Simultaneous inference procedures for the comparison of multiple characteristics of two survival functions.

Survival time is the primary endpoint of many randomized controlled trials, and a treatment effect is typically quantified by the hazard ratio under the assumption of proportional hazards. Awareness is increasing that in many settings this assumption is a priori violated, for example, due to delayed onset of drug effect. In these cases, interpretation of the hazard ratio estimate is ambiguous and statistical inference for alternative parameters to quantify a treatment effect is warranted. We consider differences or ratios of milestone survival probabilities or quantiles, differences in restricted mean survival times, and an average hazard ratio to be of interest. Typically, more than one such parameter needs to be reported to assess possible treatment benefits, and in confirmatory trials, the according inferential procedures need to be adjusted for multiplicity. A simple Bonferroni adjustment may be too conservative because the different parameters of interest typically show considerable correlation. Hence simultaneous inference procedures that take into account the correlation are warranted. By using the counting process representation of the mentioned parameters, we show that their estimates are asymptotically multivariate normal and we provide an estimate for their covariance matrix. We propose according to the parametric multiple testing procedures and simultaneous confidence intervals. Also, the logrank test may be included in the framework. Finite sample type I error rate and power are studied by simulation. The methods are illustrated with an example from oncology. A software implementation is provided in the R package nph.

Estimation of treatment effects in early-phase randomized clinical trials involving external control data.

There are good reasons to perform a randomized controlled trial (RCT) even in early phases of clinical development. However, the low sample sizes in those settings lead to high variability of the treatment effect estimate. The variability could be reduced by adding external control data if available. For the common setting of suitable subject-level control group data only available from one external (clinical trial or real-world) data source, we evaluate different analysis options for estimating the treatment effect via hazard ratios. The impact of the external control data is usually guided by the level of similarity with the current RCT data. Such level of similarity can be determined via outcome and/or baseline covariate data comparisons. We provide an overview over existing methods, propose a novel option for a combined assessment of outcome and baseline data, and compare a selected set of approaches in a simulation study under varying assumptions regarding observable and unobservable confounder distributions using a time-to-event model. Our various simulation scenarios also reflect the differences between external clinical trial and real-world data. Data combinations via simple outcome-based borrowing or simple propensity score weighting with baseline covariate data are not recommended. Analysis options which conflate outcome and baseline covariate data perform best in our simulation study.

An adaptive design for early clinical development including interim decision for single-arm trial with external controls or randomized trial.

In early clinical development, randomized controlled trials (RCT) or single-arm trials with external controls (SATwEC) are design options, which allow adjustment for confounding: RCT via design, SATwEC via analysis using propensity score methods. SATwEC requires less investment than RCT. However, if the confounder space substantially differs between the experimental and external control group, the SATwEC might lead to inappropriate decisions for further development. We develop an adaptive two-stage design (ATD) for early clinical development that reduces the risk of unreliable decision-making at the end of a SATwEC. In Stage I, subjects are solely assigned to the experimental group. If at the interim the propensity score distributions of internal and external data are comparable based on the preference score, the subjects in stage II will again be solely assigned to the experimental arm; if not, a randomized stage II will be conducted. In a simulation study guided by a motivating example, data is generated using a time-to-event model with observable and unobservable confounders. The confounder space is varied to investigate the impact on false go/stop probabilities as well as a loss function, which reflects the quality of treatment effect estimates and decision-making. The proposed ATD provides a compromise between optimizing quality (as expressed by false go/stop probabilities and the loss function) and investment (defined by sample size and trial duration).

Robust group sequential designs for trials with survival endpoints and delayed response.

Randomized clinical trials in oncology typically utilize time-to-event endpoints such as progression-free survival or overall survival as their primary efficacy endpoints, and the most commonly used statistical test to analyze these endpoints is the log-rank test. The power of the log-rank test depends on the behavior of the hazard ratio of the treatment arm to the control arm. Under the assumption of proportional hazards, the log-rank test is asymptotically fully efficient. However, this proportionality assumption does not hold true if there is a delayed treatment effect. Cancer immunology has evolved over time and several cancer vaccines are available in the market for treating existing cancers. This includes sipuleucel-T for metastatic hormone-refractory prostate cancer, nivolumab for metastatic melanoma, and pembrolizumab for advanced nonsmall-cell lung cancer. As cancer vaccines require some time to elicit an immune response, a delayed treatment effect is observed, resulting in a violation of the proportional hazards assumption. Thus, the traditional log-rank test may not be optimal for testing immuno-oncology drugs in randomized clinical trials. Moreover, the new immuno-oncology compounds have been shown to be very effective in prolonging overall survival. Therefore, it is desirable to implement a group sequential design with the possibility of early stopping for overwhelming efficacy. In this paper, we investigate the max-combo test, which utilizes the maximum of two weighted log-rank statistics, as a robust alternative to the log-rank test. The new test is implemented for two-stage designs with possible early stopping at the interim analysis time point. Two classes of weights are investigated for the max-combo test: the Fleming and Harrington (1981) Gρ,γ$G^{\rho , \gamma }$ weights and the Magirr and Burman (2019) modest (τ∗)$ (\tau ^{*})$  weights.

Progression-free survival in oncological clinical studies: Assessment time bias and methods for its correction.

Progression-free survival (PFS) is a frequently used endpoint in oncological clinical studies. In case of PFS, potential events are progression and death. Progressions are usually observed delayed as they can be diagnosed not before the next study visit. For this reason potential bias of treatment effect estimates for progression-free survival is a concern. In randomized trials and for relative treatment effects measures like hazard ratios, bias-correcting methods are not necessarily required or have been proposed before. However, less is known on cross-trial comparisons of absolute outcome measures like median survival times. This paper proposes a new method for correcting the assessment time bias of progression-free survival estimates to allow a fair cross-trial comparison of median PFS. Using median PFS for example, the presented method approximates the unknown posterior distribution by a Bayesian approach based on simulations. It is shown that the proposed method leads to a substantial reduction of bias as compared to estimates derived from maximum likelihood or Kaplan-Meier estimates. Bias could be reduced by more than 90% over a broad range of considered situations differing in assessment times and underlying distributions. By coverage probabilities of at least 94% based on the credibility interval of the posterior distribution the resulting parameters hold common confidence levels. In summary, the proposed approach is shown to be useful for a cross-trial comparison of median PFS.

Delayed treatment effects, treatment switching and heterogeneous patient populations: How to design and analyze RCTs in oncology.

In the analysis of survival times, the logrank test and the Cox model have been established as key tools, which do not require specific distributional assumptions. Under the assumption of proportional hazards, they are efficient and their results can be interpreted unambiguously. However, delayed treatment effects, disease progression, treatment switchers or the presence of subgroups with differential treatment effects may challenge the assumption of proportional hazards. In practice, weighted logrank tests emphasizing either early, intermediate or late event times via an appropriate weighting function may be used to accommodate for an expected pattern of non-proportionality. We model these sources of non-proportional hazards via a mixture of survival functions with piecewise constant hazard. The model is then applied to study the power of unweighted and weighted log-rank tests, as well as maximum tests allowing different time dependent weights. Simulation results suggest a robust performance of maximum tests across different scenarios, with little loss in power compared to the most powerful among the considered weighting schemes and huge power gain compared to unfavorable weights. The actual sources of non-proportional hazards are not obvious from resulting populationwise survival functions, highlighting the importance of detailed simulations in the planning phase of a trial when assuming non-proportional hazards.We provide the required tools in a software package, allowing to model data generating processes under complex non-proportional hazard scenarios, to simulate data from these models and to perform the weighted logrank tests.

Utility-based optimization of phase II/III programs.

Phase II and phase III trials play a crucial role in drug development programs. They are costly and time consuming and, because of high failure rates in late development stages, at the same time risky investments. Commonly, sample size calculation of phase III is based on the treatment effect observed in phase II. Therefore, planning of phases II and III can be linked. The performance of the phase II/III program crucially depends on the allocation of the resources to phases II and III by appropriate choice of the sample size and the rule applied to decide whether to stop the program after phase II or to proceed. We present methods for a program-wise phase II/III planning that aim at determining optimal phase II sample sizes and go/no-go decisions in a time-to-event setting. Optimization is based on a utility function that takes into account (fixed and variable) costs of the drug development program and potential gains after successful launch. The proposed methods are illustrated by application to a variety of scenarios typically met in oncology drug development.

Sample size planning for phase II trials based on success probabilities for phase III.

In recent years, high failure rates in phase III trials were observed. One of the main reasons is overoptimistic assumptions for the planning of phase III resulting from limited phase II information and/or unawareness of realistic success probabilities. We present an approach for planning a phase II trial in a time-to-event setting that considers the whole phase II/III clinical development programme. We derive stopping boundaries after phase II that minimise the number of events under side conditions for the conditional probabilities of correct go/no-go decision after phase II as well as the conditional success probabilities for phase III. In addition, we give general recommendations for the choice of phase II sample size. Our simulations show that unconditional probabilities of go/no-go decision as well as the unconditional success probabilities for phase III are influenced by the number of events observed in phase II. However, choosing more than 150 events in phase II seems not necessary as the impact on these probabilities then becomes quite small. We recommend considering aspects like the number of compounds in phase II and the resources available when determining the sample size. The lower the number of compounds and the lower the resources are for phase III, the higher the investment for phase II should be.