  Background. Designing trials to reduce treatment duration is important in
several therapeutic areas, including TB and antibiotics. We recently proposed a
new randomised trial design to overcome some of the limitations of standard
two-arm non-inferiority trials. This DURATIONS design involves randomising
patients to a number of duration arms, and modelling the so-called
duration-response curve. This article investigates the operating
characteristics (type-1 and type-2 errors) of different statistical methods of
drawing inference from the estimated curve. Methods. Our first estimation
target is the shortest duration non-inferior to the control (maximum) duration
within a specific risk difference margin. We compare different methods of
estimating this quantity, including using model confidence bands, the delta
method and bootstrap. We then explore the generalisability of results to
estimation targets which focus on absolute event rates, risk ratio and gradient
of the curve. Results. We show through simulations that, in most scenarios and
for most of the estimation targets, using the bootstrap to estimate variability
around the target duration leads to good results for DURATIONS
design-appropriate quantities analogous to power and type-1 error. Using model
confidence bands is not recommended, while the delta method leads to inflated
type-1 error in some scenarios, particularly when the optimal duration is very
close to one of the randomised durations. Conclusions. Using the bootstrap to
estimate the optimal duration in a DURATIONS design has good operating
characteristics in a wide range of scenarios, and can be used with confidence
by researchers wishing to design a DURATIONS trial to reduce treatment
duration. Uncertainty around several different targets can be estimated with
this bootstrap approach.
