  Background: trials to identify the minimal effective treatment duration are
needed in different therapeutic areas, including bacterial infections, TB and
Hepatitis--C. However, standard non-inferiority designs have several
limitations, including arbitrariness of non-inferiority margins, choice of
research arms and very large sample sizes.
  Methods: we recast the problem of finding an appropriate non-inferior
treatment duration in terms of modelling the entire duration-response curve
within a pre-specified range. We propose a multi-arm randomised trial design,
allocating patients to different treatment durations. We use fractional
polynomials and spline-based methods to flexibly model the duration-response
curve. We compare different methods in terms of a scaled version of the area
between true and estimated prediction curves. We evaluate sensitivity to key
design parameters, including sample size, number and position of arms.
  Results: a total sample size of $\sim 500$ patients divided into a moderate
number of equidistant arms (5-7) is sufficient to estimate the
duration-response curve within a $5\%$ error margin in $95\%$ of the
simulations. Fractional polynomials provide similar or better results than
spline-based methods in most scenarios.
  Conclusions: our proposed practical randomised trial design is an alternative
to standard non-inferiority designs, avoiding many of their limitations, and
yet being fairly robust to different possible duration-response curves. The
trial outcome is the whole duration-response curve, which could be used by
clinicians and policy makers to make informed decisions, facilitating a move
away from a forced binary hypothesis testing paradigm.
