Three recent papers have provided sequential methods for meta-analysis of two-treatment randomized clinical trials. This paper provides an alternate approach that has three desirable features. First, when carried out prospectively (i.e., we only have the results up to the time of our current analysis), we do not require knowledge of the information fraction (the fraction of the total information that is available at each analysis). Second, the methods work even if the expected values of the effect sizes vary from study to study. Finally, our methods have easily interpretable metrics that make sense under changing effect sizes. Although the other published methods can be adapted to be "group sequential" (recommended), meaning that a set number and timing of looks are specified, rather than looking after every trial, ours can be used in both a continuous or group sequential manner. We provide an example on the role of probiotics in preventing necrotizing enterocolitis in preterm infants.