Pmatch: Match Probabilities of Genotype

In forensic: Statistical Methods in Forensic Genetics

Description

Calculates match probability of the genotype of the suspect and that of the crime stain presumed to have come from an offender other than the suspect. Possible assumptions: the suspect and an unknown offender are unrelated, or are members of the same subpopulation with a given coancestry coefficient, or are close relatives.

Usage

Pmatch(prob, k = c(1, 0, 0), theta = 0)

Arguments

prob	matrix with 2 rows and L columns (L is the number of loci, each locus has 2 alleles). Contains frequencies of alleles in a population found in the crime stain. For homozygous locus just one entry is nonzero. prob can also be a vector with odd number of elements (it is then easily transformed to a matrix with two rows, the matrix is filled by columns)
k	vector of kinship coefficients (k_0, k_1, k_2), where k_i is the probability that two people (the suspect and an unknown offender) will share i alleles identical by descent, i = 0, 1, 2.
theta	number from the interval [0,1). Coancestry coefficient theta describes variation in allele proportions among subpopulations. Default is 0 (no variation, whole population in Hardy-Weinberg equilibrium). The recommended values of theta are 0.01 for large subpopulations such as USA, and 0.03 for small isolated subpopulations (National Research Council, 1996). If theta is nonzero, the allele proportions are taken from the whole population (not from the subpopulation).

Details

The match probability is calculated as

k_2 + k_1 Z_1 + k_0 Z_2,

where k_0, k_1, k_2 are the kinship coefficients (for more information see Details of Pevid.rel),

Z_2 = [2*theta + (1-theta)*p_i]*[3*theta + (1-theta)*p_i] / [(1 + theta)*(1 + 2*theta)],

Z_2 = 2*[theta + (1-theta)*p_i]*[theta + (1-theta)*p_j] / [(1 + theta)*(1 + 2*theta)]

are the match probabilities in the unrelated case for homozygotes and heterozygotes, respectively, and

Z_1 = (2θ + (1-θ) p_i)/ (1+θ)

for the homozygote case and

Z_1 = (2θ + (1-θ) (p_i+p_j))/ (2(1+θ))

for the heterozygote case. The quantity θ is the coancestry population theta. The formula is derived in Balding and Nichols (1994).

The match probability at all loci is calculated as a product of all single locus probabilities. We assume independence across loci.

Value

Pmatch returns a list with the following components:

prob	matrix of allele proportions at each locus (input value in Pmatch)
match	single locus match probabilities
total_match	match probability of genotype = multiplication of single locus match probabilities

Author(s)

Miriam Marusiakova [e-mail]

The work was supported by the project 1M06014 of the Ministry of Education, Youth and Sports of the Czech Republic.

References

Balding DJ, Nichols RA (1994), DNA profile match probability calculation: how to allow for population stratification, relatedness, database selection and single bands. Forensic Science International 64, 125-140.

Evett IW, Weir BS (1998), Interpreting DNA evidence; Statistical genetics for forensic scientists. Sinauer, Sunderland, MA.

National Research Council (1996), The evaluation of forensic DNA evidence National Academy Press, Washington, DC.

See Also

Pevid.rel, Pevid.gen

Examples

## match probability of thirteen-locus genotype 
    ## (11 heterozygous and 2 homozygous loci)
    p<-c(0.057,0.160,0.024,0.122,0.078,0.055,0.035,0.150,
      0.195,0.027,0.084,0.061,0.122,0.083,0.164,0.065,0.143,
      0.151,0.167,0.180,0.099,0.182,0.120,0,0.182,0)
    ## suspect and offender are unrelated 
    Pmatch(p)
    ## suspect and offender are unrelated but members of the same 
    ## subpopulation with the coancestry coefficient theta 
    Pmatch(p, theta = 0.03)
    ## suspect and offender are close relatives (cousins) 
    Pmatch(p, k = c(3/4, 1/4, 0))
    ## suspect and offender are close relatives (cousins) and 
    ## members of the same subpopulation with the coancestry 
    ## coefficient theta 
    Pmatch(p, k = c(3/4, 1/4, 0), theta = 0.03)
    ##
    ## one locus
    Pmatch(p[1:2], theta = 0.03)
    Pmatch(p[25:26], theta = 0.03)
    ## compare
    Pevid.gen(alleles = c(1, 2), prob = p[1:2], V = "1/2", x = 1, 
      theta = 0.03)
    Pevid.gen(alleles = "a", prob = p[25], V = "a/a", x = 1, 
      theta = 0.03)

forensic documentation built on May 2, 2019, 1:52 p.m.