The rapid increase in data available from genome-wide association 
studies poses a challenge to the scientific community. On the one 
hand, the identity of participants in these studies must not be 
revealed. On the other hand, free availability of the data can be 
used in meta-analyses that can greatly enhance our understanding 
of human genetic variation. A compromise between these 
conflicting objectives was achieved by pooling the individuals 
in the case and control groups and making the
summary statistics at each SNP publicly available. However, a 
recent paper by Homer et al showed that genome-wide SNP data 
can be exploited to detect the presence of an individual 
genotype in a mixture of DNA even when present in trace amounts. 
The possibility that presence of individual genotypes can now 
be detected using summary statistic data has resulted in such 
data being removed from the public domain.

These findings raises the following question: can we pick a 
small number of SNPs to expose so that some acceptable level 
of privacy is attained? The investigator may then decide to 
expose a small number of the most significantly associated SNPs. 
Answering this question requires a lower bound on the power 
achievable by any method for detecting an individual genotype 
in a mixture. Given the number of individuals n in the pool, 
maximum allowable power \beta and false positive rate \alpha, 
this problem can be formulated in a hypothesis testing framework 
for which the likelihood ratio test (LR-test) is provably optimal. 
We  show that the allowed number of exposed SNPs m can be written 
as $m  = n (z_{\alpha} + z_{\beta})^2 where z_x is the 100(1-x)^th 
percentile of the standard normal distribution, provided all SNPs are
common. Our theoretical and empirical results differ qualitatively 
from those of Homer et al in that we find that the power achieved 
by considering whole-genome datasets is in fact limited. We present 
analyses and/or empricial results to understand the behavior of 
the test statistic under a number of different scenarios such
as small pool sizes, genotyping errors, and non-independence 
amongst the SNPs.