A Simulation Study to Compare New Adaptive Dose–Ranging Designs

Efficient Study Design and Analysis of Longitudinal Dose-Response Data Using Fractional Polynomials

Correctly characterising the dose-response relationship and taking the correct dose forward for further study is a critical part of the drug development process. We use optimal design theory to compare different designs and show that using longitudinal data from all available timepoints in a continuous-time dose-response model can substantially increase the efficiency of estimation of the dose-response compared to a single timepoint model. We give theoretical results to calculate the efficiency gains for a large class of these models. For example, a linearly growing Emax dose-response in a population with a between/within-patient variance ratio ranging from 0.1 to 1 measured at six visits can be estimated with between 1.43 and 2.22 times relative efficiency gain, or equivalently, with 30% to a 55% reduced sample size, compared to a single model of the final timepoint. Fractional polynomials are a flexible way to incorporate data from repeated measurements, increasing precision without imposing strong constraints. Longitudinal dose-response models using two fractional polynomial terms are robust to mis-specification of the true longitudinal process while maintaining, often large, efficiency gains. These models have applications for characterising the dose-response at interim or final analyses.

A Bayesian quasi-likelihood design for identifying the minimum effective dose and maximum utility dose in dose-ranging studies

Most existing dose-ranging study designs focus on assessing the dose-efficacy relationship and identifying the minimum effective dose. There is an increasing interest in optimizing the dose based on the benefit-risk tradeoff. We propose a Bayesian quasi-likelihood dose-ranging design that jointly considers safety and efficacy to simultaneously identify the minimum effective dose and the maximum utility dose to optimize the benefit-risk tradeoff. The binary toxicity endpoint is modeled using a beta-binomial model. The efficacy endpoint is modeled using the quasi-likelihood approach to accommodate various types of data (e.g. binary, ordinal or continuous) without imposing any parametric assumptions on the dose-response curve. Our design utilizes a utility function as a measure of benefit-risk tradeoff and adaptively assign patients to doses based on the doses' likelihood of being the minimum effective dose and maximum utility dose. The design takes a group-sequential approach. At each interim, the doses that are deemed overly toxic or futile are dropped. At the end of the trial, we use posterior probability criteria to assess the strength of the dose-response relationship for establishing the proof-of-concept. If the proof-of-concept is established, we identify the minimum effective dose and maximum utility dose. Our simulation study shows that compared with some existing designs, the Bayesian quasi-likelihood dose-ranging design is robust and yields competitive performance in establishing proof-of-concept and selecting the minimum effective dose. Moreover, it includes an additional feature for further maximum utility dose selection.

Assessment of nonlinear dose-response relationships via nonparametric regression

We propose a simple approach to assess whether a nonlinear parametric model is appropriate to depict the dose-response relationships and whether two parametric models can be applied to fit a dataset via nonparametric regression. The proposed approach can compensate for the ANOVA, which is sometimes conservative, and is very easy to implement. We illustrate the performance by analyzing experimental examples and a small simulation study.

DROID: dose-ranging approach to optimizing dose in oncology drug development

In the era of targeted therapy, there has been increasing concern about the development of oncology drugs based on the "more is better" paradigm, developed decades ago for chemotherapy. Recently, the US Food and Drug Administration (FDA) initiated Project Optimus to reform the dose optimization and dose selection paradigm in oncology drug development. To accommodate this paradigm shifting, we propose a dose-ranging approach to optimizing dose (DROID) for oncology trials with targeted drugs. DROID leverages the well-established dose-ranging study framework, which has been routinely used to develop non-oncology drugs for decades, and bridges it with established oncology dose-finding designs to optimize the dose of oncology drugs. DROID consists of two seamlessly connected stages. In the first stage, patients are sequentially enrolled and adaptively assigned to investigational doses to establish the therapeutic dose range (TDR), defined as the range of doses with acceptable toxicity and efficacy profiles, and the recommended phase 2 dose set (RP2S). In the second stage, patients are randomized to the doses in RP2S to assess the dose-response relationship and identify the optimal dose. The simulation study shows that DROID substantially outperforms the conventional approach, providing a new paradigm to efficiently optimize the dose of targeted oncology drugs. DROID aligns with the approach of a randomized, parallel dose-response trial design recommended by the FDA in the Guidance on Optimizing the Dosage of Human Prescription Drugs and Biological Products for the Treatment of Oncologic Diseases.

From innovative thinking to pharmaceutical industry implementation: Some success stories

In industry, successful innovation involves not only developing new statistical methodology, but also ensuring that this methodology is implemented successfully. This includes enabling applied statisticians to understand the method, its benefits and limitations and empowering them to implement the new method. This will include advocacy, influencing in-house and external stakeholders, such that these stakeholders are receptive to the new methodology. In this paper, we describe some industry successes and focus on our colleague, Andy Grieve's role in these.

Simulation-based sequential design

We review some simulation-based methods to implement optimal decisions in sequential design problems as they naturally arise in clinical trial design. As a motivating example we use a stylized version of a dose-ranging design in the ASTIN trial. The approach can be characterized as constrained backward induction. The nature of the constraint is a restriction of the decisions to a set of actions that are functions of the current history only implicitly through a low-dimensional summary statistic. In addition, the action set is restricted to time-invariant policies. Time-dependence is only introduced indirectly through the change of the chosen summary statistic over time. This restriction allows computationally efficient solutions to the sequential decision problem. A further simplification is achieved by restricting optimal actions to be described by decision boundaries on the space of such summary statistics.

Optimal adaptive allocation using deep reinforcement learning in a dose-response study

Estimation of the dose-response curve for efficacy and subsequent selection of an appropriate dose in phase II trials are important processes in drug development. Various methods have been investigated to estimate dose-response curves. Generally, these methods are used with equal allocation of subjects for simplicity; nevertheless, they may not fully optimize performance metrics because of nonoptimal allocation. Optimal allocation methods, which include adaptive allocation methods, have been proposed to overcome the limitations of equal allocation. However, they rely on asymptotics, and thus sometimes cannot efficiently optimize the performance metric with the sample size in an actual clinical trial. The purpose of this study is to construct an adaptive allocation rule that directly optimizes a performance metric, such as power, accuracy of model selection, accuracy of the estimated target dose, or mean absolute error over the estimated dose-response curve. We demonstrate that deep reinforcement learning with an appropriately defined state and reward can be used to construct such an adaptive allocation rule. The simulation study shows that the proposed method can successfully improve the performance metric to be optimized when compared with the equal allocation, D-optimal, and TD-optimal methods. In particular, when the mean absolute error was set to the metric to be optimized, it is possible to construct a rule that is superior for many metrics.

Adaptive dose-response studies to establish proof-of-concept in learning-phase clinical trials

In learning-phase clinical trials in drug development, adaptive designs can be efficient and highly informative when used appropriately. In this article, we extend the multiple comparison procedures with modeling techniques (MCP-Mod) procedure with generalized multiple contrast tests (GMCTs) to two-stage adaptive designs for establishing proof-of-concept. The results of an interim analysis of first-stage data are used to adapt the candidate dose-response models and the dosages studied in the second stage. GMCTs are used in both stages to obtain stage-wise p -values, which are then combined to determine an overall p -value. An alternative approach is also considered that combines the t -statistics across stages, employing the conditional rejection probability principle to preserve the Type I error probability. Simulation studies demonstrate that the adaptive designs are advantageous compared to the corresponding tests in a nonadaptive design if the selection of the candidate set of dose-response models is not well informed by evidence from preclinical and early-phase studies.

Utility-Based Dose Selection for Phase II Dose-Finding Studies

BACKGROUND AND OBJECTIVES

Dose selection is a key feature of clinical development. Poor dose selection has been recognized as a major driver of development failure in late phase. It usually involves both efficacy and safety criteria. The objective of this paper is to develop and implement a novel fully Bayesian statistical framework to optimize the dose selection process by maximizing the expected utility in phase III.

METHODS

The success probability is characterized by means of a utility function with two components, one for efficacy and one for safety. Each component refers to a dose-response model. Moreover, a sequential design (with futility and efficacy rules at the interim analysis) is compared to a fixed design in order to allow one to hasten the decision to perform the late phase study. Operating characteristics of this approach are extensively assessed by simulations under a wide range of dose-response scenarios.

RESULTS AND CONCLUSIONS

Simulation results illustrate the difficulty of simultaneously estimating two complex dose-response models with enough accuracy to properly rank doses using an utility function combining the two. The probability of making the good decision increases with the sample size. For some scenarios, the sequential design has good properties: with a quite large probability of study termination at interim analysis, it enables to reduce the sample size while maintaining the properties of the fixed design.

Optimal dose-finding for efficacy-safety models

Dose-finding is an important part of the clinical development of a new drug. The purpose of dose-finding studies is to determine a suitable dose for future development based on both efficacy and safety. Optimal experimental designs have already been used to determine the design of this kind of studies, however, often that design is focused on efficacy only. We consider an efficacy-safety model, which is a simplified version of the bivariate Emax model. We use here the clinical utility index concept, which provides the desirable balance between efficacy and safety. By maximizing the utility of the patients, we get the estimated dose. This desire leads us to locally c -optimal designs. An algebraic solution for c -optimal designs is determined for arbitrary c vectors using a multivariate version of Elfving's method. The solution shows that the expected therapeutic index of the drug is a key quantity determining both the number of doses, the doses itself, and their weights in the optimal design. A sequential design is proposed to solve the complication of parameter dependency, and it is illustrated in a simulation study.

The design heatmap: A simple visualization of D -optimality design problems

Optimal experimental designs are often formal and specific, and not intuitively plausible to practical experimenters. However, even in theory, there often are many different possible design points providing identical or nearly identical information compared to the design points of a strictly optimal design. In practical applications, this can be used to find designs that are a compromise between mathematical optimality and practical requirements, including preferences of experimenters. For this purpose, we propose a derivative-based two-dimensional graphical representation of the design space that, given any optimal design is already known, will show which areas of the design space are relevant for good designs and how these areas relate to each other. While existing equivalence theorems already allow such an illustration in regard to the relevance of design points only, our approach also shows whether different design points contribute the same kind of information, and thus allows tweaking of designs for practical applications, especially in regard to the splitting and combining of design points. We demonstrate the approach on a toxicological trial where a D -optimal design for a dose-response experiment modeled by a four-parameter log-logistic function was requested. As these designs require a prior estimate of the relevant parameters, which is difficult to obtain in a practical situation, we also discuss an adaption of our representations to the criterion of Bayesian D -optimality. While we focus on D -optimality, the approach is in principle applicable to different optimality criteria as well. However, much of the computational and graphical simplicity will be lost.

Design optimization for dose-finding trials: a review

Dose selection is one of the most difficult and crucial decisions to make during drug development. As a consequence, the dose-finding trial is a major milestone in the drug development plan and should be properly designed. This article will review the most recent methodologies for optimizing the design of dose-finding studies: all of them are based on the modeling of the dose-response curve, which is now the gold standard approach for analyzing dose-finding studies instead of the traditional ANOVA/multiple testing approach. We will address the optimization of both fixed and adaptive designs and briefly outline new methodologies currently under investigation, based on utility functions.

Parametric modeling and optimal experimental designs for estimating isobolograms for drug interactions in toxicology

In toxicology and related areas, interaction effects between two substances are commonly expressed through a combination index [Formula: see text] evaluated separately at different effect levels and mixture ratios. Often, these indices are combined into a graphical representation, the isobologram. Instead of estimating the combination indices at the experimental mixture ratios only, we propose a simple parametric model for estimating the underlying interaction function. We integrate this approach into a joint model where both the parameters of the dose-response functions of the singular substances and the interaction parameters can be estimated simultaneously. As an additional benefit, this concept allows to determine optimal statistical designs for combination studies optimizing the estimation of the interaction function as a whole. From an optimal design perspective, finding the interaction parameters generally corresponds to a [Formula: see text]-optimality resp. [Formula: see text]-optimality design problem, while estimation of all underlying dose response parameters corresponds to a [Formula: see text]-optimality design problem. We show how optimal designs can be obtained in either case as well as how combination designs providing reasonable performance in regard to both criteria can be determined by putting a constraint on the efficiency in regard to one of the criteria and optimizing for the other. As all designs require prior information about model parameter values, which may be unreliable in practice, the effect of misspecifications is investigated as well.

A decision theoretical modeling for Phase III investments and drug licensing

For a new candidate drug to become an approved medicine, several decision points have to be passed. In this article, we focus on two of them: First, based on Phase II data, the commercial sponsor decides to invest (or not) in Phase III. Second, based on the outcome of Phase III, the regulator determines whether the drug should be granted market access. Assuming a population of candidate drugs with a distribution of true efficacy, we optimize the two stakeholders' decisions and study the interdependence between them. The regulator is assumed to seek to optimize the total public health benefit resulting from the efficacy of the drug and a safety penalty. In optimizing the regulatory rules, in terms of minimal required sample size and the Type I error in Phase III, we have to consider how these rules will modify the commercial optimization made by the sponsor. The results indicate that different Type I errors should be used depending on the rarity of the disease.

Dose-ranging design and analysis methods to identify the minimum effective dose (MED)

In dose ranging clinical trials, it is critical to investigate the dose-response profile and to identify a minimum effective dose (MED) to guide the dose selection for phase 3 confirmatory trials. Traditional dose ranging trials focus on pairwise comparisons between placebo and each investigational dose, while in recent years MCP-Mod (Multiple Comparison Procedures & Modeling) arose and gained popularity in the design and analysis of dose ranging trials. Comprehensive comparison between MCP-Mod and other methods have been made on continuous variables assuming a normal distribution. In this article, we extend the comparison to binary/binomial response variables. Via simulation, the rate of correct and incorrect MED identification are compared for Dunnett's test, trend test and MCP-Mod for a variety of underlying dose response profiles including both monotone and non-monotone dose responses and are compared under a large number of trial design settings. The precision of MED estimation using MCP-Mod is also evaluated comparing the design options of more dose levels and smaller sample size per dose versus fewer dose levels and larger sample size per dose.

Phase II dose-response trials: A simulation study to compare analysis method performance under design considerations

Phase II trials are intended to provide information about the dose-response relationship and to support the choice of doses for a pivotal phase III trial. Recently, new analysis methods have been proposed to address these objectives, and guidance is needed to select the most appropriate analysis method in specific situations. We set up a simulation study to evaluate multiple performance measures of one traditional and three more recent dose-finding approaches under four design options and illustrate the investigated analysis methods with an example from clinical practice. Our results reveal no general recommendation for a particular analysis method across all design options and performance measures. However, we also demonstrate that the new analysis methods are worth the effort compared to the traditional ANOVA-based approach.

A Practical Guide to Data Monitoring Committees in Adaptive Trials

Adaptive clinical trials require access to interim data to carry out trial modification as allowed by a prespecified adaptation plan. A data monitoring committee (DMC) is a group of experts that is charged with monitoring accruing trial data to ensure the safety of trial participants and that in adaptive trials may also play a role in implementing a preplanned adaptation. In this paper, we summarize current practices and viewpoints and provide guidance on evolving issues related to the use of DMCs in adaptive trials. We describe the common types of adaptive designs and point out some DMC-related issues that are unique to this class of designs. We include 3 examples of DMCs in late-stage adaptive trials that have been implemented in practice. We advocate training opportunities for researchers who may be interested in serving on a DMC for an adaptive trial since qualified DMC members are fundamental to the successful execution of DMC responsibilities.

Implementation of maximin efficient designs in dose-finding studies

This paper considers the maximin approach for designing clinical studies. A maximin efficient design maximizes the smallest efficiency when compared with a standard design, as the parameters vary in a specified subset of the parameter space. To specify this subset of parameters in a real situation, a four-step procedure using elicitation based on expert opinions is proposed. Further, we describe why and how we extend the initially chosen subset of parameters to a much larger set in our procedure. By this procedure, the maximin approach becomes feasible for dose-finding studies. Maximin efficient designs have shown to be numerically difficult to construct. However, a new algorithm, the H-algorithm, considerably simplifies the construction of these designs. We exemplify the maximin efficient approach by considering a sigmoid Emax model describing a dose-response relationship and compare inferential precision with that obtained when using a uniform design. The design obtained is shown to be at least 15% more efficient than the uniform design.

An adaptive two-stage dose-response design method for establishing proof of concept

We propose an adaptive two-stage dose-response design where a prespecified adaptation rule is used to add and/or drop treatment arms between the stages. We extend the multiple comparison procedures-modeling (MCP-Mod) approach into a two-stage design. In each stage, we use the same set of candidate dose-response models and test for a dose-response relationship or proof of concept (PoC) via model-associated statistics. The stage-wise test results are then combined to establish "global" PoC using a conditional error function. Our simulation studies showed good and more robust power in our design method compared to conventional and fixed designs.

Dose-Response Determination in Multistage Endpoint Clinical Trials

Improper dose selection remains one of the key drivers of the large attrition rates observed in confirmatory studies in clinical drug development. Many factors contribute to this problem, such as insufficient resources allocated to dose-ranging studies and the use of statistical methods better suited for phase 3 studies than for dose selection. This paper describes a model-based dose-finding method that leverages all longitudinal data collected in the trial to estimate the dose-response relationship at any desired visit, using it to estimate target doses of interest, such as the minimum dose producing a desired clinical benefit. The approach uses a Markov chain model to account for correlation in the repeated measures obtained on the same patient. An actual phase 2 study and simulations are used to illustrate the methodology.

Compound designs for dose-finding in the presence of nondesignable covariates

Compound optimal designs are considered where one component of the design criterion is a traditional optimality criterion such as the D-optimality criterion, and the other component accounts for higher efficacy with low toxicity. With reference to the dose-finding problem, we suggest the technique to choose weights for the two components that makes the optimization problem simpler than the traditional penalized design. We allow general bivariate responses for efficacy and toxicity. We then extend the procedure in the presence of nondesignable covariates such as age, sex, or other health conditions. A new breast cancer treatment is considered to illustrate the procedures.

Functional uniform priors for nonlinear modeling

This article considers the topic of finding prior distributions when a major component of the statistical model depends on a nonlinear function. Using results on how to construct uniform distributions in general metric spaces, we propose a prior distribution that is uniform in the space of functional shapes of the underlying nonlinear function and then back-transform to obtain a prior distribution for the original model parameters. The primary application considered in this article is nonlinear regression, but the idea might be of interest beyond this case. For nonlinear regression the so constructed priors have the advantage that they are parametrization invariant and do not violate the likelihood principle, as opposed to uniform distributions on the parameters or the Jeffrey's prior, respectively. The utility of the proposed priors is demonstrated in the context of design and analysis of nonlinear regression modeling in clinical dose-finding trials, through a real data example and simulation.

Modelling and simulation in the pharmaceutical industry--some reflections

Modelling and simulation (M&S) is increasingly being applied in (clinical) drug development. It provides an opportune area for the community of pharmaceutical statisticians to pursue. In this article, we highlight useful principles behind the application of M&S. We claim that M&S should be focussed on decisions, tailored to its purpose and based in applied sciences, not relying entirely on data-driven statistical analysis. Further, M&S should be a continuous process making use of diverse information sources and applying Bayesian and frequentist methodology, as appropriate. In addition to forming a basis for analysing decision options, M&S provides a framework that can facilitate communication between stakeholders. Besides the discussion on modelling philosophy, we also describe how standard simulation practice can be ineffective and how simulation efficiency can often be greatly improved.

Adaptive dose-finding: Proof of concept with type I error control

We consider an adaptive dose-finding study with two stages. The doses for the second stage will be chosen based on the first stage results. Instead of considering pairwise comparisons with placebo, we apply one test to show an upward trend across doses. This is a possibility according to the ICH-guideline for dose-finding studies (ICH-E4). In this article, we are interested in trend tests based on a single contrast or on the maximum of multiple contrasts. We are interested in flexibly choosing the Stage 2 doses including the possibility to add doses. If certain requirements for the interim decision rules are fulfilled, the final trend test that ignores the adaptive nature of the trial (naïve test) can control the type I error. However, for the more common case that these requirements are not fulfilled, we need to take the adaptivity into account and discuss a method for type I error control. We apply the general conditional error approach to adaptive dose-finding and discuss special issues appearing in this application. We call the test based on this approach Adaptive Multiple Contrast Test. For an example, we illustrate the theory discussed before and compare the performance of several tests for the adaptive design in a simulation study.