Advanced Methods for Dose and Regimen Finding During Drug Development: Summary of the EMA/EFPIA Workshop on Dose Finding (London 4-5 December 2014).

Inadequate dose selection for confirmatory trials is currently still one of the most challenging issues in drug development, as illustrated by high rates of late-stage attritions in clinical development and postmarketing commitments required by regulatory institutions. In an effort to shift the current paradigm in dose and regimen selection and highlight the availability and usefulness of well-established and regulatory-acceptable methods, the European Medicines Agency (EMA) in collaboration with the European Federation of Pharmaceutical Industries Association (EFPIA) hosted a multistakeholder workshop on dose finding (London 4-5 December 2014). Some methodologies that could constitute a toolkit for drug developers and regulators were presented. These methods are described in the present report: they include five advanced methods for data analysis (empirical regression models, pharmacometrics models, quantitative systems pharmacology models, MCP-Mod, and model averaging) and three methods for study design optimization (Fisher information matrix (FIM)-based methods, clinical trial simulations, and adaptive studies). Pairwise comparisons were also discussed during the workshop; however, mostly for historical reasons. This paper discusses the added value and limitations of these methods as well as challenges for their implementation. Some applications in different therapeutic areas are also summarized, in line with the discussions at the workshop. There was agreement at the workshop on the fact that selection of dose for phase III is an estimation problem and should not be addressed via hypothesis testing. Dose selection for phase III trials should be informed by well-designed dose-finding studies; however, the specific choice of method(s) will depend on several aspects and it is not possible to recommend a generalized decision tree. There are many valuable methods available, the methods are not mutually exclusive, and they should be used in conjunction to ensure a scientifically rigorous understanding of the dosing rationale.

Optimal designs for active controlled dose-finding trials with efficacy-toxicity outcomes.

We derive optimal designs to estimate efficacy and toxicity in active controlled dose-finding trials when the bivariate continuous outcomes are described using nonlinear regression models. We determine upper bounds on the required number of different doses and provide conditions under which the boundary points of the design space are included in the optimal design. We provide an analytical description of minimally supported optimal designs and show that they do not depend on the correlation between the bivariate outcomes.

"Threshold-crossing": A Useful Way to Establish the Counterfactual in Clinical Trials?

A central question in the assessment of benefit/harm of new treatments is: how does the average outcome on the new treatment (the factual) compare to the average outcome had patients received no treatment or a different treatment known to be effective (the counterfactual)? Randomized controlled trials (RCTs) are the standard for comparing the factual with the counterfactual. Recent developments necessitate and enable a new way of determining the counterfactual for some new medicines. For select situations, we propose a new framework for evidence generation, which we call "threshold-crossing." This framework leverages the wealth of information that is becoming available from completed RCTs and from real world data sources. Relying on formalized procedures, information gleaned from these data is used to estimate the counterfactual, enabling efficacy assessment of new drugs. We propose future (research) activities to enable "threshold-crossing" for carefully selected products and indications in which RCTs are not feasible.

Simultaneous confidence bands for nonlinear regression models with application to population pharmacokinetic analyses.

Many applications in biostatistics rely on nonlinear regression models, such as, for example, population pharmacokinetic and pharmacodynamic modeling, or modeling approaches for dose-response characterization and dose selection. Such models are often expressed as nonlinear mixed-effects models, which are implemented in all major statistical software packages. Inference on the model curve can be based on the estimated parameters, from which pointwise confidence intervals for the mean profile at any single point in the covariate region (time, dose, etc.) can be derived. These pointwise confidence intervals, however, should not be used for simultaneous inferences beyond that single covariate value. If assessment over the entire covariate region is required, the joint coverage probability by using the combined pointwise confidence intervals is likely to be less than the nominal coverage probability. In this paper we consider simultaneous confidence bands for the mean profile over the covariate region of interest and propose two large-sample methods for their construction. The first method is based on the Schwarz inequality and an asymptotic χ(2) distribution. The second method relies on simulating from a multivariate normal distribution. We illustrate the methods with the pharmacokinetics of theophylline. In addition, we report the results of an extensive simulation study to investigate the operating characteristics of the two construction methods. Finally, we present extensions to construct simultaneous confidence bands for the difference of two models and to assess equivalence between two models in biosimilarity applications.

Assessing nonsuperiority, noninferiority, or equivalence when comparing two regression models over a restricted covariate region.

In many scientific problems the purpose of the comparison of two regression models, which describe the relationship between a same response variable and several same covariates for two different groups, is to demonstrate that one model is no higher than the other by a negligible amount, or to demonstrate that the models have only negligible differences and so they can be regarded as describing practically the same relationship between the response variable and the covariates. In this article, methods based on one-sided pointwise confidence bands are proposed for assessing the nonsuperiority of one model to the other and for assessing the equivalence of two regression models. Examples from QT/QTc study and from drug stability study are used to illustrate the methods.

Ordered multiple comparisons with the best and their applications to dose-response studies.

This article considers the problem of comparing several treatments (dose levels, interventions, etc.) with the best, where the best treatment is unknown and the treatments are ordered in some sense. Order relations among treatments often occur quite naturally in practice. They may be ordered according to increasing risks, such as tolerability or safety problems with increasing dose levels in a dose-response study, for example. We tackle the problem of constructing a lower confidence bound for the smallest index of all treatments being at most marginally less effective than the (best) treatment having the largest effect. Such a bound ensures at confidence level 1 -alpha that all treatments with lower indices are relevantly less effective than the best competitor. We derive a multiple testing strategy that results in sharp confidence bounds. The proposed lower confidence bound is compared with those derived from other testing strategies. We further derive closed-form expressions for power and sample size calculations. Finally, we investigate several real data sets to illustrate various applications of our methods.

Pooling batches in drug stability study by using constant-width simultaneous confidence bands.

One important study objective in drug stability studies is to estimate the shelf-life of a drug. A key statistical problem involved in this is how to assess the practical equivalence of different batches of the same drug so that different batches can be subgrouped to produce a single shelf-life for the drug. In this paper constant-width simultaneous confidence bands are proposed to quantify the magnitude of difference between different batches, with a particular view to establish the practical equivalence of different batches. This approach is suitable for the situation that the intercepts and slopes of the regression lines for the batches cannot be assumed to be equal. It is shown how constant-width simultaneous confidence bands can be easily constructed for the multiple comparison of several general linear regression models. In particular, it is shown that constant-width simultaneous confidence bands have a better chance to establish the equivalence than, and so are preferable to, the hyperbola-shaped simultaneous confidence bands considered.

Combining multiple comparisons and modeling techniques in dose-response studies.

The analysis of data from dose-response studies has long been divided according to two major strategies: multiple comparison procedures and model-based approaches. Model-based approaches assume a functional relationship between the response and the dose, taken as a quantitative factor, according to a prespecified parametric model. The fitted model is then used to estimate an adequate dose to achieve a desired response but the validity of its conclusions will highly depend on the correct choice of the a priori unknown dose-response model. Multiple comparison procedures regard the dose as a qualitative factor and make very few, if any, assumptions about the underlying dose-response model. The primary goal is often to identify the minimum effective dose that is statistically significant and produces a relevant biological effect. One approach is to evaluate the significance of contrasts between different dose levels, while preserving the family-wise error rate. Such procedures are relatively robust but inference is confined to the selection of the target dose among the dose levels under investigation. We describe a unified strategy to the analysis of data from dose-response studies which combines multiple comparison and modeling techniques. We assume the existence of several candidate parametric models and use multiple comparison techniques to choose the one most likely to represent the true underlying dose-response curve, while preserving the family-wise error rate. The selected model is then used to provide inference on adequate doses.

Design and analysis of two-color microarray experiments using linear models.

OBJECTIVES: A variety of linear models have recently been proposed for the design and analysis of microarray experiments. This article gives an introduction to the most common models and describes their respective characteristics. METHODS: We focus on the application of linear models to logarithmized and normalized microarray data from two-color arrays. Linear models can be applied at different stages of evaluating microarray experiments, such as experimental design, background correction, normalization and hypothesis testing. Both one-stage and two-stage linear models including technical and possibly biological replicates are described. Issues related to selecting robust and efficient microarray designs are also discussed. RESULTS: Linear models provide flexible and powerful tools, which are easily implemented and interpreted. The methods are illustrated with an experiment performed in our laboratory, which demonstrates the value of using linear models for the evaluation of current microarray experiments. CONCLUSIONS: Linear models provide a flexible approach to properly account for variability, both across and within genes. This allows the experimenter to adequately model the sources of variability, which are assumed to be of major influence on the final measurements. In addition, design considerations essential for any well-planned microarray experiments are best incorporated using linear models. Results from such experimental design investigations show that the widely used common reference design is often substantially less efficient than alternative designs and its use is therefore not recommended.

Multiplicity issues in microarray experiments.

OBJECTIVES: Discussion of different error concepts relevant to microarray experiments. Review of some commonly used multiple testing procedures. Comparison of different approaches as applied to gene expression data. METHODS: This article focuses on familywise error rate (FWER) and false discovery rate (FDR) controlling procedures. Methods under investigation include: Bonferroni-type methods and their improvements (including resampling approaches), modified Bonferroni methods, data-driven approaches, as well as the linear step-up method and its modifications. Particular emphasis lies on the description of the assumptions, advantages and limitations for the investigated methods. RESULTS: FWER controlling procedures are often too conservative in high dimensional screening studies. A better balance between the raw P-values and the stringent FWER-adjusted P-values may be required in many situations, as provided by FDR controlling and related procedures. CONCLUSIONS: The questions remain open, which error concept to apply and which multiple testing procedure to use. Although we believe that the FDR or one of its variants will be applied more often in the future, longterm experience with microarray technology is missing and thus the validity of appropriate multiple test procedures cannot yet be assessed for microarray data analysis.

On a hybrid method in dose finding studies.

OBJECTIVES: Combination of multiple testing and modeling techniques in dose-response studies. Use of hypotheses tests to assess the significance of the dose-response signal associated with a given candidate dose-response model. Estimation of target dose(s) following the previous model selection step. Illustration of the method with a real data example. METHODS: We assume a set of candidate models potentially reflecting the data generating process. The appropriateness of each individual model is evaluated in terms of contrast tests, where each set of contrast weights describes a specific dose-response shape. Optimum contrast weights are computed, which maximize the non-centrality parameters associated with the contrast tests. A reference set of appropriate candidate models is obtained while controlling the familywise error rate. A single model is then selected from this reference set using standard model selection criteria. The final step is devoted to dose finding by applying inverse regression techniques. This is illustrated for estimating the minimum effective dose. RESULTS: The method is as powerful as competing standard dose-response tests to detect an overall dose-related trend. In addition, the possibility is given to estimate one or more target doses of interest. The analysis of a real data example confirms the advantages of the proposed hybrid method. CONCLUSIONS: Combining multiple testing and modeling techniques leads to a powerful tool, which uses the advantages of both approaches: Rigid error control at the significance testing step and flexibility at the dose estimation step. The method can be extended to handle more general linear models including covariates and factorial treatment structures.

Simultaneous confidence intervals for ratios with applications to the comparison of several treatments with a control.

OBJECTIVES: In this article, we illustrate and compare exact simultaneous confidence sets with various approximate simultaneous confidence intervals for multiple ratios as applied to many-to-one comparisons. Quite different datasets are analyzed to clarify the points. METHODS: The methods are based on existing probability inequalities (e.g., Bonferroni, Slepian and Sidak), estimation of nuisance parameters and re-sampling techniques. Exact simultaneous confidence sets based on the multivariate t-distribution are constructed and compared with approximate simultaneous confidence intervals. RESULTS: It is found that the coverage probabilities associated with the various methods of constructing simultaneous confidence intervals (for ratios) in manyto-one comparisons depend on the ratios of the coefficient of variation for the mean of the control group to the coefficient of variation for the mean of the treatments. If the ratios of the coefficients of variations are less than one, the Bonferroni corrected Fieller confidence intervals have almost the same coverage probability as the exact simultaneous confidence sets. Otherwise, the use of Bonferroni intervals leads to conservative results. CONCLUSIONS: When the ratio of the coefficient of variation for the mean of the control group to the coefficient of variation for the mean of the treatments are greater than one (e.g., in balanced designs with increasing effects), the Bonferroni simultaneous confidence intervals are too conservative. Therefore, we recommend not using Bonferroni for this kind of data. On the other hand, the plug-in method maintains the intended confidence coefficient quite satisfactorily; therefore, it can serve as the best alternative in any case.

Testing dose-response relationships with a priori unknown, possibly nonmonotone shapes.

Usually, a monotone dose-response dependence can be assumed for the simultaneous comparison of increasing levels of a certain drug. However, sometimes a reversal of the dose-response curve is likely to occur at the higher doses. We investigate such violations of the monotonicity assumption. Adequate alternatives are discussed and the "protected trend alternative" is introduced. Together with the umbrella patterns described in the literature, we introduce new testing approaches for both alternatives. P-values/quantiles and power values/sample sizes are made numerically available and hence are readily computed. A short power study and the analysis of a data set from the literature demonstrate the improved behavior of the new methods.

Equivalence concepts in clinical trials.

According to the recent ICH E9 Guidance Statistical Principles for Clinical Trials, efficacy is most convincingly established by demonstrating superiority to placebo, by showing superiority to an active control treatment or by demonstrating a dose-response relationship (so-called 'superiority' trials). For serious illnesses, a placebo-controlled trial may be considered unethical if a therapeutic treatment exists which has proven efficacious in relevant superiority trial(s). In that case, the scientifically sound use of an active treatment as a control should be considered. Active control trials designed to show that the efficacy of an investigational product is not relevantly worse than that of the active comparator are called 'non-inferiority' trials (1). After having confirmed non-inferiority, superiority of the alternative test treatment over the reference treatment can additionally be tested without the need to adjust the significance level (2). In contrast to cross-over bioequivalence trials based on pharmacokinetic endpoints such as AUC and Cmax, therapeutic equivalence and non-inferiority trials are based on clinical end-points. Therefore, they are often conducted as parallel group comparisons. It is important to note that the conclusion of equivalence or non-inferiority is based on the inclusion of the appropriate confidence interval in the equivalence acceptance range, and that it cannot be derived from a non-significant test result of the inappropriate null hypothesis of no treatment difference.