In this report, we evaluate a recently-published 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 false-negative rate, the accuracy of the assumed null distribution
(and hence the true false-positive 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
false-positive 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.
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
false-positive 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.
IntroductionIn the recently published article “Resolving Individuals Contributing Trace
Amounts of DNA to Highly Complex Mixtures Using High-Density SNP Genotyping
Microarrays” [1], the authors describe a method by which the
presence of a individual with a known genotype may be inferred as being part of a
mixture of genetic material for which marginal minor allele frequencies (MAFs), but
not sample genotypes, are known.The method [1] is motivated by the idea that the presence of a
specific individual's genetic material will bias the MAFs of a sample of
which they are part in a subtle but systematic manner, such that when considering
multiple loci, the bias introduced by a specific individual can be detected even
when his DNA comprises only a small fraction of the mixture. More generally, it is
well known that samples of a population will exhibit slightly different MAFs due to
sampling variance following a binomial distribution; the genotype of the individual
in question contributes to this variation, and so may be
“closer” to a sample containing him than to a sample which does
not. Based on this intuition, the article [1] defines a genetic
distance statistic to measure the distance of an individual relative to two samples,
summarized as follows:Consider an underlying population from which two samples (of size ) and (of size ) are drawn independently and identically distributed (i.i.d.)
[in [1], these are referred to as
“reference” and “mixture”
respectively]. Consider now an additional sample ; we wish to detect whether was drawn from , versus the null hypothesis that was drawn from independent of and . Given the MAFs and at locus for and , respectively, and given the MAFs for sample with (corresponding to homozygous major, heterozygous, and homozygous
minor alleles) at each locus , [1] defines the relative distance of sample from and at as:(1)By assuming only independent loci are chosen and invoking the central
limit theorem for the large number of loci genotyped in modern studies, the article
[1]
asserts that the z-score of across all loci will be normally distributed,(2)where denotes the average over all SNPs , is the number of SNPs, and Equation 2 exploits the assumption
[1]
that an individual who is in neither nor will be on average equidistant to both under the null hypothesis,
i.e., . Per Equation 2, the null hypothesis that is in neither nor is rejected for values of which exceed the quantiles of at the chosen significance level.The article [1] proposes using this approach in a forensics context,
in which is a mixture of genetic material of unknown composition (e.g.,
from a crime scene), and is suspect's genotype; by choosing an appropriate
reference sample for group , it is hypothesized that large, positive will be obtained for individuals whose genotypes are included in , and hence bias , while individuals whose genotypes are not in should have insignificant since they should intuitively be no more similar to the mixture
sample than they are to the reference sample . In [1], the authors applied this test to a multitude of
individuals , each of which are present in the samples constructed by them for or , and report near-zero false negative rates. The article concludes
that it is possible to identify the presence of DNA of specific individuals within a
series of highly complex genomic mixtures, and that these “findings show a
clear path for identifying whether specific individuals are within a study based on
summary-level statistics.” In response, many GWAS data sources have
retracted the publicly available frequency data pending further study of this method
due to the concern that the privacy of study participants can be compromised.
However, because no samples absent from both and were used, false positive rates—significant for individuals neither in nor —are not assessed in practice; rather, they are simply
assumed (Equation 2) to follow the nominal false-positive rate given by quantiles of the standard normal.The conclusion that is comparable to a standard normal rests on several assumptions:that , and are all samples of the same underlying population ;that and are similarly sized samples; andthat the SNPs used to compute are independent.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
[1] by
investigating these effects both analytically and by applying Equations 1, 2 to null
samples (those present in neither nor ). We also consider the accuracy of the classification when a
relative of is present in sample .Our tests reveal a good separation of the distributions for positive (i.e., in or ) and null (in neither) samples, suggesting that a suprising amount
of information remains in pooled data. However, our results indicate that membership
classification via Equation 2 is sensitive to the underlying assumptions such that
the distribution for null samples does not follow , yielding misleadingly large for null samples. As a result, applying the method from [1] is tricky
in practice since additional information is often necessary to set appropriate
thresholds for significance. Finally, we conclude with a discussion of the
implications of our findings, both in forensics as well as regarding identification
of individuals contributing DNA in GWAS.MethodsWe explore the performance of the method described in [1] both analytically and
empirically. For the empirical studies, we attempt to classify sample genotypes
derived from publicly available data sources in order to assess the chances that an
individual is mistakenly classified into a group which does not contain his specific
genotype.Genotype data2287 genotypes were obtained from the Cancer Genomic Markers of Susceptibility
(CGEMS) breast cancer study. The samples were sourced as described in [2].
Briefly, the samples comprised 1145 breast cancer cases and a comparable number
(1142) of matched controls from the participants of the Nurses Health Study. All
the participants were American women of European descent. The samples were
genotyped against the Illumina 550K arrays, which assays over 550,000 SNPs
across the genome. To assess the genetic identity shared between samples, we
computed the fraction of SNPs with identical alleles for all possible pairs of
individuals; none exceeded .Additionally, 90 genotypes of American individuals of European descent (CEPH) and
90 genotypes of Yoruban individuals were obtained from the HapMap Project [3]. In
both cases, the 90 individuals were members of 30 family trios comprising two
unrelated parents and their offspring. SNPs in common with those assayed by the
CGEMS study and located on chromosomes 1–22 were kept in the analysis
(sex chromosomes were excluded since the CGEMS participants were uniformly
female); a total of 481,482 SNPs met these criteria.Classification of genotypesThe method as described in [1] and summarized in the Introduction was implemented using R [4]. Subsets of the data
described above were used to construct pools and , using the remaining genotypes as test samples for which the
null hypothesis is true. A summary of the tests is provided in Table 1. In each test, SNPs
which did not achieve a minor allele frequency in both and were excluded from the computation.10.1371/journal.pgen.1000668.t001Table 1Summary of tests performed. individuals population population distribution100 CGEMS cases not in 1042 CGEMS controls1045 CGEMS cases
Figure 1
100 CGEMS controls not in 90 HapMap CEPH90 HapMap YRIHapMap YRI mothers 16–30HapMap YRI mothers 1–15 and fathers
1–15HapMap YRI children 1–15 and fathers
16–30
Figure 2
HapMap YRI children 16–30HapMap CEPH mothers 16–30HapMap CEPH mothers 1–15 and fathers
1–15HapMap CEPH children 1–15 and fathers
16–30
Figure 2
HapMap CEPH children 16–30Summary 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.ResultsThe assertion that as given in Equation 2 follows a standard normal distribution
under the null hypothesis that is in neither nor is based upon the assumptions that
, and are all samples of the same underlying population ; and are similarly sized samples; andthe SNPs used to compute are independent.We investigated the effect of deviation from these assumptions. A full treatment is
presented in Text
S1, and we summarize the results briefly here. In the case where , , and are not samples of the same underlying population, the differences
in the minor allele frequencies of the source populations dominate such that deviations from zero are no longer attributable to the
subtle influence of Y's presence in or . In the case where , , and are samples of the same population but and are of differing sizes, the larger one will be a more
representative sample of the underlying population and hence closer, on average, to
a future sample . Both violations of assumptions 1 and 2 above will lead to
non-zero for null samples. Considering that the difference in with and without the assumption in Equation 2 is(3)and that the number of SNPs is on the order of , even slight deviations away from the assumed can have a pronounced effect when comparing against a standard normal as given by Equation 2. Equation 2 also
presumes that the SNPs are independent, such that the variance of the mean of can be estimated as in the denominator of Equation 2; as shown in Text S1, even a
slight average correlation amongst the SNPs (due, for instance, to linkage
disequilibrium) will cause the distribution of in practice to be much wider than that assumed in Equation 2, once
again owing to the large number of SNPs considered. Because it appears that slight
deviations from the assumptions outlined above may have a strong effect on the
obtained values, the false-positive rate of the method proposed in [1] may in
practice be considerably higher than the nominal false-positive rate given by quantiles of .Empirical testsTo explore the performance of the method in realistic situations, we carried out
the computations described by Equations 1,2 for various , , and as described in Table 1. Distributions of for each of the tests described in Table 1 are shown in the corresponding
figures listed in the table. We find that while the distributions of
in-F, in-G and in-neither values of are distinct, calibrating thresholds for classifying an
unknown sample is difficult without additional information. This is due to the
fact that the distribution of for null samples deviates strongly from a standard normal in
practice.We begin first by considering a best-case situation in which and are both large samples of the same underlying population , and the samples to be classified are also from . Here, we randomly select 100 cases and 100 controls from
CGEMS to form an out-of-pool test sample set comprising 200 individuals, using
the remaining 1045 CGEMS cases and 1042 CGEMS controls as pools and , respectively. (Several such random subsets were created; the
results were consistent and hence we present a single representative one.) (Equation 1, 2) was computed for all the samples and compared
to a standard normal ( yields a nominal (p-value) of 0.05 and yields a nominal ). The sensitivity and specificities obtained are given in
Table 2.10.1371/journal.pgen.1000668.t002Table 2Empirical sensitivity and specificity for the tests shown in Figure 1 assuming .481,382 SNPs50,000 SNPs Sensitivity99.8%97.5%96.3%36.3%Specificity, 200 CGEMS31.0%70.5%79.0%99.5%Specificity, 90 HapMap CEPH5.5%27.7%45.5%100.0%Specificity, 90 HapMap YRI0.0%0.0%4.4%97.7%Classification results are given for two different nominal false
positive rates and .Distributions of values for all three groups of CGEMS samples are shown in
Figure 1A. Notably, the
distributions of in-F, in-G, and in-neither
samples are all quite distinct. For the positive samples (those in or ), the classifier performs fairly well, correctly classifying
2083 samples (and calling 4 as in neither nor ). However, of the 200 test samples which were in neither nor , only 62 have ; the rate of false positives is thus 69% if is used as an indicator of group membership under the
assumptions in [1] at the nominal (see Table
2).10.1371/journal.pgen.1000668.g001Figure 1Comparison of T distributions.Comparison of T distributions for true positive and null
samples versus putative null distribution, starting with 481,382 SNPs in
(A,B) and 50,000 SNPs in (C,D). In all plots, true positive (1042 CGEMS controls) is shown as a solid green curve,
true positive (1045 CGEMS cases) is shown as a solid red curve, and
the putative null is given as a thin grey curve. The dark and light grey
regions represent the areas for which the null hypothesis would be
accepted at and , respectively. In plots (A,C), CGEMS test samples in
neither nor (100 CGEMS cases and 100 CGEMS controls) are given by
a heavy black curve. The CGEMS case and CGEMS control distributions
within this group are shown as dashed red and green lines, respectively.
In plots (B,D), distributions are given for HapMap CEPHs (cyan) and
YRIs (blue). Vertical lines mark the 0.05 and 0.95 quantiles of the
negative CGEMS samples (black), HapMap CEPHs (cyan), and HapMap YRIs
(blue).Next, we consider a less ideal, yet probable, case in which the null samples are
not from the same underlying population . Here, we leave and as above, and apply Equation 1, 2 to 90 HapMap American
individuals of European descent (whom, one might assume, would be relatively
similar to the Americans of European descent comprising groups and ). A plot of the value distributions is given in cyan in Figure 1B. Again, there is little overlap
with the true positive distributions, but when comparing the values against , the sensitivity is quite low (see Table 2). A yet more extreme case, in which
90 HapMap Yoruban individuals were classified with respect to and , results in a distribution of values that overlaps with the values from group (Figure
1B, blue curve) and exceedingly low specificity (Table 2). We thus see in practice a strong
dependence of upon the assumption that , , and are samples of the same population.The reason for the high false-positive rates in practice despite the stringent
nominal false positive rate is clear from the plots Figure 1A and 1B: namely, it can be seen that
the putative null distribution (light grey line, , cf Equation 2) does not correspond to the observed
distribution for samples for which the null hypothesis is correct, with
differences in both the location and width.The overall shift in the location of the distributions is a result of violations
of the assumption that each sample , , and are drawn on from the same underlying population . The magnitude of this effect is derived in Text S1 as , where are the MAFs of the population from which is drawn (hence the different rightward shifts of the CGEMS,
CEPH, and YRI distributions). Because of the large number of SNPs in Equation 2, small deviations from are magnified; even ancestrally similar populations, such as
the 200 CGEMS test samples and the HapMap CEPHS, have different distributions of .The broadening of the distribution is a result of correlation between SNPs. In
Equation 2, it is assumed that the variance of the mean of be estimable by the mean of the variance, ie, , which is true for independent SNPs. However, if there exists
average correlation amongst the SNPs (due to linkage disequilibrium),(4)which can be quite large even for small average correlation due to the high number of SNPs. The result of increased LD is a broader distribution
of values, as observed in Figure 1A and 1B: we observe a narrower
distribution of for the HapMap YRI samples versus the Caucasian CGEMS
participants and HapMap CEPHs (the Yoruban individuals, who come from an older
population, have lower average LD).The effect of LD on the distribution of may be countered by selecting fewer SNPs; the results of this
approach can be seen in Figure 1C
and 1D and in Table
2. Here, 50,000 SNPs were selected, uniformly distributed across of the SNPs used in Figure 1A and 1B. 50,000 SNPs was shown in [1] to be a reasonable
lower bound to detect at nominal one individual amongst 1000, which is the concentration of
true positive individuals in this test. As is clear from Figure 1, reducing the number of SNPs narrows
the distributions considerably, yet at the same time brings them closer together
such that the crisp separation previously obtained is reduced. Using this
method, we see that the 200 CGEMS samples now have a distribution closer to that
of the putative null such that using a threshold of yields an improved—yet still larger than
nominal—21% false-positive rate while maintaining a high
96.3% true positive rate. However, the misclassification rate is
still over 50% for both HapMap samples, and improving these values
requires compromising the sensitivity, a direct result of the overlapping distributions for the and HapMap samples.Despite the low sensitivities obtained in our tests, it is apparent from Figure 1 that the true
positive individuals have a significantly different distribution of values than do the null samples, such that if appropriate
thresholds were selected the classification could be improved (note that in
practice, the distributions of the true positive individuals are unknown, since
reconstructing them requires full genotypes, not just the MAFs, of and ). One simple apprach, motivated by the observed separation of
distributions in Figure 1,
would be to collect a set of presumed-null genotypes from which to estimate the
null distribution. Consider a situation in which we have and , along with an individual who is one of the 200 CGEMS samples not in or , but no other genotypes. We might reasonably turn to publicly
available HapMap genotypes as a group from which to construct an empirical null
distribution for setting thresholds. The lines in Figure 1A and 1C depict this case. Using the
0.05 and 0.95 quantiles obtained from the HapMap CEPH distribution (cyan bars) as thresholds improves the accuracy
relative to using quantiles, but still incorrectly classifies half of the 200
CGEMS samples; the false positive rate is yet greater (and the true-positive
rate smaller) when using the HapMap YRI quantiles (blue bars). Likewise, roughly
a quarter of the HapMap CEPHs and the majority of HapMap YRIs lie outside the
thresholds set from the 200 CGEMS samples in Figure 1B and 1D.These examples, as well as the analytical results described in Text S1,
show that deviations from the assumptions that , , and are i.i.d. samples of the same population can produce misleadingly large values of . While Equations 1, 2 produce good separation of the , and null sample distributions, appropriately calibrating the
thresholds for classification is difficult in practice.Classification of relativesWe 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 mother-father-offspring pedigrees, we
construct pools as follows: = Mothers from
pedigrees 1–15 and fathers from pedigrees
1–15 = Children from
pedigrees 1–15 and fathers from pedigrees
16–30and then compute for mothers and children from pedigrees 16–30
using the same SNP criteria as before. The results of these tests for both
the CEPH and YRI pedigrees, given in Figure 2, are as expected, with the
children having a significantly higher distribution of than the mothers; the values for all the children were so large that
p-values were obtained when comparing to . By contrast, 5/15 of the YRI mothers from pedigrees
16–30 and 10/15 of the CEPH mothers from pedigrees 16–30
yielded (with distributions roughly centered about ). The wider distribution amongst the CEPHS again reflects
the effect of LD. In Figure
2 we can see that the method has the power to resolve three groups:
those in a group, those related to members of a group, and those who are
neither. Note, however, that without having the distribution of for true positives (which necessitates knowing the
genotypes of true positives), it is not clear that setting a threshold to
distinguish between true positives and their relatives is possible.10.1371/journal.pgen.1000668.g002Figure 2Distribution of T.Distributions of T for out-of-group samples who are
related (red line) and unrelated (blue line) to individuals in
G for HapMap YRI (A) and HapMap CEPH (B)
populations. (C) and (D) show the same distributions as (A) and (B)
respectively, with the addition (green line) of individuals who are
in G and unrelated to F (i.e.,
true positives). Dashed black lines indicate the T
significance thresholds of ±1.64 at nominal .Positive predictive value of the methodThe effect of the modest specificity—even in the best of cases
described above—on the posterior probability that the individual is in or is considerable, given that the prior probability is
likely to be relatively small in most applications of this method. Let us
consider the positive predictive value (PPV), which quantifies the post-test
probability that an individual with a positive result (i.e., significant ) is in or . This probability depends on the prior probability that
the individual is in or , i.e., on the prevalence of being a member of or . PPV follows directly from Bayes' theorem, and is
defined as(5)where the PPV is the posterior probability that is in given a prior probability of . We can write this equivalently in terms of the positive
likelihood ratio ,(6)
(7)A plot of PPV vs. prevalence is given in Figure 3. Even with the best sensitivity
(96.3%) and specificity (79%) obtained in Table 2—that
in which , , and were strictly drawn on the same underlying population , SNPs were used, and a nominal was used as a threshold—the prior probability
(prevalence) of being in needs to exceed 66% in order to achieve a
90% post-test probability that the subject is in . For a PPV of 99%, the prior probability needs
to exceed 72% for any specificity under 95%, assuming
the observed sensitivity of 99%. The low specificities obtained
in practice thus require a strong prior belief that is in or .10.1371/journal.pgen.1000668.g003Figure 3Positive predictive value (PPV) as a function of prevalence and
specificity given 99% sensitivity.In (A), PPV is shown on the y axis and color
corresponds to specificity. The black curve depicts the
87% sensitivity line—the best sensitivity
obtained in the empirical tests in Table 2. In (B), PPV is shown by
color, and the y axis corresponds to
specificity.The difference between the empirical false-positive rate and the nominal
false-positive rate based on the standard normal has a strong effect on the
posterior probabilities. Consider that at 87% specificity and 99%
sensitivity is 7.6, versus 990000 if the nominal false-positive rate were correct. For prior probability of 1/1000, the first
case yields a posterior probability of 1.1/1000, while the second yields a
posterior probability of 998/1000. These differences, which are difficult to
measure without additional, well-matched null sample genotypes and which
depend strongly on the degree to which the assumptions underlying the method
are met (consider the differences between the CGEMS and HapMap CEPH
specificities in Table
2), pose a severe limitation on the utility of using Equations 1,2 to
resolve Y's membership in samples or .DiscussionIn this work, we have further characterized and tested the genetic distance metric
initially proposed in [1]. This metric, summarized here by Equations 1,2,
quantifies the distance of an individual genotype with respect to two samples and using the marginal minor allele frequencies and of the two samples and the genotype . The article [1] proposes to use this metric to infer the presence
of the individual in one of the two samples, and the authors demonstrate the utility
of their classifier on known positive samples (i.e., samples which are in either or ) showing that in this situation their method yields
classifications of high sensitivity. Our investigations confirm that the sensitivity
is quite high (correctly classifying true positives into groups and ) and that in-F, in-G, and null
samples have distinct distributions of values. However, we also find that the distribution of for null samples does not follow the presumed standard normal, and
thus the specificity is considerably less than that predicted by the quantiles of
the putative null distribution . Calibrating a more accurate set of thresholds is difficult in
practice, limiting the utility of Equations 1, 2 to positively identify
Y's presence in samples or .In this work we have shown that high values, significant when compared against , may be obtained for samples that are in neither of the pools due
to violations of the assumptions that , and are all samples of the same underlying population; that and are similarly sized samples; and that the SNPs used to compute are independent. The high false positive rates in Table 2 result from deviations
of the first and third assumptions. These assumptions are difficult to meet; for
instance, HapMap CEPH and CGEMS samples are sufficiently dissimilar that the HapMap
CEPH samples exhibit greater deviation from violations of the first assumption,
despite the fact that both samples are Americans of European descent. Additionally,
the conclusion that high values result from Y's presence in relies upon the questionable assumption that individuals in
neither nor will be equidistant from both, resulting in false positives for
relatives of true positive individuals, even when the other assumptions are met.The low false positive rate in practice, resulting from the difficulty in accurately
calibrating the significance of , results in a likelihood ratio (and hence post-test probability)
that is also low. When the prior probability of Y's
presence in or is modest, strong evidence (i.e., high specificity) is needed to
outweigh this prior, which was not achieved in our tests. On the other hand, when
samples were known a priori to be in one of the groups
F/G, Equations 1,2 correctly identify the
sample of which the individual is part.These findings have implications both in forensics (for which the method [1] was
proposed) and GWAS privacy (which has become a topic of considerable interest in
light of [1]). We briefly consider each:Forensics implicationsThe stated purpose [1] of the method—namely, to positively
identify the presence of a particular individual in a mixed pool of genetic data
of unknown size and composition—is difficult to achieve. In this
scenario, we have (from forensic evidence) and a suspect genotype . To apply the method, we would need 1) to assume that and are indeed i.i.d. samples of the same population ; 2) to obtain a sample which is also a sample of the underlying
population , well-matched in size and composition to ; 3) to obtain an estimate of the sample size of such that sample-size effects can be appropriately discounted
(see Text
S1); and 4) to assume that the p-values at the selected
classification thresholds are accurate. The high false-positive rates which
result from even small violations of these criteria make it exceedingly likely
that an innocent party will be wrongly identified as suspicious; it is even more
likely for a relative of an individual whose DNA is present in .GWAS privacy implicationsHere 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, and are known to be samples of the same underlying population (due to the careful matching in GWAS), and their sample sizes
are large and known. However, the malefactor still needs 1) to assure that is a member of this population as well (as shown by the poor
results when HapMap samples were classified using CGEMS MAFs) and 2) to assume
that the p-values at the selected classification thresholds are
accurate. Additionally, the prior probability that any of the genotypes in the
malefactor's possession comes from a GWAS subject is likely to be quite
small, since GWAS samples are a tiny fraction of the population from which they
are drawn. Even if the malefactor were able to narrow down the prior probability
to one in three, a sensitivity of 99% and a specificity of
95% is needed to obtain a 90% posterior probability that
the individual is truly a participant.On the other hand, if the malefactor does have prior knowledge
that the individual participated in a certain GWAS but does not know
Y's case status, Equations 1, 2 permit the malefactor
to discover with high accuracy which group was in. Additionally, in the case of a priori
knowledge, the participant's genotype is not strictly necessary, since
a relative's DNA will yield a large score that falls on the appropriate side of null.Despite these limitations, we observe that the distributions of values for in-F, in-G, and
null samples separate strongly, suggesting that each individual contributes a
pattern of allele frequencies that remains in the pooled data. While calibrating
thresholds to distinguish these distributions without additional information is
not presently possible, the potential for more sophisticated methods to overcome
these barriers cannot be discounted and presents an avenue for future work.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 [1] that the sensitivity is quite high; in the
(rare) case that a sample has an insignificant , it is very likely that is in neither nor . We can also see that genetically distinct groups have distributions with little overlap (Figure 1), and so it may be worth
investigating the utility of Equations 1,2 for ancestry inference.On this note, let us once more consider the quantity which Equation 1 measures,
namely the distance of from relative to the distance of from . Referring to Figure 1A and 1C, we can see that samples which are more like those in sample have a distribution that lies to the right of samples which
are more similar to , as expected; that is, in Figure 1A and 1C, the distribution of null
(not in ) CGEMS cases (dashed red line) is shifted to the right with
respect to the distribution of null CGEMS controls, as might be expected from
Equation 1, i.e., the CGEMS case Ys are closer to CGEMS case
Gs than are the CGEMS control Ys. Although
this difference is not statistically significant, one could imagine that it may
be possible to select SNPs for which the shift is significant, i.e., a selection
of SNPs for which unknown cases are statistically more likely to be closer (via
Equation 1) to the cases in and unknown controls are statistically more likely to be
closer to the controls in . In this case, a subset of SNPs known to be associated with
disease may potentially be used with Equations 1, 2 to predict the case status
of new individuals; conversely, finding a subset of SNPs which produce
significant separations of the test samples may be indicative of a group of SNPs
which play a role in disease. Because this type of application would use fewer
SNPs and would involve the comparison of two distributions of (cases vs. controls ), it may be possible to circumvent some of the problems
stemming from the unknown width and location of the null distribution described
above; still, much work is needed to investigate this possible application. If
successful, the metric proposed in [1], while failing to
function as a tool to positively identify the presence of a specific
individual's DNA in a finite genetic sample, may if refined be a useful
tool in the analysis of GWAS data.Supporting InformationText S1
Di and T under the null
hypothesis.(0.22 MB PDF)Click here for additional data file.
Computational Biology/Genomics Genetics and Genomics Genetics and Genomics/Bioinformatics Genetics and Genomics/Genomics