We discuss in this article methods for analyzing lognormal data that may include zeros. Specifically, we are interested in interval estimation for the ratio or difference of the population means. We propose here two generalized pivotal (GP) approaches: a ``true'' GP method and an ``approximate'' GP method. Additionally, we propose two likelihood-based approaches: a signed log-likelihood ratio (SLLR) method and a modified SLLR method. Our simulation studies suggest that the approximate generalized pivotal approach outperforms all other known methods; it results in highly accurate coverage frequencies and fairly low bias, even in small sample settings.
Chen, Yea-Hung and Zhou, Xiao-Hua, "Generalized confidence intervals for the ratio or difference of two means for lognormal populations with zeros" (September 2006). UW Biostatistics Working Paper Series. Working Paper 296.