Two-Stage Single-Arm Trials Are Rarely Analyzed Effectively or Reported Adequately

When is a two-stage single-arm trial efficient? An evaluation of the impact of outcome delay

BACKGROUND

Simon's two-stage design is a widely used adaptive design, particularly in phase II oncology trials due to its simplicity and efficiency. However, its efficiency can be adversely affected when the primary end-point takes time to observe, as is common in practice.

METHODS

We propose an optimal design, taking the delay in observing treatment outcome into consideration and compare the efficiency gained from using Simon's design over a single-stage design for real-life oncology trials. Based on the results, we provide a general rule-of-thumb for determining whether a two-stage single-arm design can provide any added advantage over a single-stage design, given the recruitment rate and primary end-point length.

RESULTS

We observed an average 15-30% loss in the estimated efficiency gain in real oncology trials that used Simon's design due to the delay in observing the treatment outcome. The delay-optimal design provides some advantage over Simon's design in terms of reduced sample size when the delay is large compared to the recruitment length.

DISCUSSION

Simon's two-stage design provides large benefit over a single-stage design, in terms of reduced sample size, when the primary end-point length is no more than 10% of the total recruitment time. It provides no efficiency advantage when this ratio is above 50%.

Optimised point estimators for multi-stage single-arm phase II oncology trials

The uniform minimum variance unbiased estimator (UMVUE) is, by definition, a solution to removing bias in estimation following a multi-stage single-arm trial with a primary dichotomous outcome. However, the UMVUE is known to have large residual mean squared error (RMSE). Therefore, we develop an optimisation approach to finding estimators with reduced RMSE for many response rates, which attain low bias. We demonstrate that careful choice of the optimisation parameters can lead to an estimator with often substantially reduced RMSE, without the introduction of appreciable bias.