Drop-the-Losers Design: Binomial Case

Point estimation for adaptive trial designs II: Practical considerations and guidance

In adaptive clinical trials, the conventional end-of-trial point estimate of a treatment effect is prone to bias, that is, a systematic tendency to deviate from its true value. As stated in recent FDA guidance on adaptive designs, it is desirable to report estimates of treatment effects that reduce or remove this bias. However, it may be unclear which of the available estimators are preferable, and their use remains rare in practice. This article is the second in a two-part series that studies the issue of bias in point estimation for adaptive trials. Part I provided a methodological review of approaches to remove or reduce the potential bias in point estimation for adaptive designs. In part II, we discuss how bias can affect standard estimators and assess the negative impact this can have. We review current practice for reporting point estimates and illustrate the computation of different estimators using a real adaptive trial example (including code), which we use as a basis for a simulation study. We show that while on average the values of these estimators can be similar, for a particular trial realization they can give noticeably different values for the estimated treatment effect. Finally, we propose guidelines for researchers around the choice of estimators and the reporting of estimates following an adaptive design. The issue of bias should be considered throughout the whole lifecycle of an adaptive design, with the estimation strategy prespecified in the statistical analysis plan. When available, unbiased or bias-reduced estimates are to be preferred.

Statistical tests for two-stage adaptive seamless design using short- and long-term binary outcomes

The adaptive seamless design combining phases II and III into a single trial has been shown growing interest for improving the efficiency of drug development, becoming the most frequent adaptive design type. It typically consists of two stages, the trial objectives being often different in each stage. The primary objectives are to select optimal experimental treatment group(s) in the first stage and compare the efficacy between the selected treatment and control groups in the second stage. In this article, we focus on a two-stage adaptive seamless design, for which treatment selection is based on the short-term binary endpoint and treatment comparison is based on the long-term binary endpoint. We thus propose an exact conditional test as a final analysis, based on the bivariate binomial distribution and given the selected treatment with the most promising short-term endpoint response rate from an interim analysis. Additionally, the mid- p $$ p $$ approach is incorporated to improve conservativeness for an exact test. Simulation studies were conducted to compare the proposed methods with a method based on the combination test. The proposed exact method controlled for type I error rate at the nominal level, regardless of the number of initial treatments or the correlation between short- and long-term endpoints. In terms of the treatment comparison power, the proposed methods are more powerful than that based on the combination test in the scenarios, with only one treatment being effective.

Role of peer support in a hepatitis C elimination programme

Many people with chronic hepatitis C infection don't engage in treatment. To eliminate hepatitis C and avoid health inequalities therapy must be provided to everyone. In other diseases peers with lived experience of the condition have improved care but, for hepatitis C, studies have not shown unequivocal benefit. We completed a retrospective analysis of the English National Health Service treatment registry comparing treatment networks with and without peers using Bayesian Poisson (for count outcomes) or Bayesian Binomial (for proportion outcomes) mixed effects models with time fixed effects. For each outcome, we estimated relative ratio (RR-Poisson model) or odds ratio (Odds Ratio (OR)-Binomial model) between peer and non-peer networks. We analysed 30,729 patients within 20 operational delivery networks. In networks with peers there was an increase in the number of people initiating therapy (RR 1.12 95%, credible interval 1.02-1.21) and an increase in the proportion completing therapy (OR 2.45 95%, credible interval 1.49-3.84). However, we saw no change in proportions of people using drugs who initiated therapy nor any significant change in virological response (OR 1.14 95% credible interval 0.979-1.36). We repeated the analysis looking at the impact of peers two months after they had been introduced, when they had established networks of contacts, and saw an increase in the proportion of people treated in addiction services. In treating patients with chronic hepatitis C infection the inclusion of peer supporters may increase the number of people who initiate and complete antiviral therapy.

A two-stage drop-the-losers design for time-to-event outcome using a historical control arm

Phase II immuno-oncology clinical trials screen for efficacy an increasing number of treatments. In rare cancers, using historical control data is a pragmatic approach for speeding up clinical trials. The drop-the-losers design allows dropping off ineffective arms at interim analyses. We extended the original drop-the-losers design for a time-to-event outcome using a historical control through the one-sample log-rank statistic. Simulated trials featured three arms at the first stage, one at the second stage, nine scenarios, eight sample sizes with 5%- and 10%- nominal family-wise error rate (FWER). A numerical algorithm is provided to solve power calculations at the design stage. Our design was compared with a group of three independent single-arm trials (fixed design) with and without correction for multiplicity. Our design allowed strict control of the FWER at nominal levels while the misspecification of survival distribution and fixed design inflated the FWER up to three times the nominal level. The empirical power of our design increased with the sample size, the treatment effect and the number of effective treatments and dropped when more patients were recruited at the second stage. The fixed design with correction showed comparable power, while our design advantageously included more patients to the most promising arm. Recommendations for future applications are given. By taking advantage of the use of historical control data and a time-to-event outcome, the drop-the-losers design is a promising tool to meet the challenge of improving phase II clinical trials in immuno-oncology.

Design and analysis of drop-the-losers studies using binary endpoints in the rare disease setting

The drop-the-losers design combines a phase 2 trial of k treatments and a confirmatory phase 3 trial under a single adaptive protocol, thereby gaining efficiency over a traditional clinical development approach. Such designs may be particularly useful in the rare disease setting, where conserving sample size is paramount, and control arms may not be feasible. We propose an unconditional exact likelihood (UEL) testing and inference procedure for these designs for a binary endpoint using small sample sizes, comparing its operating characteristics to existing methods. Additional practical considerations are evaluated, including the choice of stagewise sample sizes and effect of ties.

Correcting for bias in the selection and validation of informative diagnostic tests

When developing a new diagnostic test for a disease, there are often multiple candidate classifiers to choose from, and it is unclear if any will offer an improvement in performance compared with current technology. A two-stage design can be used to select a promising classifier (if one exists) in stage one for definitive validation in stage two. However, estimating the true properties of the chosen classifier is complicated by the first stage selection rules. In particular, the usual maximum likelihood estimator (MLE) that combines data from both stages will be biased high. Consequently, confidence intervals and p-values flowing from the MLE will also be incorrect. Building on the results of Pepe et al. (SIM 28:762–779), we derive the most efficient conditionally unbiased estimator and exact confidence intervals for a classifier's sensitivity in a two-stage design with arbitrary selection rules; the condition being that the trial proceeds to the validation stage. We apply our estimation strategy to data from a recent family history screening tool validation study by Walter et al. (BJGP 63:393–400) and are able to identify and successfully adjust for bias in the tool's estimated sensitivity to detect those at higher risk of breast cancer. © 2015 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

Interim treatment selection with a flexible selection margin in clinical trials

When several treatment arms are administered along with a control arm in a trial, dropping the non-promising treatments at an early stage helps to save the resources and expedite the trial. In such adaptive designs with treatment selection, a common selection rule is to pick the most promising treatment, for example, the treatment with the numerically highest mean response, at the interim stage. However, with only a single treatment selected for final evaluation, this selection rule is often too inflexible. We modified this interim selection rule by introducing a flexible selection margin to judge the acceptable treatment difference. Another treatment could be selected at the interim stage in addition to the empirically best one if the differences of the observed treatment effect between them do not exceed this margin. We considered the study starting with two treatment arms and a control arm. We developed hypothesis testing procedures to assess the selected treatment(s) by taking into account the interim selection process. Compared with the one-winner selection designs, the modified selection rule makes the design more flexible and practical.

Estimation of treatment effect following a clinical trial with adaptive design

Parameter estimation following an adaptive design or group sequential design has been extremely challenging due to potential random high from its face value estimate. In this paper, we introduce a new framework to model clinical trial data flow based on a marked point process (MPP). The MPP model allows us to use methods of stochastic calculus for analyses of any adaptive clinical trial. As an example, we apply this method to a two stage treatment selection design and derive a procedure to estimate the treatment effect. Numerical examples will be used to evaluate the performance of the proposed procedure.

Parameter estimation following an adaptive treatment selection trial design

Two-stage, drop-the-losers designs for adaptive treatment selection have been considered by many authors. The distributions of conditional sufficient statistics and the Rao-Blackwell technique were used to obtain an unbiased estimate and to construct an exact confidence interval for the parameter of interest. In this paper, we characterize the selection process from a binomial drop-the-losers design using a truncated binomial distribution. We propose a new estimator and show that it is asymptotically consistent with a large sample size in either the first stage or the second stage. Supported by simulation analyses, we recommend the new estimator over the naive estimator and the Rao-Blackwell-type estimator based on its robustness in the finite-sample setting. We frame the concept as a simple and easily implemented procedure for phase 2 oncology trial design that can be confirmatory in nature, and we use an example to illustrate its application.

Docetaxel plus trabectedin appears active in recurrent or persistent ovarian and primary peritoneal cancer after up to three prior regimens: a phase II study of the Gynecologic Oncology Group

OBJECTIVE

This study aims to estimate the activity of docetaxel 60mg/m(2) IV over 1h followed by trabectedin 1.1mg/m(2) over 3h with filgrastim, pegfilgrastim, or sargramostim every 3weeks (one cycle).

METHODS

Patients with recurrent and measurable disease, acceptable organ function, PS≤2, and ≤3 prior regimens were eligible. A two-stage design was utilized with a target sample size of 35 subjects per stage. Another Gynecologic Oncology Group study within the same protocol queue involving a single agent taxane showed a response rate (RR) of (16%) (90% CI 8.6-28.5%) and served as a historical control for direct comparison. The present study was designed to determine if the current regimen had an RR of ≥36% with 90% power.

RESULTS

Seventy-one patients were eligible and evaluable (prior regimens: 1=28%, 2=52%, 3=20%). The median number of cycles was 6 (438 total cycles, range 1-22). The number of patients responding was 21 (30%; 90% CI 21-40%). The odds ratio for responding was 2.2 (90% 1-sided CI 1.07-Infinity). The median progression-free survival and overall survival were 4.5months and 16.9months, respectively. The median response duration was 6.2months. Numbers of subjects with grade 3/4 toxicity included neutropenia 7/14; constitutional 8/0; GI (excluding nausea/vomiting) 11/0; metabolic 9/1; pain 6/0. There were no treatment-related deaths nor cases of liver failure.

CONCLUSIONS

This combination was well tolerated and appears more active than the historical control of single agent taxane therapy in those with recurrent ovarian and peritoneal cancer after failing multiple lines of chemotherapy. Further study is warranted.