TESTING MICROBIOLOGIC RESPONSE TO ANTIINFECTIVE MEDICATIONS WITH INCOMPLETE DATA

Clinical trials of antiinfective medications often require estimates of the proportions of patients, Π, who are free of disease-causing pathogens at the end of treatment, as well as the proportions of all pathogens that have been eradicated. Each patient is infected with several species of pathogens, but the response to study medication for some of these pathogens may be unknown because some specimens were lost or because the patient received nonstudy medication that was known to be effective against these species. This paper develops a statistical model that estimates Π for each treatment and that accounts for the unknown pathogen responses as well as overdispersion of the remaining responses due to within-patient effects. The data are modeled with the Poisson distribution for the numbers of pathogen species per patient and the beta-binomial model for pathogen eradication. The Poisson and beta-binomial parameters are estimated through maximum likelihood estimation, and the treatment difference in the Π valves and its standard error are estimated by transforming the underlying parameters. Confidence intervals based on these estimates are constructed to test the hypothesis of noninferiority of the test treatment.     

Adaptive randomization to improve utility-based dose-finding with bivariate ordinal outcomes

A sequentially outcome-adaptive Bayesian design is proposed for choosing the dose of an experimental therapy based on elicited utilities of a bivariate ordinal (toxicity, efficacy) outcome. Subject to posterior acceptability criteria to control the risk of severe toxicity and exclude unpromising doses, patients are randomized adaptively among the doses having posterior mean utilities near the maximum. The utility increment used to define near-optimality is nonincreasing with sample size. The adaptive randomization uses each dose's posterior probability of a set of good outcomes, defined by a lower utility cutoff. Saturated parametric models are assumed for the marginal dose-toxicity and dose-efficacy distributions, allowing the possible requirement of monotonicity in dose, and a copula is used to obtain a joint distribution. Prior means are computed by simulation using elicited outcome probabilities, and prior variances are calibrated to control prior effective sample size and obtain a design with good operating characteristics. The method is illustrated by a Phase I/II trial of radiation therapy for children with brainstem gliomas.     

Testing microbiologic response to antiinfective medications with incomplete data

Clinical trials of antiinfective medications often require estimates of the proportions of patients, n, who are free of disease-causing pathogens at the end of treatment, as well as the proportions of all pathogens that have been eradicated. Each patient is infected with several species of pathogens, but the response to study medication for some of these pathogens may be unknown because some specimens were lost or because the patient received nonstudy medication that was known to be effective against these species. This paper develops a statistical model that estimates pi for each treatment and that accounts for the unknown pathogen responses as well as overdispersion of the remaining responses due to within-patient effects. The data are modeled with the Poisson distribution for the numbers of pathogen species per patient and the beta-binomial model for pathogen eradication. The Poisson and beta-binomial parameters are estimated through maximum likelihood estimation, and the treatment difference in the pi valves and its standard error are estimated by transforming the underlying parameters. Confidence intervals based on these estimates are constructed to test the hypothesis of noninferiority of the test treatment.     

Identification and estimation of semi‐parametric censored dynamic panel data models of short time periods

In this paper, we present a semi‐parametric identification and estimation method for censored dynamic panel data models of short time periods and their average partial effects with only two periods of data. The proposed method transforms the semi‐parametric specification of censored dynamic panel data models into a parametric family of distribution functions of observables without specifying the distribution of the initial condition. Then the censored dynamic panel data models are globally identified under a standard maximum likelihood estimation framework. The identifying assumptions are related to the completeness of the families of known parametric distribution functions corresponding to censored dynamic panel data models. Dynamic tobit models and two‐part dynamic regression models satisfy the key assumptions. We propose a sieve maximum likelihood estimator and we investigate the finite sample properties of these sieve‐based estimators using Monte Carlo analysis. Our empirical application using the Medical Expenditure Panel Survey shows that individuals consume more health care when their incomes increase, after controlling for past health expenditures.     

Use of the Beta-Binomial Model for Central Statistical Monitoring of Multicenter Clinical Trials

As part of central statistical monitoring of multicenter clinical trial data, we propose a procedure based on the beta-binomial distribution for the detection of centers with atypical values for the probability of some event. The procedure makes no assumptions about the typical event proportion and uses the event counts from all centers to derive a reference model. The procedure is shown through simulations to have high sensitivity and high specificity if the contamination rate is small and the atypical event proportions are the result of some systematic shift in the underlying data-generating mechanism.     

A Use of Monte Carlo Integration for Population Pharmacokinetics with Multivariate Population Distribution

This paper describes a use of Monte Carlo integration for population pharmacokinetics with multivariate population distribution. In the proposed approach, a multivariate lognormal distribution is assumed for a population distribution of pharmacokinetic (PK) parameters. The maximum likelihood method is employed to estimate the population means, variances, and correlation coefficients of the multivariate lognormal distribution. Instead of a first-order Taylor series approximation to a nonlinear PK model, the proposed approach employs a Monte Carlo integration for the multiple integral in maximizing the log likelihood function. Observations below the lower limit of detection, which are usually included in Phase 1 PK data, are also incorporated into the analysis. Applications are given to a simulated data set and an actual Phase 1 trial to show how the proposed approach works in practice.     

Sample Sizes Required to Detect Two-Way and Three-Way Interactions Involving Slope Differences in Mixed-Effects Linear Models

Based on maximum likelihood estimates obtained from mixed-effects linear models, closed-form power functions are derived to detect two-way and three-way interactions that involve longitudinal course of outcome over time in clinical trials. Sample size estimates are shown to decrease with increasing within-subject correlations. It is further shown that when clinical trial designs are balanced in group sizes, the sample size required to detect an effect size for a three-way interaction is exactly fourfold that required to detect the same effect size of a two-way interaction. Furthermore, this fourfold relationship virtually holds for unbalanced allocations of subjects if one factor is balanced in the three-way interaction model. Simulations are presented that verify the sample size estimates for two-way and three-way interactions.     

Use of predictive probabilities in phase II and phase III clinical trials

Predictive probability is particularly useful in aiding a decision-making process related to drug development. This is especially true for decisions occurring as the result of interim analyses of clinical trials. Examples of clinical trial applications of Bayesian predictive probability and the use of the beta-binomial distribution are described.     

A study design with conditional,serially assessed co‐primary endpoints: An application to a single‐arm,pilot non‐Hodgkin's lymphoma trial

Optimizing study designs is an important responsibility for applied statisticians supporting clinical trials. We describe the study design for an early‐phase non‐Hodgkin's lymphoma trial with two co‐primary endpoints; however, evaluation of the second endpoint on a subject is conditional on a positive response to the first endpoint. Thus, these dichotomous measures are collected conditionally and in series. We present the probability density function for this study design selected and derive the parameters that describe this distribution. We also derive the maximum likelihood estimates for the unknown parameters of interest to the trial investigator. We compare the theoretical operating characteristics (type I and type II error rates) to a simulation study for the motivating example. Using this report as a guide, others designing studies with similarly measured co‐primary endpoints can utilize these formulas to calculate the operating characteristics and analyze their resulting study data. Drug Dev Res 71: 395–403, 2010. © 2010 Wiley‐Liss, Inc.     

Model-Based Bayesian Adaptive Dose-Finding Designs for a Phase II Trial

We describe the planning of a dose-finding study for a compound currently in early Phase II clinical development. Data from a trial with the same primary endpoint are available for a marketed drug that has the same pharmacological mechanism, which provides strong prior information for some characteristics of the new compound. We develop and evaluate informative model-based Bayesian analyses. We also evaluate adaptive designs that change the allocation of patients to doses after an interim analysis. The performance of the model-based Bayesian analyses applied to the adaptive designs is compared to the performance of corresponding analyses applied to a nonadaptive design. The performance is also compared to model-based maximum likelihood estimation and simple pairwise comparison of treatment group means applied to the nonadaptive design to assess the contributions of the model, Bayesian prior distribution, and adaptive designs to improvements in decision and estimation performance.     

Flexible Design and Efficient Implementation of Adaptive Dose-Finding Studies

A dose-finding study with an adaptive design generates three computational problems: fitting the dose-response curve given the current data, identifying the dose to be given to the next patient that is optimal for learning about the dose-response curve, and pretrial simulation in order to establish operating characteristics of alternative designs. Identifying the ‘optimal’ dose is the rate-limiting step since conventional methods, estimating the full posterior predictive distribution of some utility function under each of the possible doses, are very slow. We explore a simpler strategy based on importance sampling, whereby the posterior mean of the utility at each candidate dose is estimated by taking its average across an empirical distribution for the model parameters from the current Markov chain Monte Carlo (MCMC) run, weighted according to the likelihood of one or more predicted observations. We identify appropriate settings for this algorithm and illustrate its application in the context of a normal dynamic linear model used in a dose-finding clinical trial of a neutrophil inhibitory factor in acute ischaemic stroke.     

Flexible design and efficient implementation of adaptive dose-finding studies

A dose-finding study with an adaptive design generates three computational problems: fitting the dose-response curve given the current data, identifying the dose to be given to the next patient that is optimal for learning about the dose-response curve, and pretrial simulation in order to establish operating characteristics of alternative designs. Identifying the 'optimal' dose is the rate-limiting step since conventional methods, estimating the full posterior predictive distribution of some utility function under each of the possible doses, are very slow. We explore a simpler strategy based on importance sampling, whereby the posterior mean of the utility at each candidate dose is estimated by taking its average across an empirical distribution for the model parameters from the current Markov chain Monte Carlo (MCMC) run, weighted according to the likelihood of one or more predicted observations. We identify appropriate settings for this algorithm and illustrate its application in the context of a normal dynamic linear model used in a dose-finding clinical trial of a neutrophil inhibitory factor in acute ischaemic stroke.     

Bias reduction in logistic dose-response models

In generalized linear models, such as the logistic regression model, maximum likelihood estimators are well known to be biased at smaller sample sizes. When the number of dose levels or replications per dose is small, bias in the maximum likelihood estimates can lead to very misleading results and the model often fails to converge. In order to correct the bias present in the maximum likelihood estimates and the problem of nonconvergence, the penalized maximum likelihood estimator is considered. Simulations compare the fit and empirical confidence levels of inferences made from the maximum likelihood and penalized maximum likelihood based models.     

Guest Editors' Notes on Statistical Issues in Design and Analysis of Thorough QTc Studies

In generalized linear models, such as the logistic regression model, maximum likelihood estimators are well known to be biased at smaller sample sizes. When the number of dose levels or replications per dose is small, bias in the maximum likelihood estimates can lead to very misleading results and the model often fails to converge. In order to correct the bias present in the maximum likelihood estimates and the problem of nonconvergence, the penalized maximum likelihood estimator is considered. Simulations compare the fit and empirical confidence levels of inferences made from the maximum likelihood and penalized maximum likelihood based models.     

Bayesian Inference on Risk Differences: An Application to Multivariate Meta-Analysis of Adverse Events in Clinical Trials

Multivariate meta-analysis is useful in combining evidence from independent studies that involve several comparisons among groups based on a single outcome. For binary outcomes, the commonly used statistical models for multivariate meta-analysis are multivariate generalized linear mixed effects models which assume risks, after some transformation, follow a multivariate normal distribution with possible correlations. In this article, we consider an alternative model for multivariate meta-analysis where the risks are modeled by the multivariate beta distribution proposed by Sarmanov. This model has several attractive features compared to the conventional multivariate generalized linear mixed effects models, including simplicity of likelihood function, no need to specify a link function, and a closed-form expression of distribution functions for study-specific risk differences. We investigate the finite sample performance of this model through simulation studies and illustrate its use with an application to multivariate meta-analysis of adverse events of tricyclic antidepressant treatment in clinical trials.     

Detecting Potential Safety Issues in Large Clinical or Observational Trials by Bayesian Screening When Event Counts Arise from Poisson Distributions

Patients in large clinical trials and in studies employing large observational databases report many different adverse events, most of which will not have been anticipated at the outset. Conventional hypothesis testing of between group differences for each adverse event can be problematic: Lack of significance does not mean lack of risk, the tests usually are not adjusted for multiplicity, and the data determine which hypotheses are tested. This article describes a Bayesian screening approach that does not test hypotheses, is self-adjusting for multiplicity, provides a direct assessment of the likelihood of no material drug–event association, and quantifies the strength of the observed association. The criteria for assessing drug-event associations can be determined by clinical or regulatory considerations. In contrast to conventional approaches, the diagnostic properties of this new approach can be evaluated analytically. Application of the method to findings from a vaccine trial yields results similar to those found by methods using a false discovery rate argument or a hierarchical Bayes approach.

[Supplemental materials are available for this article. Go to the publisher's online edition of Journal of Biopharmaceutical Statistics for the following free supplemental resource: Appendix R: Code for calculations.]     

A Free Gift: An Adaptive Strategy in a Single-Arm Trial Using an Exact Test Through the Binomial Distribution

For medical product development within the same generation, single-arm trial designs are commonly implemented to test the performance of the new product against an objective performance criterion. When the primary endpoint is binary and the sample size is moderate, an exact test through the binomial distribution is usually used. This article shows that it is a free gift to add an adaptive component to a fixed-sample-size design so that when the interim result is marginal, the adaptive feature can be activated without any penalty. A hypothetical example is used to illustrate the application of this method.     

Effect of Predictive Performance of a Biomarker for the Sample Size of Targeted Designs for Randomized Clinical Trials

Targeted designs based on the use of predictive biomarkers for patient enrollment have been used to increase the study efficiency. We consider the problem of efficiency of targeted design when the targeted subgroup is defined by a predictive biomarker or classifier. Here we incorporate the predictive performance of a biomarker or classifier to predict a responsive subgroup in the sample size evaluation for targeted design. Predictive performance metrics such as PPV and NPV of a predictive biomarker can usually be best estimated from preclinical studies, such as cell line panel screening. In this article, we focus on sample size calculations for clinical trial studies with time-to-event endpoint. Different assumptions on the treatment and control effects for the subgroups of patients are assumed. Patients’ accrual rate and losses to follow-up are incorporated in the sample size calculation. Simulations are used to check the performance of the sample size formulas. Also, the efficiency of a targeted versus untargeted design is evaluated using cohort size ratio and screened patient ratio. In these studies, the efficiency depends primarily on the prevalence of the subgroup targeted for trial enrollment, the treatment and control effects in subgroups defined by the biomarkers, PPV and NPV.     

Likelihood‐based cointegration tests in heterogeneous panels

This paper presents a maximum likelihood panel test of the cointegrating rank in heterogeneous panel models based on the mean of the individual rank trace statistics. The existence of the first two moments of the asymptotic distribution of the individual trace statistic is established. Based on this, the asymptotic distribution of the test statistic is shown to be normal. The small‐sample size and power properties are investigated using Monte Carlo simulations. An empirical example for a consumption model including consumption, income and inflation is estimated for 23 OECD countries over the period 19601994. The results indicate that two cointegrating relations exist in the system: one containing consumption and income and one inflation only.     

A new threshold dose-response model including random effects for data from developmental toxicity studies

Usually, in teratological dose finding studies, there are not only threshold effects but also extra variations that cannot be accounted for by the beta-binomial model alone. The beta-binomial model assumes correlation between fetuses in the same litter. The general random effect threshold (RE) model allows the additional variability that arises due to correlation and between litter variability to be modeled, in combination with threshold in the model. The goal of this research was to investigate a threshold dose-response model with random effects (RE) to model the variability that exists between litters of animals in studies of toxic agents. Data from a developmental toxicity study of a toxic agent were analysed, using the proposed RE threshold dose-response model, which is an extension of logit in form. Also, an approximate likelihood function was used to derive parameter estimates from this model, and tests were performed to determine the significance of the model parameters, in particular, the RE parameter. A simulation study was conducted to assess the performance of the RE threshold model in estimating the model parameters.