Solution 1:

This is an English question rather than statistics. Many Latin and Greek plurals are often used as singulars in English (agenda is an obvious example) and the word data is used both ways, as indeed is statistics (though with slightly different meanings).

If you want to keep your sanity and your PhD you should say something like:

The analysis should go quickly since I am familiar with the data.

Solution 2:

The article on data in ‘The Cambridge Guide to English Usage’ distinguishes between These data were gathered by intensive interviewing. They show . . . and This data was gathered by intensive interviewing. It shows . . . As the article points out

This second version actually expresses something slightly different from the first: it projects the data as a mass or block rather than a set of separable items. Data thereby becomes a mass noun.

You can indeed dodge the issue by changing the sentence altogether as Henry suggests. If, on the other hand, you want to confront it head on you have to decide on how you view data. It’s difficult to pronounce on the matter without knowing the context, but you should have no hesitation in using the pronoun it rather than them if you conclude from the preceding sentences of your text that data is to be seen, to repeat the words of the article, ‘as a mass or block rather than a set of separable items’.

Solution 3:

Agenda has passed the threshold to singularity for nearly everyone; but, as you say, many people still adhere to data plural. If you decide to go with traditional style, treat it as plural everywhere. That includes personal pronouns:

The analysis using the data should go quickly, since I am familiar with them.