Valerii V Fedorov

Statistics is an essential discipline in the biopharmaceutical research and development enterprise. The value of statistics may be even more pronounced in developing novel treatment modalities such as digital therapeutics (DTx). This chapter provides an overview of challenges and opportunities for applying statistical thinking in DTx product develo...

We discuss how to structure large pharmaceutical projects that include a relatively large number of clinical sub-trials, of which basket, umbrella and platform trials provide popular examples. Such trials may be unified under the concept of a cluster trial, and subsequently similar design methods can be applied to all of them. While presenting two a...

In clinical studies together with uncertainties associated with observed endpoints we face uncertainties caused by enrolment process that often can be viewed as stochastic process. If one observes time to event then the subject exposure intervals and censoring times are random. Thus unlike to the traditional optimal design setting the amount of inf...

In clinical studies with time-to-event end points we face uncertainties caused by the enrollment process that can often be viewed as a stochastic process. The observed endpoints are randomly censored and the amount of gained information is random and its actual value is not known at the design stage but becomes known only after the study completion...

Randomized discontinuation trial (RDT) has gained popularity across a number of therapeutic areas. Oncology is one of the most known. In the simplest case, at the initial open-label stage all patients are treated with the experimental treatment to identify a population of responders. This stage is followed by a randomized two-arm trial to compare t...

In this paper, the authors describe developments in adaptive design methodology and discuss implementation strategies and operational challenges in early-phase adaptive clinical trials. The BATTLE trial-the first completed biomarker-based Bayesian adaptive randomized study in lung cancer-is presented as a case study to illustrate main ideas and sha...

Optimal Design for Nonlinear Response Models discusses the theory and applications of model-based experimental design with a strong emphasis on biopharmaceutical studies. The book draws on the authors’ many years of experience in academia and the pharmaceutical industry. While the focus is on nonlinear models, the book begins with an explanation o...

In dose-finding clinical studies, it is common that multiple endpoints are of interest. For instance, in phase I/II studies, efficacy and toxicity are often the primary endpoints, which are observed simultaneously and which need to be evaluated together. Motivated by this, we confine ourselves to bivariate responses and focus on the most analytical...

We discuss a Matlab-based library for constructing optimal sampling schemes for pharmacokinetic (PK) and pharmacodynamic (PD) studies. The software relies on optimal design theory for nonlinear mixed effects models and, in particular, on the first-order optimization algorithm. The library includes a number of popular compartmental PK and combined P...

Ideally, a clinical trial should be able to demonstrate not only a statistically significant improvement in the primary efficacy endpoint, but also that the magnitude of the effect is clinically relevant. One approach to address this question, often proposed by clinical societies and regulatory guidance, is a responder analysis, in which a continuo...

In compartmental pharmacokinetic (PK) modelling, ordinary differential equations (ODE) are traditionally used with two sources of randomness: measurement error and population variability. In this paper we focus on intrinsic (within-subject) variability modelled with stochastic differential equations (SDE), and consider stochastic systems with posit...

After a short historical introduction, the properties and numerical methods are the focal point of discussion. Construction of discrete and adaptive designs demand more extended exposition and are beyond the scope of this article but the information about the corresponding publications is provided. Copyright © 2010 John Wiley & Sons, Inc. For furth...

Multiple-endpoint models are widely used in drug development and other fields. It is common that the endpoints have different characteristics such as all continuous, all binary, or a mixture of them. This study investigates mixed responses, one continuous and one binary, correlated and observed simultaneously. It is an extension of our previous stu...

The design of multicentre clinical studies consists of several interconnected stages including patient recruitment prediction, choosing a randomization scheme and a statistical model for analyzing patient responses, and drug supply planning. The Research Statistics Unit (RSU) at GlaxoSmithKline (GSK) has developed a risk-based supply modeling tool...

Some general points regarding efficiency in clinical trials are made. Reasons as to why fitting many covariates to adjust the estimate of the treatment effect may be less problematic than commonly supposed are given. Two methods of dynamic allocation of patients based on covariates, minimization and Atkinson's approach, are compared and contrasted...

Dichotomization is the transformation of a continuous outcome (response) to a binary outcome. This approach, while somewhat common, is harmful from the viewpoint of statistical estimation and hypothesis testing. We show that this leads to loss of information, which can be large. For normally distributed data, this loss in terms of Fisher's informat...

We introduce a two-stage design for dose-finding in the context of Phase I/II studies, where two binary correlated endpoints are available, for instance, one for efficacy and one for toxicity. The bivariate probit model is used as a working model for the dose-response relationship. Given a 'desirable point' for the marginal probabilities of efficac...

We propose a new adaptive procedure for dose-finding in clinical trials with combination of two drugs when both efficacy and toxicity responses are available. We model the distribution of this bivariate binary endpoint using the bivariate probit model. The analytic formulae for the Fisher information matrix are obtained, that form the basis for der...

Enrichment designs usually consist of two or three stages, where the first stage serves as a screening process for selecting a certain subpopulation, and the succeeding stages serve to distinguish the treatment effect from the placebo effect, within the selected (enriched) subpopulation. The efficiency of its efficacy (response) detection comes at...

This paper is focused on statistical modelling, prediction and adaptive adjustment of patient recruitment in multicentre clinical trials. We consider a recruitment model, where patients arrive at different centres according to Poisson processes, with recruitment rates viewed as a sample from a gamma distribution. A statistical analysis of completed...

There are a few sources of uncertainty/variability associated with patient recruitment in multicentre clinical trials: uncertainties in prior information, stochasticity in patient arrival and centre initiation processes. Methods of statistical modeling, prediction and adaptive adjustment of recruitment are proposed to address these issues. The proc...

In clinical studies, continuous endpoints are very commonly seen. However, either for ease of interpretation or to simplify the reporting process, some continuous endpoints are often reported and (unfortunately) analyzed as binary or ordinal responses. We emphasize the usefulness of differentiation between response and utility functions and develop...

Pharmacokinetic (PK) studies with serial sampling which are described by compartmental models are discussed. We focus on intrinsic variability induced by the noise terms in stochastic differential equations (SDE). For several models of intrinsic randomness, we find explicit expressions for mean and covariance functions of the solution of the system...

The design and analysis of multicenter trials based on a random effects model is well developed for a continuous response, but is less well developed for a binary response. Here we describe a random effects model for a binary response for two treatments and show how maximum likelihood estimates for the unknown treatment difference can be derived us...

Often in clinical trials the observed responses are continuous but a regulatory agency will approve the drug only if the probability is sufficiently large that the efficacy measure exceeds a predefined threshold and the toxicity does not exceed another given threshold. Thus the measure of interest (utility) is based on dichotomized responses. We co...

In pharmacokinetic (PK) studies, including bioavailability assessment, various population PK measures, such as area under the curve (AUC), maximal concentration (Cmax) and time to maximal concentration (Tmax) are estimated. In this paper we compare a model-based approach, where parameters of a compartmental model are estimated and the explicit form...

In this paper we consider optimal design of experiments for correlated observations. We approximate the error component of the process by an eigenvector expansion of the corresponding covariance function. Furthermore we study the limiting behavior of an additional white noise as a regularization tool. The approach is illustrated by some typical exa...

This chapter is devoted to the investigation of multicentre clinical trials with random enrolment, where the patients enter the centres at random according to doubly stochastic Poisson processes. We consider two-arm trials and use a random-effects model to describe treatment responses. The time needed to complete the trial (recruitment time) and th...

In this chapter we discuss optimal experimental designs for nonlinear models arising in various pharmaceutical applications and present a short survey of optimal design methods and numerical algorithms. We provide SAS code to implement optimal design algorithms for several examples: • quantal models such as logistic models for analyzing success or...

We propose a correlated beta-binomial model for the binary response in multi-centre trials. The likelihood function in this case has a closed-form and we avoid multivariate numerical integrations in determining the maximum likelihood estimator. Based on derived asymptotic variance-covariance matrix of the MLE, we obtain relatively simple formulae t...

We propose a new adaptive procedure for dose-finding in clinical trials when both efficacy and toxicity responses are available. We model the distribution of this bivariate binary endpoint using either Gumbel bivariate logistic regression or Cox bivariate binary model. In both cases, the analytic formulae for the Fisher information matrix are obtai...

In clinical pharmacokinetic (PK) studies multiple blood samples are taken for each enrolled patient, and various population PK measures, such as area under the curve (AUC), maximal concentration (Cmax) and time to maximal concentration (Tmax) are estimated. In this paper we compare a model-based approach, where parameters of a compartmental model a...

In a placebo-controlled vaccine safety trial, the primary interest is to demonstrate that the vaccine is sufficiently safe, rejecting the null hypothesis that the relative risk of an adverse event attributable to the vaccine is above a prespecified value, greater than one. We develop sequential as well as multistage designs for such trials where th...

We propose a new method for selection of the most informative variables from the set of variables which can be measured directly. The information is measured by metrics similar to those used in experimental design theory, such as determinant of the dispersion matrix of prediction or various functions of its eigenvalues. The basic model admits both...

We present an overview of optimal design methods, together with some new findings that can be applied in drug development. In Section 5.2, we introduce optimal design concepts via binary dose response models. In Section 5.3, examples of continuous models are given, and the optimal design problem for a general nonlinear regression model is formulate...

The analysis of data collected in multicentre trials offers challenges because the data from the individual centres must be combined in some way to give an overall evaluation of the differences between the treatments in the trial. We propose that the combined response to treatment (CRT) be used as this overall measure. The definition and estimation...

We consider the problem of analyzing multi-center clinical trials when the number of patients at each center and on each treatment arm is random and follows the Poisson distribution. Theoretical approximations are made for the first two moments of the mean square errors (MSE's) for three different estimators of treatment effect difference that are...

We propose various stochastic enrolment models and derive probability distributions for the number of patients across the centres and the number of centres with a given number of patients. To estimate parameters of these distributions we use a few difierent estimators and flnd either analytically or using Monte Carlo simulation that these estimator...

Whenever a response is naturally confined to a finite interval (such as a visual analog scale for pain severity), the beta distribution provides a simple and flexible probability distribution to model such a response. The parameters of the distribution can then be related to covariates, such as dose, in a clinical trial through the generation of a...

The three fixed effects estimators of a treatment,difference are compared under conditions of random enrollment in a multicenter clinical trial. These comparisons are performed by assuming five different enrollment schemes. The estimators are compared via simulation using their expected mean squared errors. Unlike previous discussions of these thre...

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We discuss estimation methods for multiresponse models with a variance matrix that depends on unknown parameters. An iterated estimator is proposed that is asymptotically equivalent to a maximum likelihood estimator. Numerically, this estimator is close to the iteratively reweighted least squares method. However, in the situations when the informat...

This chapter is devoted to the investigation of multicentre clinical trials with random enrolment, where the patients enter the centres at random according to doubly stochastic Poisson processes. We consider two-arm trials and use a random-effects model to describe treatment responses. The time needed to complete the trial (recruitment time) and th...

We discuss asymptotic properties of the maximum likelihood estimators for a combined response to treatment (CRT) of two-arm multicentre clinical trials under random recruitment. Responses to different treatments are described by a random effects model. The conditions of consistency and asymptotic normality of the estimator of a CRT are given under...

We discuss the construction of D-optimal designs for regression models with forced measurements. Such models may be used in dose response studies where a baseline measurement is taken for all patients, i.e. forced in the design.

Fedorov et al. (2002) gave formulae for the variance of the estimated ECRT (expected combined response to treatment) and the optimal number of centres and total number of patients to use in a multicentre trial in a setting where the number of patients on each treatment arm in each centre was considered fixed. Here we extend these results to the set...

Principal components methods and factor analysis are popular tools for the dimension-reduction problem. These techniques can be used to obtain a smaller number of new variables. However, the new variables may include all or most of the original variables. In this study, two methods are given which will select the most informative subset of variable...

In this paper we propose a methodology for evaluating the bioequivalence of two formulations of a drug that encompasses not only average bioequivalence (ABE), but also the more recently introduced measures of population bioequivalence (PBE) and individual bioequivalence (IBE). The latter two measures are concerned with prescribability (PBE) and swi...

Detection of weak signals for large size contingency tables is a common task arising from post marketing drug adverse event detection� By using di�erent measures of the strength for the potential signals� di�erent �lters may be developed� Traditional statistical methods such as PRR and � � methods targeting the association in contingency tables hav...

Model fitting when the variance function depends on unknown parameters is a popular problem in many areas of research. Iterated estimators which are asymptotically equivalent to maximum likelihood estimators are proposed and their convergence is discussed. From a computational point of view, these estimators are very close to the iteratively reweig...

In a vaccine safety trial, the primary interest is to demonstrate that the vaccine is sufficiently safe, rejecting the null hypothesis that the relative risk of an adverse event attributable to the new vaccine is above a prespecified value, greater than one. We evaluate the exact probability of type I error of the likelihood score test, with sample...

Dragalin, et al. (2001) defined a combined response to treatment (CRT) in a multicentre trial and showed how it could be estimated using fixed eects,models which are appropriate in the ”test- ground” setting. Here we extend the previous work to the situation where centres can be viewed as a sample from a population and the treatment and centre eect...

Analyses of multicenter trials consider the estimated treatment effect differences of the individual centers and combine them into an estimate of the overall treatment effect. There has been much debate in the literature concerning the best way to combine these treatment effect differences. We emphasize that first of all one should define the combi...

We discuss optimal experimental design issues for nonlinear models arising in dose response studies. The optimization is performed with respect to various criteria which depend on the Fisher information matrix. Special attention is given to models with a variance component that depends on unknown parameters.

We propose a simple method for comparison of series of matched observations. While in all our examples we address “individual bioequivalence” (IBE), which is the subject of much discussion in pharmaceutical statistics, the methodology can be applied to a wide class of cross-over experiments, including cross-over imaging. From the statistical point...

We discuss optimal design for multiresponse models with a variance matrix that depends on unknown parameters. The approach relies on optimization of convex functions of the Fisher information matrix. We propose iterated estimators which are asymptotically equivalent to maximum likelihood estimators. Combining these estimators with convex design the...

The chapters in this volume present the state of optimum experimental design at the beginning of the new millennium, with an emphasis on developing areas. The contributions range from theory to applications, starting with a glimpse back to the beginnings of optimum experimental design. Theoretical chapters cover the properties and methods of constr...

Regression models with the variance function depending on unknown parameters appear in a number of practical problems (variogram fitting and mixed effect models are popular examples). We found that estimation of parameters entering both response and variance functions can be combined in a rather simple way. The proposed estimator belongs to the cla...

An important problem in pharmaceutical research is whether individual testing of components should be made, or alternatively, the components should be tested in groups. Of more importance is that the cost of the experiment is economically viable, for multi-stage procedures the cost of additional stages must be taken into consideration along with th...

Analyses of multicentre trials consider the estimated treatment effect differences of the individual centres and combine them into an estimate of the overall treatment effect. There has been much debate in the literature concerning the best way to combine these treatment effect differences. We emphasize that first of all one should define the combi...

Standard{close_quotes} approaches such as regression analysis, Fourier analysis, Box-Jenkins procedure, et al., which handle a data series as a whole, are not useful for very large data sets for at least two reasons. First, even with computer hardware available today, including parallel processors and storage devices, there are no effective means f...

Models and Information Matrix. Most of the results in experimental design theory are related to the linear regression models: $$ E\{ y|x\} = \eta ({\theta ^T},x) and Var\{ y|x\} = \sigma 2(x), $$ (17.1.1) where the observation y is a random variable, E and Var stand for expectation and variance, respectively.

Standard" approaches, such as regression analysis, Fourier analysis, Box-Jenkins procedure, etc., that handle a data series as a whole are not useful for very large data sets for at least two reasons. First, even with computer hardware available today, including parallel processors and storage devices, there are no e ective means for manipulating a...

We consider the design of experiments when estimation is to be performed using locally weighted regression methods. We adopt criteria that consider both estimation error (variance) and error resulting from model misspecification (bias). Working with continuous designs, we use the ideas developed in convex design theory to analyze properties of the...

Salt loadings approaching 50 wt % were tolerated in cementitious waste forms that still met leach and strength criteria, addressing a Technology Deficiency of low salt loadings previously identified by the Mixed Waste Focus Area. A statistical design quantified the effect of different stabilizing ingredients and salt loading on performance at lower...

Many contemporary publications on network traffic gravitate to ideas of selfsimilarity and long-range dependence. The corresponding elegant and parsimonious mathematical techniques proved to be efficient for the description of a wide class of aggregated processes. Sharing the enthusiasm about the above ideas we also believe that whenever it is poss...

Many contemporary publications on network traffic gravitate to ideas of selfsimilarity and long-range dependence. The corresponding elegant and parsimonious mathematical techniques proved to be efficient for the description of a wide class of aggregated processes. Sharing the enthusiasm about the above ideas we also believe that whenever it is poss...

A class of model-robust optimal designs, based on an extension of the standard optimality criteria to cases where there exist some prior information on the validity of a response function, is considered. Under this set-up, the concept of the “model validity range” is introduced and explored. A necessary condition for optimality is obtained for the...

The idea of applying experimental design methodologies to develop monitoring systems for computer networks is relatively novel even though it was applied in other areas such as meteorology, seismology, and transportation. One objective of a monitoring system should always be to collect as little data as necessary to be able to monitor specific para...

The authors apply the ideas from optimal design theory to the very specific area of monitoring large computer networks. The behavior of these networks is so complex and uncertain that it is quite natural to use the statistical methods of experimental design which were originated in such areas as biology, behavioral sciences and agriculture, where t...

A number of interesting problems in the design of experiments such as sensor allocation, selection of sites for the observing stations, determining sampler positions in traffic monitoring, and which variables to survey/measure in sampling studies may be considered in the following setting: Given a covariance matrix of multi-dimension random vector...

A new class of model-robust optimality criteria, based on the mean squared error, is introduced. The motivation is to find designs when the researcher is more concerned with controlling the variance than the bias, or vice versa. The set of criteria proposed here is also appealing from a mathematical perspective in the sense that, unlike the G. E. P...

In this paper we illustrate how certain design problems can be simplified by reparametrization of the response function. This alternative viewpoint provides further insights than the more traditional approaches, like minimax, Bayesian or sequential techniques. It will also improve a practitioner’s understanding of more general situations and their...

From now on we will assume that only \(\hat \theta\) and \(Var\{ \hat \theta \}\) or some functions of these quantities are used to describe the results of an experiment. This is justified by the fact that in many cases and in particular in the case of normally distributed observations, \(\hat \theta\) and Var \(Var(\hat \theta )\) contain in some...

Almost all concepts and methods to be discussed in this book are related to the linear regression model $$y = \eta (x,\theta ) + \varepsilon = {\theta ^T}f(x) + \varepsilon .$$ (1). The variable y is called the response (or dependent or observed) variable, and mostly we assume that it is scalar. More complicated structures will occasionally be cons...

All algorithms that we are going to discuss are iterative. Let ξsbe the design that was obtained after(s— 1) iteration steps. At thes-th iteration step we hopefully will improve — as in all previous steps — the characteristics of the design. The new design, for instance, may be obtained according to $${\xi _{s + 1}} = (1 - {\alpha _s}){\xi _s} + {\...

In this section we assume that the independent variables xl… x k (and the response variable y) are observed in the space of variables t that are out of the experimenter’s control but are known. Typically, t stands for time; but t may correspond to temperature, atmospheric pressure, wind direction in environmental studies; to age, living conditions,...

In Section 2.3, an optimal design ξ*is defined as $${\xi ^*} = \arg \mathop {\min }\limits_\xi \Psi [M(\xi )];$$ (4.1.1) it is assumed and extensively used that $$\int {\xi (dx) = 1.}$$ (4.1.2) Actually, (4.1.2) may be considered as a continuous analogue of the constraint that is imposed on the number of observations, viz. $$\sum\limits_{i = 1}^n {...