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A fundamental concept in two-arm non-parametric survival analysis is the comparison of observed versus expected numbers of events on one of the treatment arms (the choice of which arm is arbitrary), where the expectation is taken assuming that the true survival curves in the two arms are identical. This concept is at the heart of the counting-process theory that provides a rigorous basis for methods such as the log-rank test. It is natural, therefore, to maintain this perspective when extending the log-rank test to deal with non-proportional hazards, for example, by considering a weighted sum of the "observed - expected" terms, where larger weights are given to time periods where the hazard ratio is expected to favor the experimental treatment. In doing so, however, one may stumble across some rather subtle issues, related to difficulties in the interpretation of hazard ratios, that may lead to strange conclusions. An alternative approach is to view non-parametric survival comparisons as permutation tests. With this perspective, one can easily improve on the efficiency of the log-rank test, while thoroughly controlling the false positive rate. In particular, for the field of immuno-oncology, where researchers often anticipate a delayed treatment effect, sample sizes could be substantially reduced without loss of power.

Background: A common feature of many recent trials evaluating the effects of immunotherapy on survival is that non-proportional hazards can be anticipated at the design stage. This raises the possibility to use a statistical method tailored towards testing the purported long-term benefit, rather than applying the more standard log-rank test and/or Cox model. Many such proposals have been made in recent years, but there remains a lack of practical guidance on implementation, particularly in the context of group-sequential designs. In this article, we aim to fill this gap. Methods: We illustrate how the POPLAR trial, which compared immunotherapy versus chemotherapy in non-small-cell lung cancer, might have been re-designed to be more robust to the presence of a delayed effect using the modestly-weighted log-rank test in a group-sequential setting. Conclusion: We provide step-by-step instructions on how to analyse a hypothetical realization of the trial, based on this new design. Basic theory on weighted log-rank tests and group-sequential methods is covered, and an accompanying R package (including vignette) is provided.

An important step in the development of targeted therapies is the identification and confirmation of sub-populations where the treatment has a positive treatment effect compared to a control. These sub-populations are often based on continuous biomarkers, measured at baseline. For example, patients can be classified into biomarker low and biomarker high subgroups, which are defined via a threshold on the continuous biomarker. However, if insufficient information on the biomarker is available, the a priori choice of the threshold can be challenging and it has been proposed to consider several thresholds and to apply appropriate multiple testing procedures to test for a treatment effect in the corresponding subgroups controlling the family-wise type 1 error rate. In this manuscript we propose a framework to select optimal thresholds and corresponding optimized multiple testing procedures that maximize the expected power to identify at least one subgroup with a positive treatment effect. Optimization is performed over a prior on a family of models, modelling the relation of the biomarker with the expected outcome under treatment and under control. We find that for the considered scenarios 3 to 4 thresholds give the optimal power. If there is a prior belief on a small subgroup where the treatment has a positive effect, additional optimization of the spacing of thresholds may result in a large benefit. The procedure is illustrated with a clinical trial example in depression.

Vistusertib is an orally bioavailable dual target of rapamycin complex (TORC) 1/2 kinase inhibitor currently under clinical investigation in various solid tumour and haematological malignancy settings. The pharmacokinetic, metabolic and excretion profiles of 14Carbon-isotope (14C)-labelled vistusertib were characterised in this open-label phase I patient study. Four patients with advanced solid malignancies received a single oral solution dose of 14C-labelled vistusertib. Blood, urine, faeces, and saliva samples were collected at various time points during the 8-day in-patient period of the study. Safety and preliminary efficacy were also assessed. 14C-labelled vistusertib was rapidly absorbed following administration (time to maximum concentration (Tmax) 90% of radioactivity was recovered with the majority recovered as metabolites in faeces (on average 80% vs. 12% recovered in urine). The majority of circulating radioactivity (~ 78%) is unchanged vistusertib. Various morpholine-ring oxidation metabolites and an N-methylamide circulate at low concentrations [each

Roychoudhury et al. (2021) presented a “straw-man guidance” on the design and analysis of clinical trials with non-proportional hazards. For the primary analysis, they propose to replace the log-ra...

In the early stages of drug development there is often uncertainty about the most promising among a set of different treatments, different doses of the same treatment, or combinations of treatments. Multi-arm multi-stage (MAMS) clinical studies provide an efficient solution to determine which intervention is most promising. In this paper we discuss the R package MAMS that allows designing such studies within the group-sequential framework. The package implements MAMS studies with normal, binary, ordinal, or time-to-event endpoints in which either the single best treatment or all promising treatments are continued at the interim analyses. Additionally unexpected design modifications can be accounted for via the use of the conditional error approach. We provide illustrative examples of the use of the package based on real trial designs.

Vistusertib is an orally bioavailable dual target of rapamycin complex (TORC) 1/2 kinase inhibitor currently under clinical investigation in various solid tumour and haematological malignancy settings. The pharmacokinetic, metabolic and excretion profiles ofFour patients with advanced solid malignancies received a single oral solution dose ofThe pharmacokinetic (PK) profile of vistusertib is similar to previous studies using the same dosing regimen in solid malignancy patients. The majority of vistusertib elimination occurred via hepatic metabolic routes.

We propose a new class of weighted logrank tests (WLRTs) that control the risk of concluding that a new drug is more efficacious than standard of care, when, in fact, it is uniformly inferior. Perhaps surprisingly, this risk is not controlled for WLRT in general. Tests from this new class can be constructed to have high power under a delayed-onset treatment effect scenario, as well as being almost as efficient as the standard logrank test under proportional hazards.

We describe a general method for finding a confidence region for a parameter vector that is compatible with the decisions of a two-stage closed test procedure in an adaptive experiment. The closed test procedure is characterized by the fact that rejection or nonrejection of a null hypothesis may depend on the decisions for other hypotheses and the compatible confidence region will, in general, have a complex, nonrectangular shape. We find the smallest cross-product of simultaneous confidence intervals containing the region and provide computational shortcuts for calculating the lower bounds on parameters corresponding to the rejected null hypotheses. We illustrate the method with an adaptive phase II/III clinical trial. Copyright 2013, Oxford University Press.

Multi-arm multi-stage designs can improve the efficiency of the drug-development process by evaluating multiple experimental arms against a common control within one trial. This reduces the number of patients required compared to a series of trials testing each experimental arm separately against control. By allowing for multiple stages experimental treatments can be eliminated early from the study if they are unlikely to be significantly better than control. Using the TAILoR trial as a motivating example, we explore a broad range of statistical issues related to multi-arm multi-stage trials including a comparison of different ways to power a multi-arm multi-stage trial; choosing the allocation ratio to the control group compared to other experimental arms; the consequences of adding additional experimental arms during a multi-arm multi-stage trial, and how one might control the type-I error rate when this is necessary; and modifying the stopping boundaries of a multi-arm multi-stage design to account for unknown variance in the treatment outcome. Multi-arm multi-stage trials represent a large financial investment, and so considering their design carefully is important to ensure efficiency and that they have a good chance of succeeding.

In early stages of drug development, there is often uncertainty about the most promising among a set of different treatments. To ensure the best use of resources in such situations, it is important to decide which, if any, of the treatments should be taken forward for further testing. In later development, it has been shown that evaluating more than one dose increases the chance of success substantially. In this work, we discuss how multi-arm multi-stage trials can be designed such that all promising treatments are kept in the study at the interim analyses. We first investigate the impact of deviating from the planned design and show how confidence intervals can be constructed before we consider the impact of important covariates. We show that under orthogonality, the inclusion of covariates has no effect on familywise error rate control in the strong sense. We further show that the derived methodology can be used to investigate non-normal endpoints.

We generalize the Dunnett test to derive efficacy and futility boundaries for a flexible multi-arm multi-stage clinical trial for a normally distributed endpoint with known variance. We show that the boundaries control the familywise error rate in the strong sense. The method is applicable for any number of treatment arms, number of stages and number of patients per treatment per stage. It can be used for a wide variety of boundary types or rules derived from α-spending functions. Additionally, we show how sample size can be computed under a least favourable configuration power requirement and derive formulae for expected sample sizes. Copyright 2012, Oxford University Press.

In a clinical trial, response-adaptive randomization (RAR) uses accumulating data to weigh the randomization of remaining patients in favour of the better performing treatment. The aim is to reduce the number of failures within the trial. However, many well-known RAR designs, in particular, the randomized play-the-winner-rule (RPWR), have a highly myopic structure which has sometimes led to unfortunate randomization sequences when used in practice. This paper introduces random permuted blocks into two RAR designs, the RPWR and sequential maximum likelihood estimation, for trials with a binary endpoint. Allocation ratios within each block are restricted to be one of 1:1, 2:1 or 3:1, preventing unfortunate randomization sequences. Exact calculations are performed to determine error rates and expected number of failures across a range of trial scenarios. The results presented show that when compared with equal allocation, block RAR designs give similar reductions in the expected number of failures to their unmodified counterparts. The reductions are typically modest under the alternative hypothesis but become more impressive if the treatment effect exceeds the clinically relevant difference.

Background Visceral leishmaniasis (VL) is a parasitic disease transmitted by sandflies and is fatal if left untreated. Phase II trials of new treatment regimens for VL are primarily carried out to evaluate safety and efficacy, while pharmacokinetic data are also important to inform future combination treatment regimens. The efficacy of VL treatments is evaluated at two time points, initial cure, when treatment is completed and definitive cure, commonly 6 months post end of treatment, to allow for slow response to treatment and detection of relapses. This paper investigates a generalization of the triangular design to impose a minimum sample size for pharmacokinetic or other analyses, and methods to estimate efficacy at extended follow-up accounting for the sequential design and changes in cure status during extended follow-up. Methods We provided R functions that generalize the triangular design to impose a minimum sample size before allowing stopping for efficacy. For estimation of efficacy at a second, extended, follow-up time, the performance of a shrinkage estimator (SHE), a probability tree estimator (PTE) and the maximum likelihood estimator (MLE) for estimation was assessed by simulation. Results The SHE and PTE are viable approaches to estimate an extended follow-up although the SHE performed better than the PTE: the bias and root mean square error were lower and coverage probabilities higher. Conclusions Generalization of the triangular design is simple to implement for adaptations to meet requirements for pharmacokinetic analyses. Using the simple MLE approach to estimate efficacy at extended follow-up will lead to biased results, generally over-estimating treatment success. The SHE is recommended in trials of two or more treatments. The PTE is an acceptable alternative for one-arm trials or where use of the SHE is not possible due to computational complexity. Trial registration NCT01067443, February 2010. Electronic supplementary material The online version of this article (doi:10.1186/s13063-015-1018-1) contains supplementary material, which is available to authorized users.

Consider a parallel group trial for the comparison of an experimental treatment to a control, where the second‐stage sample size may depend on the blinded primary endpoint data as well as on additional blinded data from a secondary endpoint. For the setting of normally distributed endpoints, we demonstrate that this may lead to an inflation of the type I error rate if the null hypothesis holds for the primary but not the secondary endpoint. We derive upper bounds for the inflation of the type I error rate, both for trials that employ random allocation and for those that use block randomization. We illustrate the worst‐case sample size reassessment rule in a case study. For both randomization strategies, the maximum type I error rate increases with the effect size in the secondary endpoint and the correlation between endpoints. The maximum inflation increases with smaller block sizes if information on the block size is used in the reassessment rule. Based on our findings, we do not question the well‐established use of blinded sample size reassessment methods with nuisance parameter estimates computed from the blinded interim data of the primary endpoint. However, we demonstrate that the type I error rate control of these methods relies on the application of specific, binding, pre‐planned and fully algorithmic sample size reassessment rules and does not extend to general or unplanned sample size adjustments based on blinded data. © 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Summary Interindividual variations in dose requirements of oral vitamin K antagonists (VKA) are attributed to several factors, including genetic variant alleles of vitamin K epoxide reductase complex subunit 1 (VKORC1) and cytochrome P450 2C9 (CYP2C9), but also interaction with co-medications. In this context, proton pump inhibitor (PPI)-related alterations of VKA maintenance dose requirements have been published. The present investigation aimed to test for an interaction profile of oral VKA-therapy and PPIs in relation to the CYP2C9 genotype. Median weekly stable VKA dose requirements over 1 year were recorded in 69 patients. Patients were genotyped for CYP2C9*2, CYP2C9*3, VKORC1c.-1639G>A and VKORC1c.174-136C>T and assessed for an association with PPI use and total VKA maintenance dose requirements. PPI users with CYP2C9 genetic variations required significantly lower weekly VKA maintenance doses than those with the wild-type genotype (t-test: P = 0·02). In contrast, in subjects without PPI use, the CYP2C9 genotype had no significant influence on oral VKA dose requirements. Further, the combined CYP2C9/VKORC1 genotype was a significant predictor for VKA dose requirements [linear regression: estimate: −1·47, standard error: 0·58 (P = 0·01)]. In conclusion, in carriers of CYP2C9 gene variations, the interference with the VKA metabolism is modified by PPI co-medication and the VCKORC1 genotype. Preceding knowledge of the genetic profile and the awareness for potentially occurring severe over-anticoagulation problems under PPI co-medication could contribute to a safer and personalized VKA pharmacotherapy.

Adaptive designs that are based on group-sequential approaches have the benefit of being efficient as stopping boundaries can be found that lead to good operating characteristics with test decisions based solely on sufficient statistics. The drawback of these so called “pre-planned adaptive” designs is that unexpected design changes are not possible without impacting the error rates. “Flexible adaptive designs”, and in particular designs based on p-value combination, on the other hand can cope with a large number of contingencies at the cost of reduced efficiency. In this presentation we focus on so called multi-arm multi-stage trials which compare several active treatments against control at a series of interim analysis. We will discuss how these “pre-planned adaptive designs” can be modified to allow for flexibility. We then show how the added flexibility can be used for treatment selection and evaluate the impact on power in a simulation study. The results show that a combination of a well chosen pre-planned design and an application of the conditional error principle to allow flexible treatment selection results in an impressive overall procedure.