While it is not the best practice to use unpublished work particularly in a research study, as long as the study in question is scholarly done, it could be used in your work in part. Note, the fact that a work is unpublished does not mean it is invalid. Any study with adequate and corroborative emperic facts could be sited in any research work. I recommend that you equally reflect on other comments as may be provided by other scholars on this forum and make your informed decision. I hope my viewpoint is helpful?

It wouldn't be impolite to contact the authors. In fact, it is a strategy recommended by renowned textbook writers (e.g. Cooper, 2017: Research synthesis and meta-analysis: A step-by-step approach). Some reports are incomplete, sometimes researchers don't have enough place to report all the data and sometimes the data a meta-analyst needs just isn't the main objective of the primary study. Thus, you can ask for additional information.

However, sometimes it is difficult to get the relevant data, because the authors:

- don't answer or answer slowly

- don't have the relevant data anymore.

You can increase the success rate by making your request easy to fulfill (specify the paper and pages you are referring to and what exactly do you need).

When conducting a meta-analysis it is a common practice to include unpublished data in order to avoid publication bias. Furthermore, gray literature doesn't necessarily have lower quality than studies published in peer-reviewed journals (Conn et al., 2003).

http://dx.doi.org/10.1097/00006199-200307000-00008

You can use unpublished data, however, it is better to mention in the M&M how do you access the data. Avoid repetitive data collection as sometimes unpublished data are reported in various formats (e.g. conferences paper, supplementary data, posters). If you were able to get information from author about specific data it is always a good idea to acknowledge them.   

Yes, unpublished data can be used. We recommend contacting the authors for any data that are not presented in the format you need to calculate an effect size for the meta analysis. In addition, we also recommend contacting experts in the field for additional studies not identified through your search process. They may have unpublished data (usually null results), that can help balance your true estimate of the effect at the population level. I agree with @Utsala ShresthaJust make sure that you identify the dates authors were contacted, how the unpublished data came in to your possession, etc.

Renowned textbook writers such as Cooper (2017) also stress that an unbiased meta-analysis should indeed include a comprehensive search for unpublished studies in what has been dubbed the gray literature or fugitive literature. There are many reasons why good studies may not be published, including that researchers may not submit papers without statistically significant findings for publication because they fear they will be rejected by publishers, or when they are submitted, they may face difficulties in getting them accepted (known as the "file drawer" problem). Other unpublished findings may result from studies by foundations and government agencies, but findings may be reported on their web sites. The findings from unpublished studies are an important part of the knowledge base and their absence from meta-analyses that include only published studies may lead to publication bias, which may be detected in a funnel plot.

Finally, studies with small samples may be more common in less prevalent disease conditions, or when it is difficult to recruit participants. These small sample studies may lack the statistical power to detect actual effects within the data, which may mean they are more likely to be unpublished. However, their data remains valid, and when pooled within a meta-analysis, may lead to statistically significant findings. Thus, the meta-analysis may lead to statistically significant findings across the pooled data even when none of the individual primary studies has sufficient statistical power to detect the effect.