Evaluation of standard error and confidence interval of estimated multilocus genotype probabilities, and their implications in DNA forensics

Multilocus genotype probabilities, estimated using the assumption of independent association of alleles within and across loci, are subject to sampling fluctuation, since allele frequencies used in such computations are derived from samples drawn from a population. We derive exact sampling variances of estimated genotype probabilities and provide simple approximation of sampling variances. Computer simulations conducted using real DNA typing data indicate that, while the sampling distribution of estimated genotype probabilities is not symmetric around the point estimate, the confidence interval of estimated (single-locus or multilocus) genotype probabilities can be obtained from the sampling of a logarithmic transformation of the estimated values. This, in turn, allows an examination of heterogeneity of estimators derived from data on different reference populations. Applications of this theory to DNA typing data at VNTR loci suggest that use of different reference population data may yield significantly different estimates. However, significant differences generally occur with rare (less than 1 in 40,000) genotype probabilities. Conservative estimates of five-locus DNA profile probabilities are always less than 1 in 1 million in an individual from the United States, irrespective of the racial/ethnic origin.