LR: Likelihood ratio for DNA evidence interpretation

Description

The LR function calculates the likelihood ratio for a DNA evidence, when two competing hypotheses Hd and Hp, respectively the defence and the prosecution hypotheses, are weighted about the origin of the DNA evidence. The evidence can either be a simple or a mixed stain.

Usage

LR(stain, freq, xp=0, xd=0, Tp=NULL, Vp=NULL, Td=NULL, Vd=NULL, theta=0)

Arguments

stain

a vector giving the set of (distinct) alleles present in the DNA stain

freq

vector of the corresponding allele frequencies in the global population

the number of unknown contributors to the stain under the prosecution hypothesis Hp. Default is 0.

the number of unknown contributors to the stain under the defence hypothesis Hd. Default is 0.

a vector of strings where each string contains two alleles separated by '/', corresponding to one known contributor under the prosecution hypothesis Hp. The length of the vector equals the number of known contributors. Default is NULL.

a vector of strings where each string contains two alleles separated by '/', corresponding to one known non-contributor under the prosecution hypothesis Hp. The length of the vector equals the number of known non-contributors. Default is NULL.

a vector of strings where each string contains two alleles separated by '/', corresponding to one known contributor under the defence hypothesis Hd. The length of the vector equals the number of known contributors. Default is NULL.

a vector of strings where each string contains two alleles separated by '/', corresponding to one known non-contributor under the defence hypothesis Hd. The length of the vector equals the number of known non-contributors. Default is NULL.

theta

a float in [0,1[. theta is equivalent to Wright's Fst. In case of population subdivision, it allows a correction of the allele frequencies in the subpopulation of interest

Details

LR is the implementation of the general formula of Curran et al (1999) for the evaluation of forensic DNA mixtures through likelihood ratios. The likelihood ratio is computed as a ratio of two probabilities of the DNA evidence, $E$, conditional on the evaluated hypotheses: $$LR=\frac{P(E|H_p)}{P(E|H_d)},$$ where $H_p$ denotes the prosecution hypothesis and $H_d$ the defence hypothesis. In case of population subdivision, contributors to the DNA stain are considered to come from the same subpopulation. Allele dependencies within subpopulations are accounted for through Wright's Fst coefficient, denoted here $\theta$.

References

Curran JM, Triggs CM, Buckleton J, Weir BS. Interpreting DNA Mixtures in Structured Populations. J Forensic Sci 1999;44(5): 987-995

Examples

Run this code

# A rape case in Hong Kong (Hu and Fung, Int J Legal Med 2003)
# The stain shows alleles 14, 15, 17 and 18 at locus D3S1358.
stain =c(14,15,17,18)
# suspect's profile: "14/17"
suspect<-"14/17"
# victim's profile: "15/18"
victim<-"15/18"
# corresponding allele frequencies 
freq<-c(0.033,0.331,0.239,0.056)

# Prosecution hypothesis: Contributors were the victim and the suspect 
# defence hypothesis: Contributors were the victim and 1 unknown contributor
# Likelihood ratios for DNA evidence for different alternatives:
LR(stain,freq,xp=0,Tp=c(victim,suspect),Vp=NULL,Td=victim,Vd=suspect,xd=1)