One-stage and two-stage designs for phase II clinical trials with survival endpoints

Sample size determination and evaluation for two-stage adaptive designs of single arm clinical trials based on median event time test

Clinical trials play a critical role in drug development which involves a series of phases and requires a significant amount of time and effort. Efficient clinical trial designs are necessary to investigate a new drug. Investigators strongly desire to use the time-to-event endpoint as the primary endpoint for Phase II studies, which evaluates the therapeutic efficacy of the new drug, with the hypothesis that the new drug improves the median survival time. The one-sample log-rank test has been used for single-arm Phase II trials, but it generally requires more samples. Recently, the median event time test was proposed to provide a simple, straightforward decision rule, which compares the observed median survival time for the new drug with the threshold, which is determined through the numerical search. We improve the computation of the method for the two-stage design of single-arm clinical trials based on the median event time test. By utilizing the large sample theory of order statistics, we provide the explicit formulas to calculate the sample size for the first and second stages and propose the testing procedure. The performance of the proposed method is evaluated through simulations and a trial example.

TMBserval: a statistical explainable learning model reveals weighted tumor mutation burden better categorizing therapeutic benefits

A high tumor mutation burden (TMB) is known to drive the response to immune checkpoint inhibitors (ICI) and is associated with favorable prognoses. However, because it is a one-dimensional numerical representation of non-synonymous genetic alterations, TMB suffers from clinical challenges due to its equal quantification. Since not all mutations elicit the same antitumor rejection, the effect on immunity of neoantigens encoded by different types or locations of somatic mutations may vary. In addition, other typical genomic features, including complex structural variants, are not captured by the conventional TMB metric. Given the diversity of cancer subtypes and the complexity of treatment regimens, this paper proposes that tumor mutations capable of causing various degrees of immunogenicity should be calculated separately. TMB should therefore, be segmented into more exact, higher dimensional feature vectors to exhaustively measure the foreignness of tumors. We systematically reviewed patients' multifaceted efficacy based on a refined TMB metric, investigated the association between multidimensional mutations and integrative immunotherapy outcomes, and developed a convergent categorical decision-making framework, TMBserval (Statistical Explainable machine learning with Regression-based VALidation). TMBserval integrates a multiple-instance learning concept with statistics to create a statistically interpretable model that addresses the broad interdependencies between multidimensional mutation burdens and decision endpoints. TMBserval is a pan-cancer-oriented many-to-many nonlinear regression model with discrimination and calibration power. Simulations and experimental analyses using data from 137 actual patients both demonstrated that our method could discriminate between patient groups in a high-dimensional feature space, thereby rationally expanding the beneficiary population of immunotherapy.

Point and interval estimation in two-stage adaptive designs with time to event data and biomarker-driven subpopulation selection

In personalized medicine, it is often desired to determine if all patients or only a subset of them benefit from a treatment. We consider estimation in two-stage adaptive designs that in stage 1 recruit patients from the full population. In stage 2, patient recruitment is restricted to the part of the population, which, based on stage 1 data, benefits from the experimental treatment. Existing estimators, which adjust for using stage 1 data for selecting the part of the population from which stage 2 patients are recruited, as well as for the confirmatory analysis after stage 2, do not consider time to event patient outcomes. In this work, for time to event data, we have derived a new asymptotically unbiased estimator for the log hazard ratio and a new interval estimator with good coverage probabilities and probabilities that the upper bounds are below the true values. The estimators are appropriate for several selection rules that are based on a single or multiple biomarkers, which can be categorical or continuous.

Two-stage optimal designs based on exact variance for a single-arm trial with survival endpoints

Sample size calculation based on normal approximations is often associated with the loss of statistical power for a single-arm trial with a time-to-event endpoint. Recently, Wu (2015) derived the exact variance for the one-sample log-rank test under the alternative and showed that a single-arm one-stage study based on exact variance often has power above the nominal level while the type I error rate is controlled. We extend this approach to a single-arm two-stage design by using exact variances of the one-sample log-rank test for the first stage and the two stages combined. The empirical power of the proposed two-stage optimal designs is often not guaranteed under a two-stage design setting, which could be due to the asymptotic bi-variate normal distribution used to estimate the joint distribution of the test statistics. We adjust the nominal power level in the design search to guarantee the simulated power of the identified optimal design being above the nominal level. The sample size and the study time savings of the proposed two-stage designs are substantial as compared to the one-stage design.

Two-stage optimal designs with survival endpoint when the follow-up time is restricted

BACKGROUND

Survival endpoint is frequently used in early phase clinical trials as the primary endpoint to assess the activity of a new treatment. Existing two-stage optimal designs with survival endpoint either over estimate the sample size or compute power outside the alternative hypothesis space.

METHODS

We propose a new single-arm two-stage optimal design with survival endpoint by using the one-sample log rank test based on exact variance estimates. This proposed design with survival endpoint is analogous to Simon's two-stage design with binary endpoint, having restricted follow-up.

RESULTS

We compare the proposed design with the existing two-stage designs, including the two-stage design with survival endpoint based on the nonparametric Nelson-Aalen estimate, and Simon's two-stage designs with or without interim accrual. The new design always performs better than these competitors with regards to the expected total study length, and requires a smaller expected sample size than Simon's design with interim accrual.

CONCLUSIONS

The proposed two-stage minimax and optimal designs with survival endpoint are recommended for use in practice to shorten the study length of clinical trials.

A two-stage design for phase II trials with time-to-event endpoint using restricted follow-up

In phase II oncology trials, the use of new cytostatic drugs raises some questions regarding the endpoint. Time-to-event endpoints such as Progression-Free Survival have been recommended and led to new designs. In 2003, Case and Morgan proposed a design based on the comparison of the cumulative hazards at a clinically relevant timepoint. In 2013, Kwak proposed a design based on the one-sample log-rank test. If all the patients are followed from their entry time to the analysis date, the Kwak and Jung's design leads to a smaller sample size as compared to the Case-Morgan's design. However, the Case and Morgan's design requires less information since it only needs to follow every patient during a fixed interval of time. We propose a trade-off between these two approaches that corresponds to an adaptation of Kwak and Jung's design when the follow-up is expected to be restricted. Our proposal is based on the one-sample log-rank test as the Kwak and Jung's design but it uses the same follow-up information as the Case-Morgan's design. Simulation study shows that our proposal allows reducing the sample size as compared to the Case-Morgan's design (median difference of 23% [15%-33%]). Type I and type II error rates are close to their nominal rates planned in the protocol. A real phase II clinical trial in cervical cancer illustrated the interest of this new design. Thus, our proposal can be recommended as an alternative to the Kwak's design when patients' follow-up is restricted.

Mixed response and time-to-event endpoints for multistage single-arm phase II design

BACKGROUND

The objective of phase II cancer clinical trials is to determine if a treatment has sufficient activity to warrant further study. The efficiency of a conventional phase II trial design has been the object of considerable debate, particularly when the study regimen is characteristically cytostatic. At the time of development of a phase II cancer trial, we accumulated clinical experience regarding the time to progression (TTP) for similar classes of drugs and for standard therapy. By considering the time to event (TTE) in addition to the tumor response endpoint, a mixed-endpoint phase II design may increase the efficiency and ability of selecting promising cytotoxic and cytostatic agents for further development.

METHODS

We proposed a single-arm phase II trial design by extending the Zee multinomial method to fully use mixed endpoints with tumor response and the TTE. In this design, the dependence between the probability of response and the TTE outcome is modeled through a Gaussian copula.

RESULTS

Given the type I and type II errors and the hypothesis as defined by the response rate (RR) and median TTE, such as median TTP, the decision rules for a two-stage phase II trial design can be generated. We demonstrated through simulation that the proposed design has a smaller expected sample size and higher early stopping probability under the null hypothesis than designs based on a single-response endpoint or a single TTE endpoint.

CONCLUSIONS

The proposed design is more efficient for screening new cytotoxic or cytostatic agents and less likely to miss an effective agent than the alternative single-arm design.

Bayesian methods for setting sample sizes and choosing allocation ratios in phase II clinical trials with time-to-event endpoints

Conventional phase II trials using binary endpoints as early indicators of a time-to-event outcome are not always feasible. Uveal melanoma has no reliable intermediate marker of efficacy. In pancreatic cancer and viral clearance, the time to the event of interest is short, making an early indicator unnecessary. In the latter application, Weibull models have been used to analyse corresponding time-to-event data. Bayesian sample size calculations are presented for single-arm and randomised phase II trials assuming proportional hazards models for time-to-event endpoints. Special consideration is given to the case where survival times follow the Weibull distribution. The proposed methods are demonstrated through an illustrative trial based on uveal melanoma patient data. A procedure for prior specification based on knowledge or predictions of survival patterns is described. This enables investigation into the choice of allocation ratio in the randomised setting to assess whether a control arm is indeed required. The Bayesian framework enables sample sizes consistent with those used in practice to be obtained. When a confirmatory phase III trial will follow if suitable evidence of efficacy is identified, Bayesian approaches are less controversial than for definitive trials. In the randomised setting, a compromise for obtaining feasible sample sizes is a loss in certainty in the specified hypotheses: the Bayesian counterpart of power. However, this approach may still be preferable to running a single-arm trial where no data is collected on the control treatment. This dilemma is present in most phase II trials, where resources are not sufficient to conduct a definitive trial.