It is well established that approximately 85.473% of the battle when it comes to NIH Grantsmithing is making it easy for the reviewers to grasp your point.
Many bloggers have described the fact that you need to think about your audience. The grant reviewer in my mind's eye is an overworked, grant-stressed, paper-decision-major-revision, lab disaster supervising PI who has finally cracked your grant open at 10 pm after putting his kids to bed, throwing some laundry in, running the dishes and making lunches for tomorrow's schoolday. . Plus, she may have an infant squirming and latching on poorly at the same time. Still licking wounds from the last disappointing summary statement from his or her own grant application.That's if you are lucky.
If you are unlucky she is getting serious about reviewing your grant while crammed in coach on the way to Bethesda for the actual meeting. And is planning on submitting the written critique the moment she hits the free wifi at the airport....
Then, should your application be so lucky as to be discussed, realize this, Dear Reader. The three assigned reviewers may have had the time, if they had the inclination, to pour over your application at leisure.
The rest of the panel? Not so much.
It is the rare reviewer who has read through the entire panel's worth of applications in detail. And if there appears to be a disagreement between the three assigned reviewers during discussion, these other reviewers have something on the order of 10-15 minutes to scan through your application to attempt to resolve matters in their own mind.
You want their job to be as easy as possible. This is why I hammer away at the creation of blank space, headings, clear figures and direct writing. You know this. What many people don't seem to realize is that your selection of citation style matters as well.
Some folks seem to think that it doesn't matter or that the NIH insists on numbered citation styles.
[As a bit of a sidebar, before I go too deep, there is absolutely nothing about grant review that is fixed in stone. So if you know people who always use the numbered citations and get funded, bully for them. But realize they got the award despite a lapse in grantsmithing, not because it is unimportant.]
Back to our story, it appears some of this confusion may be attributable to Endnote, as one authority claims that the Endnote style for "NIH" is numbered[7,8]. I have recently tested this on my Endnote X4 for Windows and I find this assertion to be untrue. My style for NIH (default installation) is Author, Date style, not numbered.
but still. If you have some version of Endnote that has a particular style for "NIH" don't you think you'd better check to see what the rules say? I mean, you could have a template grant from some idiot that uses Georgia font but you know to put it in the Arial, no? Or if your sample page is in 12pt font, you go and see what the rules actually say, right? So why would you take what some non-NIH entity says about the style for citation? I mean, you could ask the Twitts[8a]...but why not check the source .
Provide a bibliography of any references cited in the Project Narrative. Each reference must include the names of all authors (in the same sequence in which they appear in the publication), the article and journal title, book title, volume number, page numbers, and year of publication.
emphasis added- no reshuffling of "co-contribution" authors permitted!
When citing articles that fall under the Public Access Policy, were authored or co-authored by the applicant and arose from NIH support, provide the NIH Manuscript Submission reference number (e.g., NIHMS97531) or the PubMed Central (PMC) reference number (e.g., PMCID234567) for each article. If the PMCID is not yet available because the Journal submits articles directly to PMC on behalf of their authors, indicate “PMC Journal – In Process.”
That's it though. No mention of a required citation style or of a bibliographic style, so long as the pertinent information is included.
Now, I know why you are tempted to use the gawdawful numbered citations. You think you are saving space and can squeeze yet more blabbedy-blah text in there to overhwhelm the reviewers.
Resist the urge.
It is hard to read academic text with numbered citations if you are actually using the citations to create the argument in your mind. Now maybe I am weird. But for me, especially in my subfields of interest, Name, Date for a paper citation is sufficient cueing to dredge up any number of details about the paper in question. With a mental image of the findings, interpretations, etc. Call me crazy, but your random schema for numbering the references doesn't do the job.
Even if I flip back and forth between my place in the text and the reference list, I've probably forgotten what the hell  refers to a paragraph later. There is a prayer that (Schmelmitz et al, 1968) will trigger me to remember the paper without any need to flip to the citation list at all. And I'll likely remember which one you mean, if I've flipped back to check the full citation, for longer than a few sentences.
Oh, and speaking of flipping to the Bibliography. Much easier to do with hardcopy grant applications. Much harder to do when reading the PDF on a computer. Maybe there are some fancy double pane views but I sure as heck don't use them...are you gambling your average reviewers knows some way to do this?
So numbered citations are a clearly inferior way to cite an academic work. In fact, when I am the boss of science, whomever came up with this or perpetuates it as a good way to cite papers is going to be in the second group up against the wall. They make it hard for the reader to figure out what work you are citing. Let's face it, you aren't wasting the space to explain the prior finding, either, are you? You are using the mere citation itself in hopes that it makes the point for you! Why would you want to make it hard on the reviewers? It's only going to annoy them.
 Drugmonkey, 2012
Dr Zen, 2012
Application Guide for NIH and Other PHS Agencies
Unless they are also a GlamourMag editor, then they go with their regular group.