Statistical procedures for testing hypotheses of equivalence in the safety evaluation of a genetically modified crop

SUMMARYSafety evaluation of a genetically modified crop entails assessing its equivalence to conventional crops under multi-site randomized block field designs. Despite mounting petitions for regulatory approval, there lack a scientifically sound and powerful statistical method for establishing equivalence. The current paper develops and validates two procedures for testing a recently identified class of equivalence uniquely suited to crop safety. One procedure employs the modified large sample (MLS) method; the other is based on generalized pivotal quantities (GPQs). Because both methods were originally created under balanced designs, common issues associated with incomplete and unbalanced field designs were addressed by first identifying unfulfilled theoretical assumptions and then replacing them with user-friendly approximations. Simulation indicated that the MLS procedure could be very conservative in many occasions irrespective of the balance of the design; the GPQ procedure was mildly liberal with its type I error rate near the nominal level when the design is balanced. Additional pros and cons of these two procedures are also discussed. Their utility is demonstrated in a case study using summary statistics derived from a real-world dataset.