The World Health Organization (WHO) recommends that children with severe pneumonia (characterized by cough or difficult breathing, as well as lower chest wall indrawing) be hospitalized and treated with parenteral penicillin. Oral amoxicillin, if equally effective for treating severe pneumonia, would address challenges associated with providing parenteral therapy, including risk of transmission of bloodborne pathogens from contaminated needles, exposure to nosocomial pathogens during hospitalization, inadequate access to health care facilities, and cost. The recently completed multicenter international trial of oral amoxicillin versus parenteral penicillin for treatment of severe pneumonia demonstrated the equivalency of these agents in children with severe pneumonia. This article focuses on the challenges of designing an equivalence study and the threats to the validity of the trial results, particularly the implications of the bias toward finding equivalence when subjects are unlikely to respond to either study therapy. These considerations have implications for use of the Amoxicillin Penicillin Pneumonia International Study (APPIS) results in clinical practice and for potential modification of WHO treatment guidelines.