Time to the first medical treatment of farmed salmon to control salmon lice, a survival analysis approach.

The spread of salmon lice has long been and continues to be an increasing problem for the fish farming industry, causing economic and environmental problems. In this thesis, in cooperation with the Norwegian Veterinary Institute, I wished to increase the understanding of this problem. The main interest was analysing what factors that cause lice to appear and require fish to be treated against lice, and whether those factors can be controlled by fish farmers. By using data from the Aquaculture Registry and the Aquaculture Database I was able to construct a dataset including many of the explanatory variables that were essential, and that were worth consideration in regards to appearance of salmon lice. The modelling approach used in this study has been multiple Cox regression. This method is widely used in survival analyses. I analysed the hazard rates related to first bath treatments against salmon lice at the farms along the Norwegian coast, and used them to model the "survival" times, i.e. time till treatment. A general Cox model is constructed by using proportional hazard assumptions, and therefore the covariates in a Cox analysis must remain fixed throughout study. However, in real life, many potential explanatory variables that can be obtained from the Aquaculture Database vary with time since the reported measurements are delivered each week. For this reason I first constructed a general Cox model with all covariate values collected at time of stocking, and then extended the constructed model to include time-dependent covariates to explore how time-dependency in the covariates affect the treatment hazard rate and whether the results change. The results showed that factors mostly addressing to the neighbor's situation (distances, neighbor's lice amount and the infection spread from them) are most significant for time till first bath treatment. Seawater temperature and amount of fish at the farm of interest also appeared to be significant in the analysis, but only when they were allowed to vary each month. I could also see that the lice situations are different in different parts of Norway, and vary from one year to the next. Both constructed models produced similar results, and a validation of the Cox model indicated that the model is proper for the dataset