Conceived and designed the experiments: RB WR CS JZ KB. Performed the experiments: RB. Analyzed the data: RB. Contributed reagents/materials/analysis tools: RB. Wrote the paper: RB.
The authors have declared that no competing interests exist.
Recent publications have described and applied a novel metric that quantifies the genetic distance of an individual with respect to two population samples, and have suggested that the metric makes it possible to infer the presence of an individual of known genotype in a sample for which only the marginal allele frequencies are known. However, the assumptions, limitations, and utility of this metric remained incompletely characterized. Here we present empirical tests of the method using publicly accessible genotypes, as well as analytical investigations of the method's strengths and limitations. The results reveal that the null distribution is sensitive to the underlying assumptions, making it difficult to accurately calibrate thresholds for classifying an individual as a member of the population samples. As a result, the falsepositive rates obtained in practice are considerably higher than previously believed. However, despite the metric's inadequacies for identifying the presence of an individual in a sample, our results suggest potential avenues for future research on tuning this method to problems of ancestry inference or disease prediction. By revealing both the strengths and limitations of the proposed method, we hope to elucidate situations in which this distance metric may be used in an appropriate manner. We also discuss the implications of our findings in forensics applications and in the protection of GWAS participant privacy.
In this report, we evaluate a recentlypublished method for resolving whether individuals are present in a complex genomic DNA mixture. Based on the intuition that an individual will be genetically “closer” to a sample containing him than to a sample not, the method investigated here uses a distance metric to quantify the similarity of an individual relative to two population samples. Although initial applications of this approach showed a promising falsenegative rate, the accuracy of the assumed null distribution (and hence the true falsepositive rate) remained uninvestigated; here, we explore this question analytically and describe tests of this method to assess the likelihood that an individual who is not in the mixture is mistakenly classified as being a member. Our results show that the method has a high falsepositive rate in practice due to its sensitivity to underlying assumptions, limiting its utility for inferring the presence of an individual in a population. By revealing both the strengths and limitations of the proposed method, we elucidate situations in which this distance metric may be used in an appropriate manner in forensics and medical privacy policy.
In the recently published article “Resolving Individuals Contributing Trace
Amounts of DNA to Highly Complex Mixtures Using HighDensity SNP Genotyping
Microarrays”
The method
Consider an underlying population
The article
The conclusion that
that
that
that the SNPs
Because these assumptions are difficult to control in practice, the effect of
deviations from these assumptions is of interest. In this manuscript, we expand on
Our tests reveal a good separation of the distributions for positive (i.e., in
We explore the performance of the method described in
2287 genotypes were obtained from the Cancer Genomic Markers of Susceptibility
(CGEMS) breast cancer study. The samples were sourced as described in
Additionally, 90 genotypes of American individuals of European descent (CEPH) and
90 genotypes of Yoruban individuals were obtained from the HapMap Project
The method as described in
100 CGEMS cases not in 
1042 CGEMS controls  1045 CGEMS cases 

100 CGEMS controls not in 

90 HapMap CEPH  
90 HapMap YRI  
HapMap YRI mothers 16–30  HapMap YRI mothers 1–15 and fathers 1–15  HapMap YRI children 1–15 and fathers 16–30 

HapMap YRI children 16–30  
HapMap CEPH mothers 16–30  HapMap CEPH mothers 1–15 and fathers 1–15  HapMap CEPH children 1–15 and fathers 16–30 

HapMap CEPH children 16–30 
Summary of tests described. In the last four rows, the numbers refer to the families in the HapMap YRI and CEPH populations, such that child 1 is the offspring of mother 1 and father 1, et cetera.
The assertion that
the SNPs
We investigated the effect of deviation from these assumptions. A full treatment is
presented in
To explore the performance of the method in realistic situations, we carried out
the computations described by Equations 1,2 for various
We begin first by considering a bestcase situation in which
481,382 SNPs  50,000 SNPs  





Sensitivity  99.8%  97.5%  96.3%  36.3% 
Specificity, 200 CGEMS  31.0%  70.5%  79.0%  99.5% 
Specificity, 90 HapMap CEPH  5.5%  27.7%  45.5%  100.0% 
Specificity, 90 HapMap YRI  0.0%  0.0%  4.4%  97.7% 
Classification results are given for two different nominal false
positive rates
Distributions of
Comparison of
Next, we consider a less ideal, yet probable, case in which the null samples are
not from the same underlying population
The reason for the high falsepositive rates in practice despite the stringent
nominal false positive rate is clear from the plots
The overall shift in the location of the distributions is a result of violations
of the assumption that each sample
The broadening of the
The effect of LD on the distribution of
Despite the low sensitivities obtained in our tests, it is apparent from
These examples, as well as the analytical results described in
We briefly consider the classification of individuals who are relatives of true positives. This can be investigated by using HapMap trios, since we can reasonably expect that the children will bear a greater resemblance to their parents than their parents do to one another. Recalling that the HapMap pools consist of thirty individual motherfatheroffspring pedigrees, we construct pools as follows:
and then compute
Distributions of
The effect of the modest specificity—even in the best of cases
described above—on the posterior probability that the individual
In (A), PPV is shown on the
The difference between the empirical falsepositive rate and the nominal
falsepositive rate based on the standard normal has a strong effect on the
posterior probabilities. Consider that
In this work, we have further characterized and tested the genetic distance metric
initially proposed in
In this work we have shown that high
The low false positive rate in practice, resulting from the difficulty in accurately
calibrating the significance of
These findings have implications both in forensics (for which the method
The stated purpose
Here the scenario of concern is that of a malefactor with the genotype of one (or
many) individuals, and access to the case and control MAFs from published
studies; could the malefactor use this method to discern whether one of the
genotypes in his possession belongs to a GWAS subject? In this case,
On the other hand, if the malefactor
Despite these limitations, we observe that the distributions of
Moreover, we believe that the distance metric (Equations 1, 2) as presented may
still have forensic and research utility. It is clear from both our studies and
the original paper
On this note, let us once more consider the quantity which Equation 1 measures,
namely the distance of
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