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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.