Sub-studies addressing specific research questions may necessitate selecting a random sample from different eligibility groups of The World Trade Center Health Registry (WTCHR) for estimating population parameters like means or proportions. However, many enrollees are members of multiple eligibility groups. This complicates sample selection as well as the construction of an estimate for a population parameter. In such a situation, Osahan (2018: Model Assisted Statistics and Applications) recently proposed three two-stage sampling strategies in overlapping eligibility groups from the WTCHR and compared their estimates for bias and efficiency. Single-stage sampling strategies are always preferred over two-stage sampling strategies for their convenience of use. Thus, the goal of the present investigation is to propose four single-stage sampling strategies in overlapping eligibility groups of the WTCHR population to estimate a population parameter (mean and/ or proportion). Comparison of the sampling strategies, using WTCHR's overlapping eligibility groups, will be shown in terms of their bias, efficiency and convenience.