I got thinking this evening about APOE, which includes a very well-known polymorphism of three alleles, where the most ancient (ApoE4) is associated significantly with Alzheimer's Disease risk in European population samples. The association is not significant in all genetic backgrounds, including African American population samples, so it's not necessarily a case where we could predict the phenotype of an ancient genome from observing the allele. But it is one of the most commonly known disease risk polymorphisms, and I hadn't happened to look it up to see what Neandertals and Denisovans are like.
There are two constituent SNP loci -- rs429358 and rs7412. For both these loci, the Denisova genome data include one relevant read, together indicating the ApoE4 allele. The alignment quality of these reads is indicated as poor and I wouldn't take the result to the bank. A third locus, rs4420638 in the nearbyAPOC1 gene is typically linked to the APOE status in living people, and four Denisova reads indicate the allele that is today usually linked to ApoE4. The Neandertal data have no reads at all for the two key SNPs in APOE, and only a single read for the linked SNP in APOC1 is likewise the one usually linked to ApoE4.
None of this is surprising, because ApoE4 is the more ancestral allele. Still, the other common alleles (ApoE2 and ApoE3) are relatively ancient as human polymorphisms go, and could very well have existed in populations contemporary to Neandertals and Denisovans, or in some individuals in those populations. But as it stands, the data suggest that the Denisova genome carried an ApoE4 allele.