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We generalize the Dunnett test to derive efficacy and futility boundaries for a flexible multi-arm multistage clinical trial for a normally distributed endpoint with known variance. We show that the boundaries control the familywise error rate in the strong sense. The method is applicable for any number of treatment arms, number of stages and number of patients per treatment per stage. It can be used for a wide variety of boundary types or rules derived from á-spending functions. Additionally, we show how sample size can be computed under a least favourable configuration power requirement and derive formulae for expected sample sizes.

We describe a general method for finding a confidence region for a parameter vector that is compatible with the decisions of a two-stage closed test procedure in an adaptive experiment. The closed test procedure is characterized by the fact that rejection or nonrejection of a null hypothesis may depend on the decisions for other hypotheses and the compatible confidence region will, in general, have a complex, nonrectangular shape. We find the smallest cross-product of simultaneous confidence intervals containing the region and provide computational shortcuts for calculating the lower bounds on parameters corresponding to the rejected null hypotheses. We illustrate the method with an adaptive phase II/III clinical trial.

Background Platform trials can evaluate the efficacy of several experimental treatments compared to a control. The number of experimental treatments is not fixed, as arms may be added or removed as the trial progresses. Platform trials are more efficient than independent parallel group trials because of using shared control groups. However, for a treatment entering the trial at a later time point, the control group is divided into concurrent controls, consisting of patients randomised to control when that treatment arm is in the platform, and non-concurrent controls, patients randomised before. Using non-concurrent controls in addition to concurrent controls can improve the trial’s efficiency by increasing power and reducing the required sample size, but can introduce bias due to time trends. Methods We focus on a platform trial with two treatment arms and a common control arm. Assuming that the second treatment arm is added at a later time, we assess the robustness of recently proposed model-based approaches to adjust for time trends when utilizing non-concurrent controls. In particular, we consider approaches where time trends are modeled either as linear in time or as a step function, with steps at time points where treatments enter or leave the platform trial. For trials with continuous or binary outcomes, we investigate the type 1 error rate and power of testing the efficacy of the newly added arm, as well as the bias and root mean squared error of treatment effect estimates under a range of scenarios. In addition to scenarios where time trends are equal across arms, we investigate settings with different time trends or time trends that are not additive in the scale of the model. Results A step function model, fitted on data from all treatment arms, gives increased power while controlling the type 1 error, as long as the time trends are equal for the different arms and additive on the model scale. This holds even if the shape of the time trend deviates from a step function when patients are allocated to arms by block randomisation. However, if time trends differ between arms or are not additive to treatment effects in the scale of the model, the type 1 error rate may be inflated. Conclusions The efficiency gained by using step function models to incorporate non-concurrent controls can outweigh potential risks of biases, especially in settings with small sample sizes. Such biases may arise if the model assumptions of equality and additivity of time trends are not satisfied. However, the specifics of the trial, scientific plausibility of different time trends, and robustness of results should be carefully considered.

Background Visceral leishmaniasis (VL) is a parasitic disease transmitted by sandflies and is fatal if left untreated. Phase II trials of new treatment regimens for VL are primarily carried out to evaluate safety and efficacy, while pharmacokinetic data are also important to inform future combination treatment regimens. The efficacy of VL treatments is evaluated at two time points, initial cure , when treatment is completed and definitive cure , commonly 6 months post end of treatment, to allow for slow response to treatment and detection of relapses. This paper investigates a generalization of the triangular design to impose a minimum sample size for pharmacokinetic or other analyses, and methods to estimate efficacy at extended follow-up accounting for the sequential design and changes in cure status during extended follow-up. Methods We provided R functions that generalize the triangular design to impose a minimum sample size before allowing stopping for efficacy. For estimation of efficacy at a second, extended, follow-up time, the performance of a shrinkage estimator (SHE), a probability tree estimator (PTE) and the maximum likelihood estimator (MLE) for estimation was assessed by simulation. Results The SHE and PTE are viable approaches to estimate an extended follow-up although the SHE performed better than the PTE: the bias and root mean square error were lower and coverage probabilities higher. Conclusions Generalization of the triangular design is simple to implement for adaptations to meet requirements for pharmacokinetic analyses. Using the simple MLE approach to estimate efficacy at extended follow-up will lead to biased results, generally over-estimating treatment success. The SHE is recommended in trials of two or more treatments. The PTE is an acceptable alternative for one-arm trials or where use of the SHE is not possible due to computational complexity. Trial registration NCT01067443 , February 2010.