A statistical simulation model for field testing of non-target organisms in environmental risk assessment of genetically modified plants

Abstract

Genetic modification of plants may result in unintended effects causing potentially adverse effects on the environment. A comparative safety assessment is therefore required by authorities, such as the European Food Safety Authority, in which the genetically modified plant is compared with its conventional counterpart. Part of the environmental risk assessment is a comparative field experiment in which the effect on non-target organisms is compared. Statistical analysis of such trials come in two flavors: difference testing and equivalence testing. It is important to know the statistical properties of these, for example, the power to detect environmental change of a given magnitude, before the start of an experiment. Such prospective power analysis can best be studied by means of a statistical simulation model. This paper describes a general framework for simulating data typically encountered in environmental risk assessment of genetically modified plants. The simulation model, available as Supplementary Material, can be used to generate count data having different statistical distributions possibly with excess-zeros. In addition the model employs completely randomized or randomized block experiments, can be used to simulate single or multiple trials across environments, enables genotype by environment interaction by adding random variety effects, and finally includes repeated measures in time following a constant, linear or quadratic pattern in time possibly with some form of autocorrelation. The model also allows to add a set of reference varieties to the GM plants and its comparator to assess the natural variation which can then be used to set limits of concern for equivalence testing. The different count distributions are described in some detail and some examples of how to use the simulation model to study various aspects, including a prospective power analysis, are provided.

Keywords: Difference testing; environmental risk assessment; equivalence testing; field trials; simulation model; statistical distributions; statistical power.

Figure 1

Examples of probabilities of statistical distributions for counts for means μ = 1, 4, and 10. The variance of the overdispersed Poisson distribution equals ϕμ. The variance of the negative binomial and Poisson-lognormal equals μ + ωμ².

Figure 2

Examples of probabilities of statistical distributions for presence/absence data for n = 16 with mean nπ and variance ωnπ (1 −π). For the binomial distribution, ω = 1.

Figure 3

Power of a likelihood ratio difference test with α = 0.05 for the negative binomial distribution with dispersion parameter ω, a mean μ for the comparator and a mean θμ for the GM plant for replication levels N = 6 (black), 10 (red), 20 (green), and 40 (blue).

Figure 4

Power of a likelihood ratio difference test with α = 0.05 for negative binomial data with dispersion parameter ω, a mean μ for the comparator, and a mean θμ for the GM plant for replication level N = 40 when analyzed employing a negative binomial model (black), a quasi-Poisson model (red), and a log transformation (green).

Figure 5

95% likelihood ratio confidence intervals for the ratio of the Poisson means of the GM plant and the comparator when the underlying mean of both is μ = 5 and various numbers of replication N. The red vertical lines denote the artificial equivalence limits set at 1/2 and 2.

Figure 6

Power of a likelihood ratio difference test with α = 0.05 for negative binomial data with overdispersion parameter ω = 0.25 and additional excess-zeros with probability δ = 0 (black), 0.1 (red), 0.2 (blue), and 0.5 (green). The comparator has mean μ(1 −δ), and the GM plant has a mean of 2μ(1 − δ).

Figure 7

Power of a likelihood ratio difference test for Poisson-lognormal data with overdispersion parameter ω = 0.25 and a single observation (black), the sum of 5 independent observations (red), and the sum of 5 dependent observations (blue). The mean of both the comparator and the GM plant follows a quadratic polynomial on the log scale with a maximum mean count of μ for the comparator and 2μ for the GM plant (see text).