In current clinical oncology practice, it often takes weeks or months of cancer therapy until a response to treatment can be identified by evaluation of tumor size in images. It is hypothesized that changes in relative localization of the apoptosis imaging agent Tc-99m Annexin before and after the administration of chemotherapy may be useful as an early indicator of the success of therapy. The objective of this study was to determine the minimum relative change in tumor localization that could be confidently determined as an increased localization. A modified version of the Data Spectrum Anthropomorphic Torso phantom, in which four spheres could be positioned in the lung region, was filled with organ concentrations of Tc-99m representative of those observed in clinical imaging of Tc-99m Annexin. Five acquisitions of an initial sphere to lung concentration, and at concentrations of 1.1, 1.2, 1.3, and 1.4 times the initial concentration, were acquired at clinically realistic count levels. The acquisitions were reconstructed by filtered backprojection, ordered subset expectation maximization (OSEM) without attenuation compensation (AC), and OSEM with AC. Permutation methodology was used to create multiple region-of-interest count ratios from the five noise realizations at each concentration and between the elevated and initial concentrations. The resulting distributions were approximated by Gaussians, which were then used to estimate the likelihood of Type 1 and Type 2 Errors. It was determined that for the cases investigated, greater than a 20% to 30% or more increase was needed to confidently determine that an increase in localization had occurred depending on sphere size and reconstruction strategy.