Search

Clinical trials disruption has always represented a non negligible part of the ending of interventional studies. While the SARS-CoV-2 (COVID-19) pandemic has led to an impressive and unprecedented initiation of clinical research, it has also led to considerable disruption of clinical trials in other disease areas, with around 80% of non-COVID-19 trials stopped or interrupted during the pandemic. In many cases the disrupted trials will not have the planned statistical power necessary to yield interpretable results. This paper describes methods to compensate for the information loss arising from trial disruptions by incorporating additional information available from auxiliary data sources. The methods described include the use of auxiliary data on baseline and early outcome data available from the trial itself and frequentist and Bayesian approaches for the incorporation of information from external data sources. The methods are illustrated by application to the analysis of artificial data based on the Primary care pediatrics Learning Activity Nutrition (PLAN) study, a clinical trial assessing a diet and exercise intervention for overweight children, that was affected by the COVID-19 pandemic. We show how all of the methods proposed lead to an increase in precision relative to use of complete case data only.

Sequential likelihood ratio testing is found to be most powerful in sequential studies with early stopping rules when grouped data come from the one-parameter exponential family. First, to obtain this elusive result, the probability measure of a group sequential design is constructed with support for all possible outcome events, as is useful for designing an experiment prior to having data. This construction identifies impossible events that are not part of the support. The overall probability distribution is dissected into stage specific components. These components are sub-densities of interim test statistics first described by Armitage, McPherson and Rowe (1969) that are commonly used to create stopping boundaries given an $\alpha$-spending function and a set of interim analysis times. Likelihood expressions conditional on reaching a stage are given to connect pieces of the probability anatomy together. The reduction of the support caused by the adoption of an early stopping rule induces sequential truncation (not nesting) in the probability distributions of possible events. Multiple testing induces mixtures on the adapted support. Even asymptotic distributions of inferential statistics are mixtures of truncated distributions. In contrast to the classical result on local asymptotic normality (Le Cam 1960), statistics that are asymptotically normal without stopping options have asymptotic distributions that are mixtures of truncated normal distributions under local alternatives with stopping options; under fixed alternatives, asymptotic distributions of test statistics are degenerate., Comment: 23 pages

When there is a predictive biomarker, enrichment can focus the clinical trial on a benefiting subpopulation. We describe a two-stage enrichment design, in which the first stage is designed to efficiently estimate a threshold and the second stage is a "phase III-like" trial on the enriched population. The goal of this paper is to explore design issues: sample size in Stages 1 and 2, and re-estimation of the Stage 2 sample size following Stage 1. By treating these as separate trials, we can gain insight into how the predictive nature of the biomarker specifically impacts the sample size. We also show that failure to adequately estimate the threshold can have disastrous consequences in the second stage. While any bivariate model could be used, we assume a continuous outcome and continuous biomarker, described by a bivariate normal model. The correlation coefficient between the outcome and biomarker is the key to understanding the behavior of the design, both for predictive and prognostic biomarkers. Through a series of simulations we illustrate the impact of model misspecification, consequences of poor threshold estimation, and requisite sample sizes that depend on the predictive nature of the biomarker. Such insight should be helpful in understanding and designing enrichment trials.

This work studies the properties of the maximum likelihood estimator (MLE) of a multidimensional parameter in a nonlinear model with additive Gaussian errors. The observations are collected in a two-stage experimental design and are dependent because the second stage design is determined by the observations at the first stage. The MLE maximizes the total likelihood. Unlike most theory in the literature, the approximation made to the distribution of the MLE only involves taking the second stage sample size to infinity, as the resulting approximate model retains the dependency between stages, and therefore, more closely reflects the actual two-stage experiment. It is proved that the MLE is consistent and that its asymptotic distribution is a specific Gaussian mixture, via stable convergence. Finally, the efficiency of the adaptive procedure relative to the fixed procedure is illustrated by a simulation study under three parameter dose–response Emax and Exponential models.

Summary For the task of estimating a target benchmark dose such as the ED50 (the dose that would be effective for half the population), an adaptive dose-finding design is more effective than the standard approach of treating equal numbers of patients at a set of equally spaced doses. Up-and-down is the most popular family of dose-finding designs and is in common use in anesthesiology. Despite its widespread use, many aspects of up-and-down are not well known, implementation is often misguided, and standard, up-to-date reference material about the design is very limited. This article provides an overview of up-and-down properties, recent methodologic developments, and practical recommendations, illustrated with the help of simulated examples. Additional reference material is offered in the Supplemental Digital Content.

The COVID-19 pandemic continues to affect the conduct of clinical trials globally. Complications may arise from pandemic-related operational challenges such as site closures, travel limitations and interruptions to the supply chain for the investigational product, or from health-related challenges such as COVID-19 infections. Some of these complications lead to unforeseen intercurrent events in the sense that they affect either the interpretation or the existence of the measurements associated with the clinical question of interest. In this article, we demonstrate how the ICH E9(R1) Addendum on estimands and sensitivity analyses provides a rigorous basis to discuss potential pandemic-related trial disruptions and to embed these disruptions in the context of study objectives and design elements. We introduce several hypothetical estimand strategies and review various causal inference and missing data methods, as well as a statistical method that combines unbiased and possibly biased estimators for estimation. To illustrate, we describe the features of a stylized trial, and how it may have been impacted by the pandemic. This stylized trial will then be re-visited by discussing the changes to the estimand and the estimator to account for pandemic disruptions. Finally, we outline considerations for designing future trials in the context of unforeseen disruptions.

We congratulate Dr. Nigel Stallard on his stimulating paper on adaptive enrichment designs with a continuous biomarker. Dr. Stallard details a framework for a large and interesting class of enrichment procedures. His work has motivated us to offer some thoughts in response. Dr. Stallard's strategy is to use the maximum of a test statistic over a set of possible threshold values to define the enriched population to be sampled in a second stage. This reminds us of procedures for identifying a change point, a biomarker value beyond which the effect of treatment is increased. For simplicity we focus our comments on Dr. Stallard's Rule 1 for selecting the second-stage sampling threshold. Using this rule, we present the likelihood ratio approach for adaptive testing and compare it to Dr. Stallard's approach for a few scenarios.

Two-stage enrichment designs can be used to target the benefiting population in clinical trials based on patients’ biomarkers. In the case of continuous biomarkers, we show that using a bivariate model that treats biomarkers as random variables more accurately identifies a treatment-benefiting enriched population than assuming biomarkers are fixed. Additionally, we show that under the bivariate model, the maximum likelihood estimators (MLEs) follow a randomly scaled mixture of normal distributions. Using random normings, we obtain asymptotically standard normal MLEs and construct hypothesis tests. Finally, in a simulation study, we demonstrate that our proposed design is more powerful than a single stage design when outcomes and biomarkers are correlated; the model-based estimators have smaller bias and mean square error (MSE) than weighted average estimators.

Asymptotic distribution theory for maximum likelihood estimators under fixed alternative hypotheses is reported in the literature even though the power of any realistic test converges to one under fixed alternatives. Under fixed alternatives, authors have established that nuisance parameter estimates are inconsistent when sample size re-estimation (SSR) follows blinded randomization. These results have helped to inhibit the use of SSR. In this paper, we argue for local alternatives to be used instead of fixed alternatives. Motivated by Gould and Shih (1998), we treat unavailable treatment assignments in blinded experiments as missing data and rely on single imputation from marginal distributions to fill in for missing data. With local alternatives, it is sufficient to proceed only with the first step of the EM algorithm mimicking imputation under the null hypothesis. Then, we show that blinded and unblinded estimates of the nuisance parameter [Formula: see text] are consistent, and re-estimated sample sizes converge to their locally asymptotically optimal values. This theoretical finding is confirmed through Monte-Carlo simulation studies. Practical utility is illustrated through a multiple logistic regression example. We conclude that, for hypothesis testing with a predetermined minimally clinically relevant local effect size, both blinded and unblinded SSR procedures lead to similar sample sizes and power.

There is a long literature on bias in maximum likelihood estimators. Here we demonstrate that adaptive dose-finding procedures (such as Continual Reassessment Methods, Up-and-Down and Interval Designs) themselves induce bias. In particular, with Bernoulli responses and dose assignments that depend on prior responses, we provide an explicit formula for the bias of observed response rates. We illustrate the patterns of bias for designs that aim to concentrate dose allocations around a target dose, which represents a specific quantile of a cumulative response-threshold distribution. For such designs, bias tends to be positive above the target dose and negative below it. To our knowledge, this property of dose-finding designs has not previously been recognized by design developers. We discuss the implications of this bias and suggest a simple shrinkage mitigation formula that improves estimation at doses away from the target.

This manuscript investigates sample sizes for interim analyses in group sequential designs. Traditional group sequential designs (GSD) rely on "information fraction" arguments to define the interim sample sizes. Then, interim maximum likelihood estimators (MLEs) are used to decide whether to stop early or continue the data collection until the next interim analysis. The possibility of early stopping changes the distribution of interim and final MLEs: possible interim decisions on trial stopping excludes some sample space elements. At each interim analysis the distribution of an interim MLE is a mixture of truncated and untruncated distributions. The distributional form of an MLE becomes more and more complicated with each additional interim analysis. Test statistics that are asymptotically normal without a possibly of early stopping, become mixtures of truncated normal distributions under local alternatives. Stage-specific information ratios are equivalent to sample size ratios for independent and identically distributed data. This equivalence is used to justify interim sample sizes in GSDs. Because stage-specific information ratios derived from normally distributed data differ from those derived from non-normally distributed data, the former equivalence is invalid when there is a possibility of early stopping. Tarima and Flournoy [3] have proposed a new GSD where interim sample sizes are determined by a pre-defined sequence of ordered alternative hypotheses, and the calculation of information fractions is not needed. This innovation allows researchers to prescribe interim analyses based on desired power properties. This work compares interim power properties of a classical one-sided three stage Pocock design with a one-sided three stage design driven by three ordered alternatives.

This manuscript investigates sample sizes for interim analyses in group sequential designs. Traditional group sequential designs (GSD) define interim sample sizes in terms of “information fractions”. Then, interim maximum likelihood estimators (MLEs) are used to decide whether to stop [for full text, please go to the a.m. URL], 65th Annual Meeting of the German Association for Medical Informatics, Biometry and Epidemiology (GMDS), Meeting of the Central European Network (CEN: German Region, Austro-Swiss Region and Polish Region) of the International Biometric Society (IBS)

In the first phase of pharmaceutical development, and assuming that the probability of positive response increases with dose, the main statistical goal is to estimate a percentile of the dose–response function for a given target Г. We compare the Maximum Likelihood and centred isotonic regression estimators of the target dose and we discuss several performance criteria to assess inferential precision, the amount of toxicity exposure and the trade-off between them for a set of some exemplary adaptive designs. We compare these designs using graphical tools. Several scenarios are considered using simulation, including the use of several start-up rules, the change of slope of the dose-toxicity function at the target dose and also different theoretical models, as logistic, normal or skew-normal distribution functions. Fernando Plo and Jose Moler acknowledge the financial support received from the projects Ministerio de Economía y Competitividad (MTM2014‐53340‐P) and Secretaría de Estado de Investigación, Desarrollo e Innovación (MTM2016‐77015‐R).

Univariate isotonic regression (IR) has been used for nonparametric estimation in dose–response and dose-finding studies. One undesirable property of IR is the prevalence of piecewise-constant stretches in its estimates, whereas the dose–response function is usually assumed to be strictly increasing. We propose a simple modification to IR, called centered isotonic regression (CIR). CIR's estimates are strictly increasing in the interior of the dose range. In the absence of monotonicity violations, CIR and IR both return the original observations. Numerical examination indicates that for sample sizes typical of dose–response studies and with realistic dose–response curves, CIR provides a substantial reduction in estimation error compared with IR when monotonicity violations occur. We also develop analytical interval estimates for IR and CIR, with good coverage behavior. An R package implements these point and interval estimates. Supplementary materials for this article are available online.

The beta distribution is a simple and flexible model in which responses are naturally confined to the finite interval (0,1). Its parameters can be related to covariates such as dose and gender through a regression model. The ballooned beta-logistic (BBL) model expands the response boundaries from (0,1) to (L,U), where L and U are unknown parameters. Under the BBL model, expected responses follow a logistic function that can be made equal to that of the four-parameter logistic (4PL) model. But the distribution of responses differs from the classical 4PL model that has additive normal errors. In contrast, the BBL model naturally has bounded responses and inhomogenous variance. The asymptotic normality of maximum likelihood estimators (MLEs) is obtained even though the support of this nonregular regression model depends on unknown parameters. We find MLEs converge faster to L and U than extreme values do at the minimum and maximum concentrations. Given enzyme-linked immunosorbent assay data from multiple plates, we study a motivating validation objective, which is to set suitability criteria for estimates of L and U; after this, plates with boundary estimates outside these limits would be considered “reference failures.” We show the BBL model has advantages over the 4PL model. Supplementary materials for this article are available online.

Consider an experiment in which the primary objective is to determine the significance of a treatment effect at a predetermined type I error and statistical power. Assume that the sample size required to maintain these type I error and power will be re-estimated at an interim analysis. A secondary objective is to estimate the treatment effect. Our main finding is that the asymptotic distributions of standardized statistics are random mixtures of distributions, which are non-normal except under certain model choices for sample size re-estimation (SSR). Monte-Carlo simulation studies and an illustrative example highlight the fact that asymptotic distributions of estimators with SSR may differ from the asymptotic distribution of the same estimators without SSR.

A two-stage adaptive optimal design is an attractive option for increasing the efficiency of clinical trials. In these designs, based on interim data, the locally optimal dose is chosen for further exploration, which induces dependencies between data from the two stages. When the maximum likelihood estimator (MLE) is used under nonlinear regression models with independent normal errors in a pilot study where the first stage sample size is fixed, and the second stage sample size is large, the Fisher information fails to normalize the estimator adequately asymptotically, because of dependencies. In this situation, three alternative random information measures are presented and are shown to provide better normalization of the MLE asymptotically. The performance of random information measures is investigated in simulation studies, and the results suggest that the observed information performs best when the sample size is small.

The three parameter log-normal distribution is a popular non-regular model, but surprisingly, whether the local maximum likelihood estimator (MLE) for parameter estimation is consistent or not has been speculated about since the 1960s. This note gives a rigorous proof for the existence of a consistent MLE for the three parameter log-normal distribution, which solves a problem that has been recognized and unsolved for 50 years. Our results also imply a uniform local asymptotic normality condition for the three parameter log-normal distribution. In addition, we give results on the asymptotic normality and the uniqueness of the local MLE.

Under general parametric models, Claeskens and Hjort (J Am Stat Assoc 98:900–916, 2003) proposed a focused information criterion for model selection which emphasizes the accuracy of estimation for particular parameters of interest. This paper extends their framework to include a semi-parametric varying-coefficient partially linear model when covariates in both the parametric and the non-parametric parts are subject to measurement errors. We allow the covariance matrices of the measurement errors to be unknown and be estimated by replicated observations. Also, we derive the asymptotic properties of the frequentist model average estimator for the model in consideration, which generalizes the results obtained by Wang et al. (Electron J Stat 6:1017–1039, 2012). In addition to asymptotic properties, finite sample performance of the proposed methods are examined in a simulation study, and a data set obtained from Continuing Survey of Food Intakes by Individuals conducted by the U.S. Department of Agriculture’s (CSFII) is considered.

Summary In manufacturing industry, it may be important to study the relationship between machine component failures under stress. Examples include the failures of integrated circuits and memory chips in electronic merchandise given various levels of electronic shock. Such studies are important for the development of new products and for the improvement of existing products. We assume two-component systems for simplicity and we assume that the joint probability of failures increases with stress as a cumulative bivariate Weibull function. Optimal designs have been developed for two correlated binary responses by using the Gumbel model, the bivariate binary Cox model and the bivariate probit model. In all these models, the amount of damage ranges from −∞ to ∞. In the Weibull model, the amount of damage is positive, which is natural for experimental factors such as voltage, tension or pressure. We describe locally optimal designs under bivariate Weibull assumptions. Since locally optimal designs with non-linear models depend on predetermined parameter values, misspecified parameter values may lead to inefficient designs. However, we find that optimal designs under the Weibull model are surprisingly efficient over a wide range of misspecified parameter values. To improve the efficiency, we recommend a multistage procedure. We show how using a two-stage procedure can provide a substantial improvement over a design that was optimal for misspecified parameters.

In adaptive optimal designs, each stage uses a locally optimal design evaluated at the maximum likelihood estimates derived using cumulative data from all prior stages. This dependency on prior stages affects Fisher's information, the asymptotic covariance matrix of the maximum likelihood estimates. Fisher's information is motivated for use in adaptive designs with small samples by deriving the Cramer–Rao lower bound for such experiments. Then the usefulness of Fisher's information is shown from both a design and an analysis perspective. From a design perspective, the locally optimal stage one sample size is defined in terms of Fisher's information and a procedure to approximate it is suggested. From an analysis perspective, Fisher's information is compared to a commonly used information measure derived by ignoring the stage dependencies and to the observed information. To make the analysis explicit, a two stage design with fixed first stage is examined in the context of a general nonlinear regression model.

In this paper we introduce a new regression model in which the response variable is bounded by two unknown parameters. A special case is a bounded alternative to the four parameter logistic model. The four parameter model which has unbounded responses is widely used, for instance, in bioassays, nutrition, genetics, calibration and agriculture. In reality, the responses are often bounded although the bounds may be unknown, and in that situation, our model reflects the data-generating mechanism better. Complications arise for the new model, however, because the likelihood function is unbounded, and the global maximizers are not consistent estimators of unknown parameters. Although the two sample extremes, the smallest and the largest observations, are consistent estimators for the two unknown boundaries, they have a slow convergence rate and are asymptotically biased. Improved estimators are developed by correcting for the asymptotic biases of the two sample extremes in the one sample case; but even these consistent estimators do not obtain the optimal convergence rate. To obtain efficient estimation, we suggest using the local maximizers of the likelihood function, i.e., the solution to the likelihood equations. We prove that, with probability approaching one as the sample size goes to infinity, there exists a solution to the likelihood equation that is consistent at the rate of the square root of the sample size and it is asymptotically normally distributed.

Response-adaptive randomization procedures have a dual goal of estimating the treatment effect and randomizing patients with a higher probability of receiving the superior treatment. These are competing objectives, and no procedure in the literature is “perfect” with respect to both objectives. For clinical trials of two treatments, we discuss metrics for comparing response-adaptive randomization procedures that can be represented graphically to compare designs. These metrics involve the simulated distribution of the set of jointly sufficient statistics for estimating functions of the unknown parameters. We explore the binary response and normal cases, and compare numerous procedures found in the literature. We distinguish between metrics of efficiency and metrics that measure ethical cost. Each of these is a function of the joint sufficient statistics. When graphed against each other, we can gauge competing designs in obtaining these competing objectives. We find that, contrary to asymptotic results, tun...

We study two-stage adaptive designs in which data accumulated in the first stage are used to select the design for a second stage. Inference following such experiments is often conducted by ignoring the adaptive procedure and treating the design as fixed. Alternative inference procedures approximate the variance of the parameter estimates by approximating the inverse of expected Fisher information. Both of these inferential methods often rely on normal distribution assumptions in order to create confidence intervals. In an effort to improve inference, we develop bootstrap methods that condition on a non-ancillary statistic that defines the second stage design.

Resume Les plans d’experiences qui s’adaptent aux reponses deja acquises sont de plus en plus frequemment utilises dans les applications, et c’est tout particulierement vrai pour les essais cliniques en phase precoce. Cet article est une revue dediee a une classe de plans adaptatifs qui ont pour propriete de selectionner le meilleur traitement avec une probabilite tendant vers un. D’un point de vue ethique, ceci est une propriete souhaitable pour les essais cliniques. Pour de tels plans, le modele sous-jacent est un modele d’urne aleatoirement renforcee. Cet article presente un panorama des resultats concernant ces plans, allant de l’article seminal de Durham et Yu (1990) jusqu’au travail recent de Flournoy et al. (2010). Summary Response-adaptive designs are being used increasingly in applications, and this is especially so in early phase clinical trials. This paper reviews a particular class of response-adaptive designs that have the property of picking the superior treatment with probability tending to one. This is a desirable property from an ethical point of view in clinical trials. The model underlying such designs is a randomly reinforced urn. This paper provides an overview of results for these designs, starting from the early paper of Durham and Yu (1990) until the recent work by Flournoy, May, Moler and Plo (2010).

In many toxicological assays, interactions between primary and secondary effects may cause a downturn in mean responses at high doses. In this situation, the typical monotonicity assumption is invalid and may be quite misleading. Prior literature addresses the analysis of response functions with a downturn, but so far as we know, this paper initiates the study of experimental design for this situation. A growth model is combined with a death model to allow for the downturn in mean doses. Several different objective functions are studied. When the number of treatments equals the number of parameters, Fisher information is found to be independent of the model of the treatment means and on the magnitudes of the treatments. In general, A- and DA-optimal weights for estimating adjacent mean differences are found analytically for a simple model and numerically for a biologically motivated model. Results on c-optimality are also obtained for estimating the peak dose and the EC50 (the treatment with response half way between the control and the peak response on the increasing portion of the response function). Finally, when interest lies only in the increasing portion of the response function, we propose composite D-optimal designs.

We compare several decision rules for allocating subjects to dosages that are based on sequential isotonic estimates of a monotone dose-toxicity curve. We conclude that the decision rule in which the next assignment is to the dose having probability of toxicity closest to target does not work well. The best rule in our comparison is given by the cumulative cohort design. According to this design, the dose for the next subject is decreased, increased, or repeated depending on the distance between the estimated toxicity rate at the current dose and the target quantile.

Assume that the probability of success is unimodal as a function of dose, such as may be the case when too much of a drug is toxic and too little is ineffective. We characterize a class of up-and-down designs, that is, treatment allocation methodologies, for identifying the dose that maximizes the patients' success probability. These designs are constructed to use accruing information to limit the number of patients that are exposed to doses with high probabilities of failure. This treatment allocation procedure is motivated by Kiefer–Wolfowitz's stochastic approximation procedure. However, we take the response to be binary and the possible treatment space to be a lattice. The procedure is shown to allocate treatments to pairs of subjects in a way that causes the treatment distribution to center around the treatment with maximum success probability. The procedure defines a nonhomogeneous random walk, so well-known theory is used to explicitly characterize the treatment distribution. As an estimat...

We introduce a new design for dose-finding in the context of toxicity studies for which it is assumed that toxicity increases with dose. The goal is to identify the maximum tolerated dose, which is taken to be the dose associated with a prespecified “target” toxicity rate. The decision to decrease, increase or repeat a dose for the next subject depends on how far an estimated toxicity rate at the current dose is from the target. The size of the window within which the current dose will be repeated is obtained based on the theory of Markov chains as applied to group up-and-down designs. But whereas the treatment allocation rule in Markovian group up-and-down designs is only based on information from the current cohort of subjects, the treatment allocation rule for the proposed design is based on the cumulative information at the current dose. We then consider an extension of this new design for clinical trials in which the subject's outcome is not known immediately. The new design is compared to the continual reassessment method.

Let toxicity to treatment be a Bernoulli random variable for which the probability of failure increases with dose. Consider the problem of identifying a dose μ having pre-specified probability of failure using data from groups of subjects who arrive sequentially for treatment. There is considerable theory available in this setting for fully sequential up-and-down procedures. This paper presents asymptotic and finite theoretical results for Markovian up-and-down procedures when subjects are treated in groups. Practical instructions are given on how to select the design parameters so as to cause the treatments to cluster around the unknown dose μ. Examples are given to illustrate how this group procedure behaves for small sample sizes.

A non-parametric multi-dimensional isotonic regression estimator is developed for use in estimating a set of target quantiles from an ordinal toxicity scale. We compare this estimator to the standard parametric maximum likelihood estimator from a proportional odds model for extremely small data sets. A motivating example is from phase I oncology clinical trials, where various non-parametric designs have been proposed that lead to very small data sets, often with ordinal toxicity response data. Our comparison of estimators is performed in conjunction with three of these non-parametric sequential designs for ordinal response data, two from the literature and a new design based on a random walk rule. We also compare with a non-parametric design for binary response trials, by keeping track of ordinal data for estimation purposes, but dichotomizing the data in the design phase. We find that a multidimensional isotonic regression-based estimator far exceeds the others in terms of accuracy and efficiency. A rule by Simon et al. (J. Natl. Cancer Inst. 1997; 89:1138-1147) yields particularly efficient estimators, more so than the random walk rule, but has higher numbers of dose-limiting toxicity. A small data set from a leukemia clinical trial is analysed using our multidimensional isotonic regression-based estimator.

Competing risks analysis of the case-cohort design is often required in epidemiological studies and for this, some methods have been proposed under the proportional hazards model. It is known that the proportional hazards model may not fit survival data well sometimes. This paper considers the analysis under the additive hazards model. Methods are proposed for estimating regression parameters and cumulative baseline hazard functions as well as cumulative incidence functions. The proposed estimators are shown to be consistent and asymptotically normal using the martingale central limit theory. Simulation studies are conducted and suggest that the proposed methods perform well.

We are interested in finding a dose that has a prespecified toxicity rate in the target population. In this article, we investigate five estimators of the target dose to be used with the up-and-down biased coin design (BCD) introduced by Durham and Flournoy (1994, Statistical Decision Theory and Related Topics). These estimators are derived using maximum likelihood, weighted least squares, sample averages, and isotonic regression. A linearly interpolated isotonic regression estimate is shown to be simple to derive and to perform as well as or better than the other target dose estimators in terms of mean square error and average number of subjects needed for convergence in most scenarios studied.

Up-and-down designs are useful for evaluating and comparing the toxicity of pesticides and other chemical compounds. In particular, the primary goal of an up-and-down design in toxicity studies is to estimate the dose having a prespecified toxicity rate Γ,0

Estimation and inference for dependent trials are important issues in response-adaptive allocation designs; maximum likelihood estimation is one route of interest. We present three noval response-driven designs and derive their maximum likelihood estimators. We also provide convenient regularity conditions that ensure the maximum likelihood estimator from a multiparameter stochastic process exists and is asymptotically multivariate normal. While these conditions may not be the most general, they are easily verified for our applications.

Wang and Flournoy (2012) developed estimation procedures for the bounded log-linear regression model, an alternative to the four parameter logistic model which has a bounded response with non-homogeneous variance. In the present paper, we prove that an optimal design that minimizes an information-based criterion requires at most five design points including the two boundary points of the design space. The D-optimal design does not depend on the two parameters representing the boundaries of the response, but it does depend on the variance of the error. Furthermore, if the error variance is known and bigger than a certain constant, we prove that the D-optimal design is the two-point design supported at boundary points with equal weights. Numerical examples are provided.

In the framework of clinical trials, legal and ethical restrictions make a population model unrealistic for sampling. Randomization tests are a viable alternative to classical inference. Their theoretical properties depend heavily on the random rule used to allocate patients to treatments, so that Ad-Hoc theoretical studies are necessary for each allocation design. In this paper, we obtain theoretical results for randomization tests when the drop-the-loser rule is used.

Often, in dose-response studies, it is desirable to arrange treatments in a region defined by the unknown surface. We accomplish such arrangements using sequential designs that are functions of previous outcomes. Here, for a class of randomized up-and-down designs for dichotomous responses (e.g., toxicity/no toxicity) and predetermined sample size, distributional results for the total number of toxic responses are derived. These results are useful in selecting sequential design parameters and have obvious ethical implications.