Observational and interventional studies for HIV cure research often use single-copy assays to quantify rare entities in blood or tissue samples. Statistical analysis of such measurements presents challenges due to tissue sampling variability and frequent findings of 0 copies in the sample analysed. We examined four approaches to analysing such studies, reflecting different ways of handling observations of 0 copies: (A) replace observations of 0 copies with 1 copy; (B) add 1 to all observed numbers of copies; (C) treat observations of 0 copies as left-censored at 1 copy; and (D) leave the data unaltered and apply a method for count data, negative binomial regression. Because research seeks to estimate general patterns rather than individuals' values, we argue that unaltered use of 0 copies is suitable for research purposes and that altering those observations can introduce bias. When applied to a simulated study comparing preintervention to postintervention measurements within 12 participants, methods A-C showed more attenuation than method D in the estimated intervention effect, less chance of finding P < 0.05 for the intervention effect and a lower chance of including the true intervention effect within the 95% confidence interval. Application of the methods to actual data from a study comparing multiply-spliced HIV RNA among men and women estimated smaller differences by methods A-C than by method D. We recommend that negative binomial regression, which is readily available in many statistical software packages, be considered for analysis of studies of rare entities that are measured by single-copy assays.