We performed a research in the large-scale randomized design, based on the result of a pilot study in the small, non-randomized design. When writing the manuscript, the expression in the sections of introduction, methods and discussion are inevitable to be similar or duplicated with the ones of the manuscript for the pilot study. Even if we state the background (like the 1st sentence in this question), is this submission regarded as a duplicate submission?
I don't think it will be considered a duplicate submission if you are transparent. You should explain the situation in the cover letter and mention right at the beginning of your paper that this study is based on an earlier pilot study and cite the source. You should also discuss the pilot study in the introduction and mention how it led to the large scale study. If you are clear about this from the outset, the larger study is likely to be regarded as a follow up or a second phase of the pilot study rather than a duplication.
Related reading:
- What can be the reason behind two papers by the same author having similar content?
- Can two papers with same data but different analysis be considered duplicate publication?
- Duplicate publications and simultaneous submissions