loose_eag: Loose an EAG

In gschofl/HLAsim: Simulate allelic dropouts in HLA data

Description

Randomly loose an EAG number.

Usage

loose_eag(x, pE, odds = 1)

Arguments

x	A <eag_numbers> instance.
pE	The absolute probability that an error occurs.
odds	The odds in favour of loosing an EAG on Exon 2 rather than Exon 3. E.g. odds = 2 means a 2:1 chance that the loss occurs on Exon 2; odds = 0.25 means a 1:4 chance that the loss occurs on Exon 3.

Details

We generally deal with the following scenario on any HLA locus currently:

	Exon A	Exon B
EAG 1	a	c
EAG 2	b	d

We know (have a guesstimate of) the total error rate due to loss of EAGs at a given DNA concentration, P(E), and we know the odds, ω, that we'll loose an EAG at one or the other exon.

E.g. if we perform two independent PCR reactions for exon 2 and only one PCR reaction for exon 3, the odds of loosing an EAG are 4 in 1 for exon 3. I. e. in order for an error to manifest on exon 2 we must loose the same EAG in both reactions, the probability of which is ¼ of loosing an EAG in a single reaction.

What we want to know is:

• P(A ∩ ¬ B | E)

  The probability that we loose an EAG on exon A but not on exon B, given that we make an error at all.

• P(¬ A ∩ B | E)

  The probability that we loose an EAG on exon B but not on exon A, given that we make an error at all.

• P(A ∩ B | E)

  The probability that we loose an EAG on exon A and on exon B, given that we make an error at all.

To get there we need to know the error rate for exon A, ε_A, and the error rate for exon B, ε_B, since:

• P(A ∩ ¬ B; | E) = ε_A(1 - ε_B) ⁄ (ε_A + ε_B - ε_Aε_B)
• P(¬ A ∩ B; | E) = ε_B(1 - ε_A) ⁄ (ε_A + ε_B - ε_Aε_B)
• P(¬ A ∩ B; | E) = ε_Bε_A ⁄ (ε_A + ε_B - ε_Aε_B)

Considering that ε_A + ε_B - ε_Aε_B = P(E) and ε_B = ¹⁄_ω ε_A we can arrive after some rearrangements at:

• ε_A = ½(1 + ω - ω √ (1 + 1⁄ω)² - 4P(E)⁄ω)
• ε_B = ¹⁄_ω ε_A

These error rates allow now to randomly loose EAGs with the correct probabilities.

Value

An <eag_numbers> instance

gschofl/HLAsim documentation built on May 17, 2019, 8:51 a.m.