Studies on genomic privacy have traditionally focused on identifying individuals using DNA variants. In contrast, molecular phenotype data, such as gene expression levels, are generally assumed free of such identifying information. Although there is no explicit genotypic information in them, adversaries can statistically link phenotypes to genotypes using publicly available genotype-phenotype correlations, for instance, expression quantitative trait loci (eQTLs). This linking can be accurate when high-dimensional data (many expression levels) are used, and the resulting links can then reveal sensitive information, for example, an individual having cancer. Here, we develop frameworks for quantifying the leakage of individual characterizing information from phenotype datasets. These can be used for estimating the leakage from large datasets before release. We also present a general three-step procedure for practically instantiating linking attacks and a specific attack using outlier gene-expression levels that is simple yet accurate. Finally, we describe the effectiveness of this outlier attack under different scenarios.