Development of a randomized two-dimensional response surface pathway design with two interventional and one response variables

Background: The response surface pathway (RSP) design obtains a random walk pathway, does not need an assumed statistical model, reduces the sample size without reducing accuracy, and covers predefined dose windows. RSP includes one interventional and one result variable without random allocation of doses between design levels. This study aims to present RSP with two interventional and one result variables, combining between- and within-patient models and introduce a randomization procedure in a clinical situation. Methods: To estimate optimal efficacy dose and spreading duration of particulate CaO powder, material consisting of 18 net pens with salmon indicated for lice treatment was required. The study was performed as a randomized “between-patient” RSP designed trial with CaO dose as the interventional variable and percentage lice reduction as the outcome. Each net pen received three treatments with 24-hour intervals of unchanged CaO dose and a starting spreading duration of 2 hours. The change in spreading duration followed a “within-patient” RSP procedure with percentage lice reduction as the outcome. In all participating fish farms, one net pen remained untreated and was used as control. Results: The minimum and the optimal efficacy doses were estimated to be 6.1 g/kg and 8.5 g/kg biomass (bm), respectively. In order to optimize lice reduction, the spreading duration increases with increasing CaO dose. The minimum efficacy combination was predicted to be 6.1 g/kg bm administered in 2:00 (h:mm) and the optimal to be 8.5 g/kg bm in 3:00. Three of the seven net pens allocated to 7.4 g/kg bm erroneously received 8.5 g/kg and due to weather circumstances three other net pens became untreated. Consequently, accuracy of the predictions was slightly reduced. Conclusion: The two-dimensional RSP design combining between- and within-patient RSP detected its power and predicted the two interventional variables to obtain minimum and optimal efficacy with sufficient accuracy.