Statistical modelling of neighbor treatment effects in aquaculture clinical trials

In the design of clinical trials involving fish observed over time in tanks, there may be advantages in housing several treatment groups within the same tank. In particular, such "within-tank" designs will be more efficient than designs with treatment groups in separate tanks when substantial between-tank variability is expected. One potential problem with within-tank designs is that it may not be possible to include all treatments in one tank; in statistical terms this means that the blocks (tanks) are incomplete. In incomplete block designs, there may be a concern that the treatments present in the same tank (denoted here as "neighbors") affect each other in their performance; thus the need for an assessment of neighbor effects. In this paper, we propose two statistical approaches to assess and account for neighbor effects. The first approach is based on a non-linear mixed model and the second involves cross-classified and multiple membership models. Both approaches are illustrated on simulated data as well as data from a clinical ISAV (Infectious Salmon Anaemia Virus) trial; corresponding computer code is available online. The simulation studies demonstrated that both models show promise in capturing neighbor treatment effects of the type assumed for the models, whenever such neighbor effects are of at least moderate magnitude. In the absence of or with low magnitudes of neighbor effects, the non-linear mixed model faced numerical challenges and produced noisy results. One version of the cross-classified and multiple membership model was shown to depend strongly on prior information about variance-covariance parameters for datasets similar to the ISAV data. Analyses of the ISAV trial data by both models did not provide any evidence of substantial neighbor effects.