Comparative analysis of genetically-modified crops: Part 1. Conditional difference testing with a given genetic background.

The European Food Safety Authority (EFSA) mandates two sets of statistical tests in the comparative assessment of a genetically-modified (GM) crop: difference testing to demonstrate whether the GM crop is different from its appropriate non-traited control; and equivalence testing to demonstrate whether it is equivalent to conventional references with an history-of-safe-use. The equivalence testing method prescribed by EFSA confounds the so-called GM trait effect with genotypic differences between the reference varieties and non-traited control. Critically, these genotypic differences, which we define as a 'control background effect', are the result of conventional plant breeding. Thus, the result of EFSA equivalence testing often has little or nothing to do with the GM trait effect, which should be the sole focus of the comparative assessment. Here, an integrated method is introduced for both difference and equivalence testing that considers the differences of the three genotype groups (GM, control, and references) as a two-dimensional random variable. A novel statistical model is proposed, called the trait model, that treats the effects of the GM and control materials as fixed for their difference, and as random for their common background. For significance testing, the covariance structure of the three genotype groups is utilized to decompose the differences into the trait effect and the control background effect. The trait difference is then derived as a conditional mean, given the background effect. The comparative assessment can then focus on the conditional mean difference, which is independent of the control background effect. Furthermore, the trait model is flexible enough to include various types of genotype-by-environment (G×E) interactions inherent to the experimental design of the trial. Numerical evaluations and simulations show that this new method is substantially more efficient than the current EFSA method in reducing both Type I and Type II errors (protecting both the consumer and producer risk) after the background effect is removed from the test statistic, and successfully addresses two major criticisms (i.e. statistical model lack of G×E, and study-specific equivalence criterion) that have been raised.