Optimal futility stopping boundaries for binary endpoints.

BACKGROUND: Group sequential designs incorporating the option to stop for futility at the time point of an interim analysis can save time and resources. Thereby, the choice of the futility boundary importantly impacts the design's resulting performance characteristics, including the power and probability to correctly or wrongly stop for futility. Several authors contributed to the topic of selecting good futility boundaries. For binary endpoints, Simon's designs (Control Clin Trials 10:1-10, 1989) are commonly used two-stage designs for single-arm phase II studies incorporating futility stopping. However, Simon's optimal design frequently yields an undesirably high probability of falsely declaring futility after the first stage, and in Simon's minimax design often a high proportion of the planned sample size is already evaluated at the interim analysis leaving only limited benefit in case of an early stop. METHODS: This work focuses on the optimality criteria introduced by Schüler et al. (BMC Med Res Methodol 17:119, 2017) and extends their approach to binary endpoints in single-arm phase II studies. An algorithm for deriving optimized futility boundaries is introduced, and the performance of study designs implementing this concept of optimal futility boundaries is compared to the common Simon's minimax and optimal designs, as well as modified versions of these designs by Kim et al. (Oncotarget 10:4255-61, 2019). RESULTS: The introduced optimized futility boundaries aim to maximize the probability of correctly stopping for futility in case of small or opposite effects while also setting constraints on the time point of the interim analysis, the power loss, and the probability of stopping the study wrongly, i.e. stopping the study even though the treatment effect shows promise. Overall, the operating characteristics, such as maximum sample size and expected sample size, are comparable to those of the classical and modified Simon's designs and sometimes better. Unlike Simon's designs, which have binding stopping rules, the optimized futility boundaries proposed here are not adjusted to exhaust the full targeted nominal significance level and are thus still valid for non-binding applications. CONCLUSIONS: The choice of the futility boundary and the time point of the interim analysis have a major impact on the properties of the study design. Therefore, they should be thoroughly investigated at the planning stage. The introduced method of selecting optimal futility boundaries provides a more flexible alternative to Simon's designs with non-binding stopping rules. The probability of wrongly stopping for futility is minimized and the optimized futility boundaries don't exhibit the unfavorable properties of an undesirably high probability of falsely declaring futility or a high proportion of the planned sample evaluated at the interim time point.

Correction to: Optimality criteria for futility stopping boundaries for group sequential designs with a continuous endpoint.

An amendment to this paper has been published and can be accessed via the original article.

Optimality criteria for futility stopping boundaries for group sequential designs with a continuous endpoint.

BACKGROUND: In clinical trials with fixed study designs, statistical inference is only made when the trial is completed. In contrast, group sequential designs allow an early stopping of the trial at interim, either for efficacy when the treatment effect is significant or for futility when the treatment effect seems too small to justify a continuation of the trial. Efficacy stopping boundaries based on alpha spending functions have been widely discussed in the statistical literature, and there is also solid work on the choice of adequate futility stopping boundaries. Still, futility boundaries are often chosen with little or completely without theoretical justification, in particular in investigator initiated trails. Some authors contributed to fill this gap. In here, we rely on an idea of Schüler et al. (2017) who discuss optimality criteria for futility boundaries for the special case of trials with (multiple) time-to-event endpoints. Their concept can be adopted to define "optimal" futility boundaries (with respect to given performance indicators) for continuous endpoints. METHODS: We extend Schülers' definition for "optimal" futility boundaries to the most common study situation of a single continuous primary endpoint compared between two groups. First, we introduce the analytic algorithm to derive these futility boundaries. Second, the new concept is applied to a real clinical trial example. Finally, the performance of a study design with an "optimal" futility boundary is compared to designs with arbitrarily chosen futility boundaries. RESULTS: The presented concept of deriving futility boundaries allows to control the probability of wrongly stopping for futility, that means stopping for futility even if the treatment effect is promizing. At the same time, the loss in power is also controlled by this approach. Moreover, "optimal" futility boundaries improve the probability of correctly stopping for futility under the null hypothesis of no difference between two groups. CONCLUSIONS: The choice of futility boundaries should be thoroughly investigated at the planning stage. The sometimes met, arbitrary choice of futility boundaries can lead to a substantial negative impact on performance. Applying futility boundaries with predefined optimization criteria increases efficiency of group sequential designs. Other optimization criteria than proposed in here might be incorporated.

Treosulfan vs busulfan conditioning for allogeneic bmt in children with nonmalignant disease: a randomized phase 2 trial.

Optimal conditioning prior to allogeneic hematopoietic stem cell transplantation for children with non-malignant diseases is subject of ongoing research. This prospective, randomized, phase 2 trial compared safety and efficacy of busulfan with treosulfan based preparative regimens. Children with non-malignant diseases received fludarabine and either intravenous (IV) busulfan (4.8 to 3.2 mg/kg/day) or IV treosulfan (10, 12, or 14 g/m2/day). Thiotepa administration (2 × 5 mg/kg) was at the investigator's discretion. Primary endpoint was freedom from transplantation (treatment)-related mortality (freedom from TRM), defined as death between Days -7 and +100. Overall, 101 patients (busulfan 50, treosulfan 51) with at least 12 months follow-up were analyzed. Freedom from TRM was 90.0% (95% CI: 78.2%, 96.7%) after busulfan and 100.0% (95% CI: 93.0%, 100.0%) after treosulfan. Secondary outcomes (transplantation-related mortality [12.0% versus 3.9%]) and overall survival (88.0% versus 96.1%) favored treosulfan. Graft failure was more common after treosulfan (n = 11), than after busulfan (n = 2) while all patients were rescued by second procedures except one busulfan patient. CTCAE Grade III adverse events were similar in both groups. This study confirmed treosulfan to be an excellent alternative to busulfan and can be safely used for conditioning treatment in children with non-malignant disease.

Population pharmacokinetic modeling of treosulfan and rationale for dose recommendation in children treated for conditioning prior to allogeneic hematopoietic stem cell transplantation.

Intravenously infused treosulfan was evaluated in adult and pediatric patients for conditioning regimen prior to allogeneic hematopoietic stem cell transplantation. A population pharmacokinetic (PK) model was initially developed on 116 adult and pediatric PK profiles from historical trials, to support treosulfan dose recommendations for children in 2 prospective trials. The aim was to assess and update the initial population PK model by inclusion of additional 83 pediatric PK profiles from these 2 trials. The final population PK model was 2-compartmental with dosing in the central compartment, linear elimination, and inter-compartmental clearance. Inter-individual variability was included on clearance (CL), central volume (V1), peripheral volume (V2), and inter-compartmental clearance (Q). The final model described an effect of the body surface area (BSA) on CL, V1, V2, and Q. The final model resulted in a modified dose recommendation for children and advises treosulfan doses of 10 g/m2, 12 g/m2, and 14 g/m2 for BSAs of <0.4 m2, ≥0.4 to <0.9 m2, and ≥0.9 m2, respectively. This simplified BSA-dependent dose recommendation was developed for children, ensuring a well comparable treosulfan exposure as a dose of 14 g/m2 in adults - irrespective of their age and without applying individual therapeutic drug monitoring.