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Table 1 Conditional probability distributions

From: A robust and efficient statistical method for genetic association studies using case and control samples from multiple cohorts

a.

 

AA

  

Aa

  

aa

 

MM

Mm

mm

MM

Mm

mm

MM

Mm

mm

g 11

g 12

g 13

g 21

g 22

g 23

g 31

g 32

g 33

Q 2

2Q(1-Q)

(1-Q)2

QR

Q + R-2QR

(1-Q)(1-R)

R 2

2R(1-R)

(1-R)2

where Q = p + D/q and R = p - D/(1-q)

b.

 

MM

  

Mm

  

mm

 

AA

Aa

aa

AA

Aa

aa

AA

Aa

aa

h 11

h 12

h 13

h 21

h 22

h 23

h 31

h 32

h 33

Q 2

2Q(1-Q)

(1-Q)2

QR

Q + R-2QR

(1-Q)(1-R)

R 2

2R(1-R)

(1-R)2

where Q = q + D/p and R = q - D/(1-p)

c.

  

Cases

  

Controls

 
 

MM

Mm

mm

MM

Mm

mm

AA

f 1  × g 11

f 1  × g 12

f 1  × g 13

(1-f 1 ) × g 11

(1-f 1 ) × g 12

(1-f 1 ) × g 13

Aa

f 2  × g 21

f 2  × g 22

f 2  × g 23

(1-f 2 ) × g 21

(1-f 2 ) × g 22

(1-f 2 ) × g 23

aa

f 3  × g 31

f 3  × g 32

f 3  × g 33

(1-f 3 ) × g 31

(1-f 3 ) × g 32

(1-f 3 ) × g 33

#observed

n 11

n 12

n 13

n 21

n 22

n 23

  1. Conditional probability distribution of (a) marker genotypes on a given disease genotype, (b) disease genotypes on a given marker genotype and (c) marker genotypes given a genotype at the disease locus under the penetrance model of the disease gene in case/control samples. fi is the penetrance that an individual in the population is affected with disease given its genotype at the disease locus is i (i = 1, 2 and 3 for genotypes AA, Aa and aa respectively).