Analysis of time-to-event data with nonuniform patient entry and loss to follow-up under a two-stage seamless adaptive design with weibull distribution

Cancer patient survival can be parametrized to improve trial precision and reveal time-dependent therapeutic effects

Individual participant data (IPD) from oncology clinical trials is invaluable for identifying factors that influence trial success and failure, improving trial design and interpretation, and comparing pre-clinical studies to clinical outcomes. However, the IPD used to generate published survival curves are not generally publicly available. We impute survival IPD from ~500 arms of Phase 3 oncology trials (representing ~220,000 events) and find that they are well fit by a two-parameter Weibull distribution. Use of Weibull functions with overall survival significantly increases the precision of small arms typical of early phase trials: analysis of a 50-patient trial arm using parametric forms is as precise as traditional, non-parametric analysis of a 90-patient arm. We also show that frequent deviations from the Cox proportional hazards assumption, particularly in trials of immune checkpoint inhibitors, arise from time-dependent therapeutic effects. Trial duration therefore has an underappreciated impact on the likelihood of success.

Analysis of more than 150 Phase 3 oncology clinical trials supports parametric statistical analysis, significantly increasing the precision of small early-phase trials and relating deviations from the Cox proportional hazards model to trial duration.

Critical review of oncology clinical trial design under non-proportional hazards

In trials of novel immuno-oncology drugs, the proportional hazards (PH) assumption often does not hold for the primary time-to-event (TTE) efficacy endpoint, likely due to the unique mechanism of action of these drugs. In practice, when it is anticipated that PH may not hold for the TTE endpoint with respect to treatment, the sample size is often still calculated under the PH assumption, and the hazard ratio (HR) from the Cox model is still reported as the primary measure of the treatment effect. Sensitivity analyses of the TTE data using methods that are suitable under non-proportional hazards (non-PH) are commonly pre-planned. In cases where a substantial deviation from the PH assumption is likely, we suggest designing the trial, calculating the sample size and analyzing the data, using a suitable method that accounts for non-PH, after gaining alignment with regulatory authorities. In this comprehensive review article, we describe methods to design a randomized oncology trial, calculate the sample size, analyze the trial data and obtain summary measures of the treatment effect in the presence of non-PH. For each method, we provide examples of its use from the recent oncology trials literature. We also summarize in the Appendix some methods to conduct sensitivity analyses for overall survival (OS) when patients in a randomized trial switch or cross-over to the other treatment arm after disease progression on the initial treatment arm, and obtain an adjusted or weighted HR for OS in the presence of cross-over. This is an example of the treatment itself changing at a specific point in time - this cross-over may lead to a non-PH pattern of diminishing treatment effect.

Clinical endpoints and adaptive clinical trials in precirrhotic nonalcoholic steatohepatitis: Facilitating development approaches for an emerging epidemic

Due to the increasing prevalence of nonalcoholic steatohepatitis (NASH) and its associated health burden, there is a high need to develop therapeutic strategies for patients with this disease. Unfortunately, its long and asymptomatic natural history, the uncertainties about disease progression, the fact that most patients are undiagnosed, and the requirement for sequential liver biopsies create substantial challenges for clinical development. Adaptive design methods are increasingly used in clinical research as they provide the flexibility and efficiency for identifying potential signals of clinical benefit of the test treatment under investigation and make prompt preplanned adaptations without undermining the validity or integrity of the trial. Given the high unmet medical need and the lack of validated surrogate endpoints in NASH, the use of adaptive design methods appears reasonable. Furthermore, due to the limited number of patients willing to have multiple liver biopsies and the need for long‐term exposure to assess an impact in outcomes, a continuous seamless adaptive design may reduce the overall sample size while allowing patients to continue after each one of the phases. Here, we review strategic frameworks that include potential surrogate endpoints as well as statistical and logistical approaches that could be considered for applying adaptive designs to clinical trials in NASH with the goal of facilitating drug development for this growing medical need. (Hepatology Communications 2017;1:577–585)

Power and sample size for randomized phase III survival trials under the Weibull model

Two parametric tests are proposed for designing randomized two-arm phase III survival trials under the Weibull model. The properties of the two parametric tests are compared with the nonparametric log-rank test through simulation studies. Power and sample size formulas of the two parametric tests are derived. The sensitivity of sample size under misspecification of the Weibull shape parameter is also investigated. The study can be designed by planning the study duration and handling nonuniform entry and loss to follow-up under the Weibull model using either the proposed parametric tests or the well-known nonparametric log-rank test.

Group Sequential Design for Randomized Phase III Trials under the Weibull Model

In this article, a parametric sequential test is proposed under the Weibull model. The proposed test is asymptotically normal with an independent increment structure. The sample size for a fixed sample test is derived for the purpose of group sequential trial design. In addition, a multi-stage group sequential procedure is given under the Weibull model by applying the Brownian motion property of the test statistic and sequential conditional probability ratio test methodology.