In the essay that I'm writing, I claim that women are more likely to be victims of abduction than are men. As evidence, I cite a study on child abduction (the NISMART, if you must know) stating that the majority of kidnapped children were females. Because abductions rarely happen, any data on abductions in general (child and adult), if it exists, is very difficult to find, even with a search in my college library's databases.
If you don't have enough reliable data to support your claims, then you should state that your findings are based on certain assumptions. It would further help your cause if you then give explanations for why you made those assumptions. Before you do this, however, you should probably make more of an effort to locate data to support your position. Relying solely on your college library is going to be very limiting.
As this answer says, it's important to state your assumptions, whatever they are.
Sometimes there just isn't enough data, though, and I understand your question to be about what to do in that case. There are two basic approaches:
Only write about things you can back up. For example, Consumer Reports publishes ratings, including predicted reliability, of all new cars once a year. They list everything, but where they have insufficient data they just leave out the predicted reliability. That doesn't stop them from reporting other things about those cars or making recommendations. They're saying "we don't know this, but we can say these other things".
Be more liberal in what you write but be explicit about what data you're basing it on. You'll sometimes see news analyses of, say, crime patterns, with a note like "in 2011, the last year for which data is available, ..." -- well, it's 2015 now and 2011 data might not tell us enough, but it's the best they have so they extrapolate from it. In this approach you leave it to the reader to decide how much that matters.
In your essay, if you need to talk about abductions in general and you only have data for child abductions, you can take the latter approach. Say what you base your conclusions on, and perhaps you can anticipate and pre-emptively address arguments about why that data isn't representative.
The other approach is to focus your essay on what you can directly support with data, in this case writing about child abductions rather than all of them.