Multiarm, multistage randomized controlled trials with stopping boundaries for efficacy and lack of benefit: An update to nstage

Royston et al.’s (2011, Trials 12: 81) multiarm, multistage (MAMS) framework for the design of randomized clinical trials uses intermediate outcomes to drop research arms early for lack of benefit at interim stages, increasing efficiency in multiarm designs. However, additionally permitting interim evaluation of efficacy on the primary outcome measure could increase adoption of the design and result in practical benefits, such as savings in patient numbers and cost, should any efficacious arm be identified early. The nstage command, which aids the design of MAMS trial designs, has been updated to support this methodological extension. Operating characteristics can now be calculated for a design with binding or nonbinding stopping rules for lack of benefit and with efficacy stopping boundaries. An additional option searches for a design that strongly controls the familywise error rate at the desired level. We illustrate how the new features can be used to design a trial with the drop-down menu, using the original comparisons from the MAMS trial STAMPEDE as an example. The new functionality of the command will serve a broader range of trial objectives and increase efficiency of the design and thus increase uptake of the MAMS design in practice

Impact of lack-of-benefit stopping rules on treatment effect estimates of two-arm multi-stage (TAMS) trials with time to event outcome

In 2011, Royston et al. described technical details of a two-arm, multi-stage (TAMS) design. The design enables a trial to be stopped part-way through recruitment if the accumulating data suggests a lack of benefit of the experimental arm. Such interim decisions can be made using data on an available 'intermediate' outcome. At the conclusion of the trial, the definitive outcome is analyzed. Typical intermediate and definitive outcomes in cancer might be progression-free and overall survival, respectively. In TAMS designs, the stopping rule applied at the interim stage(s) affects the sampling distribution of the treatment effect estimator, potentially inducing bias that needs addressing

Type I error rates of multi-arm multi-stage clinical trials: strong control and impact of intermediate outcomes

BACKGROUND: The multi-arm multi-stage (MAMS) design described by Royston et al. [Stat Med. 2003;22(14):2239-56 and Trials. 2011;12:81] can accelerate treatment evaluation by comparing multiple treatments with a control in a single trial and stopping recruitment to arms not showing sufficient promise during the course of the study. To increase efficiency further, interim assessments can be based on an intermediate outcome (I) that is observed earlier than the definitive outcome (D) of the study. Two measures of type I error rate are often of interest in a MAMS trial. Pairwise type I error rate (PWER) is the probability of recommending an ineffective treatment at the end of the study regardless of other experimental arms in the trial. Familywise type I error rate (FWER) is the probability of recommending at least one ineffective treatment and is often of greater interest in a study with more than one experimental arm. METHODS: We demonstrate how to calculate the PWER and FWER when the I and D outcomes in a MAMS design differ. We explore how each measure varies with respect to the underlying treatment effect on I and show how to control the type I error rate under any scenario. We conclude by applying the methods to estimate the maximum type I error rate of an ongoing MAMS study and show how the design might have looked had it controlled the FWER under any scenario. RESULTS: The PWER and FWER converge to their maximum values as the effectiveness of the experimental arms on I increases. We show that both measures can be controlled under any scenario by setting the pairwise significance level in the final stage of the study to the target level. In an example, controlling the FWER is shown to increase considerably the size of the trial although it remains substantially more efficient than evaluating each new treatment in separate trials. CONCLUSIONS: The proposed methods allow the PWER and FWER to be controlled in various MAMS designs, potentially increasing the uptake of the MAMS design in practice. The methods are also applicable in cases where the I and D outcomes are identical

Quantifying the uptake of user-written commands over time

A major factor in the uptake of new statistical methods is the availability of user-friendly software implementations. One attractive feature of Stata is that users can write their own commands and release them to other users via Statistical Software Components at Boston College. Authors of statistical programs do not always get adequate credit, because programs are rarely cited properly. There is no obvious measure of a program’s impact, but researchers are under increasing pressure to demonstrate the impact of their work to funders. In addition to encouraging proper citation of software, the number of downloads of a user-written package can be regarded as a measure of impact over time. In this article, we explain how such information can be accessed for any month from July 2007 and summarized using the new ssccount command

The extension of total gain (TG) statistic in survival models: Properties and applications

Background: The results of multivariable regression models are usually summarized in the form of parameter estimates for the covariates, goodness-of-fit statistics, and the relevant p-values. These statistics do not inform us about whether covariate information will lead to any substantial improvement in prediction. Predictive ability measures can be used for this purpose since they provide important information about the practical significance of prognostic factors. R 2 -type indices are the most familiar forms of such measures in survival models, but they all have limitations and none is widely used. Methods: In this paper, we extend the total gain (TG) measure, proposed for a logistic regression model, to survival models and explore its properties using simulations and real data. TG is based on the binary regression quantile plot, otherwise known as the predictiveness curve. Standardised TG ranges from 0 (no explanatory power) to 1 ('perfect' explanatory power). Results: The results of our simulations show that unlike many of the other R 2 -type predictive ability measures, TG is independent of random censoring. It increases as the effect of a covariate increases and can be applied to different types of survival models, including models with time-dependent covariate effects. We also apply TG to quantify the predictive ability of multivariable prognostic models developed in several disease areas. Conclusions: Overall, TG performs well in our simulation studies and can be recommended as a measure to quantify the predictive ability in survival models

Facilities for optimizing and designing multiarm multistage (MAMS) randomized controlled trials with binary outcomes

We introduce two commands, nstagebin and nstagebinopt, that can be used to facilitate the design of multiarm multistage (MAMS) trials with binary outcomes. MAMS designs are a class of efficient and adaptive randomized clinical trials that have successfully been used in many disease areas, including cancer, tuberculosis, maternal health, COVID-19, and surgery. The nstagebinopt command finds a class of efficient “admissible” designs based on an optimality criterion using a systematic search procedure. The nstagebin command calculates the stagewise sample sizes, trial timelines, and overall operating characteristics of MAMS designs with binary outcomes. Both commands allow the use of Dunnett’s correction to account for multiple testing. We also use the ROSSINI 2 MAMS design, an ongoing MAMS trial in surgical wound infection, to illustrate the capabilities of both commands. The new commands facilitate the design of MAMS trials with binary outcomes where more than one research question can be addressed under one protocol

Assessing the impact of efficacy stopping rules on the error rates under the multi-arm multi-stage framework

BACKGROUND: The multi-arm multi-stage framework uses intermediate outcomes to assess lack-of-benefit of research arms at interim stages in randomised trials with time-to-event outcomes. However, the design lacks formal methods to evaluate early evidence of overwhelming efficacy on the definitive outcome measure. We explore the operating characteristics of this extension to the multi-arm multi-stage design and how to control the pairwise and familywise type I error rate. Using real examples and the updated nstage program, we demonstrate how such a design can be developed in practice. METHODS: We used the Dunnett approach for assessing treatment arms when conducting comprehensive simulation studies to evaluate the familywise error rate, with and without interim efficacy looks on the definitive outcome measure, at the same time as the planned lack-of-benefit interim analyses on the intermediate outcome measure. We studied the effect of the timing of interim analyses, allocation ratio, lack-of-benefit boundaries, efficacy rule, number of stages and research arms on the operating characteristics of the design when efficacy stopping boundaries are incorporated. Methods for controlling the familywise error rate with efficacy looks were also addressed. RESULTS: Incorporating Haybittle–Peto stopping boundaries on the definitive outcome at the interim analyses will not inflate the familywise error rate in a multi-arm design with two stages. However, this rule is conservative; in general, more liberal stopping boundaries can be used with minimal impact on the familywise error rate. Efficacy bounds in trials with three or more stages using an intermediate outcome may inflate the familywise error rate, but we show how to maintain strong control. CONCLUSION: The multi-arm multi-stage design allows stopping for both lack-of-benefit on the intermediate outcome and efficacy on the definitive outcome at the interim stages. We provide guidelines on how to control the familywise error rate when efficacy boundaries are implemented in practice