Statistical considerations in model-based dose finding for binary responses under model uncertainty

The statistical methodology for model-based dose finding under model uncertainty has attracted increasing attention in recent years. While the underlying principles are simple and easy to understand, developing and implementing an efficient approach for binary responses can be a formidable task in practice. Motivated by the statistical challenges encountered in a phase II dose finding study, we explore several key design and analysis issues related to the hybrid testing-modeling approaches for binary responses. The issues include candidate model selection and specifications, optimal design and efficient sample size allocations, and, notably, the methods for dose-response testing and estimation. Specifically, we consider a class of generalized linear models suited for the candidate set and establish D-optimal designs for these models. Additionally, we propose using permutation-based tests for dose-response testing to avoid asymptotic normality assumptions typically required for contrast-based tests. We perform trial simulations to enhance our understanding of these issues.

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.

Comparison of Lethal Doses Calculated Using Logit/Probit-Log(Dose) Regressions With Arbitrary Slopes Using R

The median lethal dose (LD50) is commonly used to indicate acute toxicity of an insecticide to an insect species. Approximate confidence intervals for LD50s are often calculated using the Fieller and delta methods. It is often necessary to compare the relative potencies of several insecticides with a population or of one insecticide with different populations. Comparing the LD50s using probit/logit-log(dose) regressions with parallel slopes can be implemented in many software packages, but for the cases with arbitrary slopes are not generally available. We used the glm function in R to calculate and compare lethal doses without assuming equal slopes. Bioassay datasets from the literature fitted using the logit model gave the 95% confidence limits (95% CLs) for the lethal doses using Fieller's theorem and incorporating a heterogeneity factor identical to the 95% CLs determined using the PoloPlus software. The delta method gave 95% CLs identical to the 95% CLs determined using the R drc package. The same datasets fitted using the probit model gave 95% CLs similar to the 95% CLs determined using PoloPlus and the drc package. The natural response rates for the control group were included using Abbott's equation. When the potency ratio method and the z-test were used to identify differences between two lethal doses, and when the χ2 and log likelihood ratio tests were used to determine whether the regression lines were parallel, the conclusions were the same as those gave by PoloPlus and the drc package.

Opportunity for efficiency in clinical development: An overview of adaptive clinical trial designs and innovative machine learning tools, with examples from the cardiovascular field

Modern data analysis tools and statistical modeling techniques are increasingly used in clinical research to improve diagnosis, estimate disease progression and predict treatment outcomes. What seems less emphasized is the importance of the study design, which can have a serious impact on the study cost, time and statistical efficiency. This paper provides an overview of different types of adaptive designs in clinical trials and their applications to cardiovascular trials. We highlight recent proliferation of work on adaptive designs over the past two decades, including some recent regulatory guidelines on complex trial designs and master protocols. We also describe the increasing role of machine learning and use of metaheuristics to construct increasingly complex adaptive designs or to identify interesting features for improved predictions and classifications.

cLRT-Mod: An efficient methodology for pharmacometric model-based analysis of longitudinal phase II dose finding studies under model uncertainty

Within the challenging context of phase II dose-finding trials, longitudinal analyses may increase drug effect detection power compared to an end-of-treatment analysis. This work proposes cLRT-Mod, a pharmacometric adaptation of the MCP-Mod methodology, which allows the use of nonlinear mixed effect models to first detect a dose-response signal and then identify the doses for the confirmatory phase while accounting for model structure uncertainty. The method was evaluated through extensive clinical trial simulations of a hypothetical phase II dose-finding trial using different scenarios and comparing different methods such as MCP-Mod. The results show an increase in power using cLRT with longitudinal data compared to an EOT multiple contrast tests for scenarios with small sample size and weak drug effect while maintaining pre-specifiability of the models prior to data analysis and the nominal type I error. This work shows how model averaging provides better coverage probability of the drug effect in the prediction step, and avoids under-estimation of the size of the confidence interval. Finally, for illustration purpose cLRT-Mod was applied to the analysis of a real phase II dose-finding trial.

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.

Generalized multiple contrast tests in dose-response studies

In the process of developing drugs, proof-of-concept studies can be helpful in determining whether there is any evidence of a dose-response relationship. A global test for this purpose that has gained popularity is a component of the multiple comparisons procedure with modeling techniques (MCP-Mod), which involves the specification of a candidate set of several plausible dose-response models. For each model, a test is performed for significance of an optimally chosen contrast among the sample means. An overall P-value is obtained from the distribution of the maximum of the contrast statistics. This is equivalent to basing the test on the minimum of the P-values arising from these contrast statistics and, hence, can be viewed as a method for combining dependent P-values. We generalize this idea to the use of different statistics for combining the dependent P-values, such as Fisher's combination method or the inverse normal combination method. Simulation studies show that the generalized multiple contrast tests (GMCTs) based on the Fisher and inverse normal methods are generally more powerful than the MCP-Mod procedure based on the minimum of the P-values except for cases where the true dose-response model is, in a sense, near the extremes of the candidate set of dose-response models. The proposed GMCTs can also be used for model selection and dosage selection by employing a closed testing procedure.

The Case for an Unblinded Modeler in Early Clinical Development

The current trend for clinical pharmacology is toward more complex studies (eg, umbrella protocols covering single and multiple ascending doses, food effect, metabolism pathways), requiring many decisions to be made during their conduct. This article discusses guidance of such early clinical studies by modeling and simulation. The ability to make use of all available information each time new data become available during the study requires the modeling scientist to be unblinded. This must of course not jeopardize the blinding of the clinical team, and this article discusses how unblinding can be prevented. Although modeling and simulation are established for guidance of the drug development process overall, they are not frequently used for guidance on a small scale, that is, during studies with the largest uncertainty, the first-in-human studies. Application of a quantitative model backbone makes early clinical drug development a more efficient process and provides additional safety for healthy subjects and patients. Real clinical impact is illustrated by 3 case studies that show different contributions from unblinded modeling: dose escalation based on safety data, modeling and predicting with explicit incorporation of in vitro data, and dose escalation supported by unblinded analysis of adverse event data, which resulted in new insights of the clinical team without being unblinded and made it possible to proceed with dose escalation and to extend the study with an up-titration group.

Implementing Optimal Designs for Dose-Response Studies Through Adaptive Randomization for a Small Population Group

In dose-response studies with censored time-to-event outcomes, D-optimal designs depend on the true model and the amount of censored data. In practice, such designs can be implemented adaptively, by performing dose assignments according to updated knowledge of the dose-response curve at interim analysis. It is also essential that treatment allocation involves randomization-to mitigate various experimental biases and enable valid statistical inference at the end of the trial. In this work, we perform a comparison of several adaptive randomization procedures that can be used for implementing D-optimal designs for dose-response studies with time-to-event outcomes with small to moderate sample sizes. We consider single-stage, two-stage, and multi-stage adaptive designs. We also explore robustness of the designs to experimental (chronological and selection) biases. Simulation studies provide evidence that both the choice of an allocation design and a randomization procedure to implement the target allocation impact the quality of dose-response estimation, especially for small samples. For best performance, a multi-stage adaptive design with small cohort sizes should be implemented using a randomization procedure that closely attains the targeted D-optimal design at each stage. The results of the current work should help clinical investigators select an appropriate randomization procedure for their dose-response study.

Clinical dose-response for a broad set of biological products: A model-based meta-analysis

Characterizing clinical dose-response is a critical step in drug development. Uncertainty in the dose-response model when planning a dose-ranging study can often undermine efficiency in both the design and analysis of the trial. Results of a previous meta-analysis on a portfolio of small molecule compounds from a large pharmaceutical company demonstrated a consistent dose-response relationship that was well described by the maximal effect model. Biologics are different from small molecules due to their large molecular sizes and their potential to induce immunogenicity. A model-based meta-analysis was conducted on the clinical efficacy of 71 distinct biologics evaluated in 91 placebo-controlled dose-response studies published between 1995 and 2014. The maximal effect model, arising from receptor occupancy theory, described the clinical dose-response data for the majority of the biologics (81.7%, n = 58). Five biologics (7%) with data showing non-monotonic trend assuming the maximal effect model were identified and discussed. A Bayesian model-based hierarchical approach using different joint specifications of prior densities for the maximal effect model parameters was used to meta-analyze the whole set of biologics excluding these five biologics ( n = 66). Posterior predictive distributions of the maximal effect model parameters were reported and they could be used to aid the design of future dose-ranging studies. Compared to the meta-analysis of small molecules, the combination of fewer doses, narrower dosing ranges, and small sample sizes further limited the information available to estimate clinical dose-response among biologics.

Model selection versus model averaging in dose finding studies

A key objective of Phase II dose finding studies in clinical drug development is to adequately characterize the dose response relationship of a new drug. An important decision is then on the choice of a suitable dose response function to support dose selection for the subsequent Phase III studies. In this paper, we compare different approaches for model selection and model averaging using mathematical properties as well as simulations. We review and illustrate asymptotic properties of model selection criteria and investigate their behavior when changing the sample size but keeping the effect size constant. In a simulation study, we investigate how the various approaches perform in realistically chosen settings. Finally, the different methods are illustrated with a recently conducted Phase II dose finding study in patients with chronic obstructive pulmonary disease. Copyright © 2016 John Wiley & Sons, Ltd.

Designing dose finding studies with an active control for exponential families

Optimal design of dose-finding studies with an active control has only been considered in the literature for regression models with normally distributed errors and known variances, where the focus is on estimating the smallest dose that achieves the same treatment effect as the active control. This paper discusses such dose-finding studies from a broader perspective. We consider a general class of optimality criteria and models arising from an exponential family. Optimal designs are constructed for several situations and their efficiency is illustrated with examples.

Spline-based procedures for dose-finding studies with active control

In a dose-finding study with an active control, several doses of a new drug are compared with an established drug (the so-called active control). One goal of such studies is to characterize the dose–response relationship and to find the smallest target dose concentration d^*, which leads to the same efficacy as the active control. For this purpose, the intersection point of the mean dose–response function with the expected efficacy of the active control has to be estimated. The focus of this paper is a cubic spline-based method for deriving an estimator of the target dose without assuming a specific dose–response function. Furthermore, the construction of a spline-based bootstrap CI is described. Estimator and CI are compared with other flexible and parametric methods such as linear spline interpolation as well as maximum likelihood regression in simulation studies motivated by a real clinical trial. Also, design considerations for the cubic spline approach with focus on bias minimization are presented. Although the spline-based point estimator can be biased, designs can be chosen to minimize and reasonably limit the maximum absolute bias. Furthermore, the coverage probability of the cubic spline approach is satisfactory, especially for bias minimal designs. © 2014 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Optimizing Sedative Dose in Preterm Infants Undergoing Treatment for Respiratory Distress Syndrome

The Intubation-Surfactant-Extubation (INSURE) procedure is used worldwide to treat pre-term newborn infants suffering from respiratory distress syndrome, which is caused by an insufficient amount of the chemical surfactant in the lungs. With INSURE, the infant is intubated, surfactant is administered via the tube to the trachea, and at completion the infant is extubated. This improves the infant's ability to breathe and thus decreases the risk of long term neurological or motor disabilities. To perform the intubation safely, the newborn infant first must be sedated. Despite extensive experience with INSURE, there is no consensus on what sedative dose is best. This paper describes a Bayesian sequentially adaptive design for a multi-institution clinical trial to optimize the sedative dose given to pre-term infants undergoing the INSURE procedure. The design is based on three clinical outcomes, two efficacy and one adverse, using elicited numerical utilities of the eight possible elementary outcomes. A flexible Bayesian parametric trivariate dose-outcome model is assumed, with the prior derived from elicited mean outcome probabilities. Doses are chosen adaptively for successive cohorts of infants using posterior mean utilities, subject to safety and efficacy constraints. A computer simulation study of the design is presented.

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.

Web-based tools for finding optimal designs in biomedical studies

Experimental costs are rising and applications of optimal design ideas are increasingly applied in many disciplines. However, the theory for constructing optimal designs can be esoteric and its implementation can be difficult. To help practitioners have easier access to optimal designs and better appreciate design issues, we present a web site at http://optimal-design.biostat.ucla.edu/optimal/ capable of generating different types of tailor-made optimal designs for popular models in the biological sciences. This site also evaluates various efficiencies of a user-specified design and so enables practitioners to appreciate robustness properties of the design before implementation.