(GP) given by allele frequencies • e.g. P(AAxAa) = 4p3q • P(D|GP) given by disease model and Mendelian segregation = ΣGO P(D|GO) P(GO|GP) • e.g. P(D | AAxAa) = P(D|AA) / 2 + P(D|Aa) / 2 • P(GP|D) given by Bayes’ Theorem • i.e. P(GP|D) = P(D|GP)P(GP) / ΣGPP(D|GP)P(GP)

  3. Step 2 : P(GO|GP,D) • Application of Bayes’ Theorem • P(GO|GP, D) = P(D|GO) P(GO|GP) • ΣGO P(D|GO) P(GO|GP) • e.g. P(Aa | AAxAa , D ) • P(D|Aa) x 0.5 • P(D|aa) x 0 + P(D|Aa) x 0.5 + P(D|AA) x 0.5 =

  4. Step 3 : P(T) • To calculate expected # of informative transmissions T, conditional on parental mating type • E(T=A | GP, D) = ΣGONA|GO,GPP(GO|GP,D) • where N is the number of informative transmissions of T, e.g., • NA|aa,Aaxaa = 0NA|AA,AAxAa = 1 NA|AA,AaxAa = 2 • e.g. • P(T=A | AAxAa) = 0 x P(aa | AAxAa, D) + 0 x P(Aa | AAxAa, D) + 1 x P(AA | AAxAa, D) • ii. Sum over all parental mating types: • E(T=A| D ) = ΣGPP(GP|D) E(T=A | GP, D)

  5. Step 4 : TDT statistic & power • ( E(T=A) – E(T=a) )2 • E(T=A) + E(T=a) • Threshold-based TDT • Similar to threshold-based case-control, except every possible parental mating type / offspring genotype combination must be considered TDT per trio =

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