forensic (version 0.2)

LR.ind: Likelihood Ratio for DNA Evidence (Independent Alleles Within and Between Ethnic Groups)

Description

Calculates likelihood ratio for DNA evidence, comparing two hypotheses about the origin of the mixture at the crime scene. Contributors to the mixture may come from one or more ethnic groups. Independence of alleles within and between ethnic groups is assumed.

Usage

LR.ind(alleles, prob, x1, x2, u1 = NULL, u2 = NULL)

Arguments

alleles

vector of distinct alleles (from one specific locus) found in the crime sample

prob

matrix of allele proportions in a population. Element (i, j) contains proportion of the i-th allele from alleles in the j-th ethnic group

x1

vector of nonnegative integers. The j-th element contains number of unknown contributors from the j-th ethnic group under the prosecution proposition.

x2

vector of nonnegative integers. The j-th element contains number of unknown contributors from the j-th ethnic group under the defence proposition.

u1

vector of alleles from the mixture, which are not carried by known contributors under the prosecution proposition. If u1=NULL (default), all alleles from the crime sample are carried by known contributors.

u2

vector of alleles from the mixture, which are not carried by known contributors under the defence proposition. Default is u2=NULL.

Value

likelihood ratio for DNA evidence at the crime scene

Details

Likelihood ratio (LR) is computed as a ratio of two conditional probabilities of DNA evidence $E$ $$LR=\frac{P(E|H_0)}{P(E|H_A)},$$ where $H_0$ denotes the prosecution proposition and $H_A$ the defence proposition. For calculation of $P(E|H)$ see Pevid.ind.

Likelihood ratio is used for assigning the weight of evidence for one locus. The overall LR can be obtained by multiplying over all loci, under the assumption of independent alleles between loci.

References

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

Fukshansky N, Bar W (1998), Interpreting forensic DNA evidence on the basis of hypotheses testing. International Journal of Legal Medicine 111, 62-66.

Fung WK, Hu YQ (2001), The evaluation of mixed stains from different ethnic origins: general result and common comments. International Journal of Legal Medicine 115, 48-53.

Weir BS, Triggs CM, Starling L, Stowell LI, Walsh KAJ, Buckleton J (1997), Interpreting DNA mixtures. Journal of Forensic Sciences 42, 213-222.

See Also

Pevid.ind, Pevid.gen

Examples

## Simpson case (Fung and Hu (2001))
## From the crime scene: mixed profile a,b,c at a locus D2S44 
m = c("a", "b", "c")
## profile of the defendant: a,b
## profile of the victim: a,c
## allele frequencies (African - American, Caucasian)
p_aa <- c(0.0316, 0.0842, 0.0926)
p_c <- c(0.0859, 0.0827, 0.1073)
## the number of contributors to the mixed sample is taken 2
## Prosecution proposition: Contributors were the victim and the suspect 
## Defence proposition: Contributors were 2 unknown people
##
## Likelihood ratios for DNA evidence for different alternatives:
## two unknown people are African-American
LR.ind(alleles = m, prob = cbind(p_aa, p_c), x1 = c(0, 0), 
  x2 = c(2, 0), u2 = m)
LR.ind(alleles = m, prob = p_aa, x1 = 0, x2 = 2, u2 = m)
## one unknown person is African-American and one is Caucasian 
LR.ind(alleles = m, prob = cbind(p_aa, p_c), x1 = c(0, 0), 
  x2 = c(1, 1), u2 = m)
## two unknown people are Caucasian
LR.ind(alleles = m, prob = cbind(p_aa, p_c), x1 = c(0, 0), 
  x2 = c(0, 2), u2 = m)
LR.ind(alleles = m, prob = p_c, x1 = 0, x2 = 2, u2 = m)