Randomized response surface pathway design with odd response outcomes in a Latin Square designed study

Abstract

Background: Response surface pathway (RSP) design has been recently developed and described for dose-finding studies. The aim of this paper was to introduce and demonstrate additional procedures to strengthen and generalize the design and combine RSP with classical study design. Materials and methods: Nine bull calves and six heifer calves were included in an unbalanced 2 × 2 Latin Square (LSQ) designed study with large and small aperture bottle teats. The two LSQ sequences were performed with independent randomized three-level between-patient RSP design with an odd number of response classifications. The milk temperature window was 8°C–38°C with a mid temperature of 23°C. X-rays of the abdominal cavity were taken before, during, and immediately after intake of milk and recorded as “milk”, “trace”, or “no milk”. Based on the results of the first design level, the milk temperatures for five calves in the second design level were obtained by a randomization procedure. A similar procedure was performed for seven calves in the third design level. Adjustment of the dose from one design level to the next was based on a k-adjustment factor estimated to ensure coverage of the entire predefined dose window. Results: Starting with a low number of subjects and increasing this number with increasing design levels reduces the sample size without reducing the power. The suggested randomization procedure worked as expected. No milk in Rumen was recorded and minimum milk temperature (MMT) was estimated to be ≤8°C for both teats. The odd number of response categories increases the flexibility of RSP, enabling category redefinition in hindsight from “trace” to “uncertain”. After category redefinition, MMT for large bottle teat was estimated to be 14.3°C (95% confidence interval: 8.3–20.3°C), but 8°C for small. Conclusion: The suggested changes and additional procedures increase the strength and flexibility of the RSP design.