A lack of information exists about the health issues of lesbian, gay, bisexual, transgender, and queer (LGBTQ) people who are often excluded from national demographic assessments, health studies, and clinical trials. As a result, medical experts and researchers lack a holistic understanding of the health disparities facing these populations. Fortunately, publicly available social media data such as Twitter data can be utilized to support the decisions of public health policy makers and managers with respect to LGBTQ people. This research employs a computational approach to collect tweets from gay users on health-related topics and model these topics. To determine the nature of health-related information shared by men who have sex with men on Twitter, we collected thousands of tweets from 177 active users. We sampled these tweets using a framework that can be applied to other LGBTQ sub-populations in future research. We found 11 diseases in 7 categories based on ICD 10 that are in line with the published studies and official reports.