Showing papers in "Journal of Biopharmaceutical Statistics in 2005"

The Fallback Procedure for Evaluating a Single Family of Hypotheses

Abstract: In testing multiple hypotheses, control of the familywise error rate is often considered. We develop a procedure called the "fallback procedure" to control the familywise error rate when multiple primary hypotheses are tested. With the fallback procedure, the Type I error rate (alpha) is partitioned among the various hypotheses of interest. Unlike the standard Bonferroni adjustment, however, testing hypotheses proceeds in an order determined a priori. As long as hypotheses are rejected, the Type I error rate can be accumulated, making tests of later hypotheses more powerful than under the Bonferroni procedure. Unlike the fixed sequence test, the fallback test allows consideration of all hypotheses even if one or more hypotheses are not rejected early in the process, thereby avoiding a common concern about the fixed sequence procedure. We develop properties of the fallback procedure, including control of the familywise error rate for an arbitrary number of hypotheses via illustrating the procedure as a closed testing procedure, as well as making the test more powerful via alpha exhaustion. We compare it to other procedures for controlling familywise error rates, finding that the fallback procedure is a viable alternative to the fixed sequence procedure when there is some doubt about the power for the first hypothesis. These results expand on the previously developed properties of the fallback procedure (Wiens, 2003). Several examples are discussed to illustrate the relative advantages of the fallback procedure.

Statistical consideration of adaptive methods in clinical development.

Abstract: In recent years, the use of adaptive methods in clinical development based on accrued data has become very popular due to its flexibility in modifying trial procedures and/or statistical procedures of on-going clinical trials. However, it is a concern that the actual patient population after the modifications could deviate from the originally targeted patient population. Major modifications of trial procedures and/or statistical procedures of on-going trials may result in a totally different trial, which is unable to address the scientific/medical questions that the trial intends to answer.

Two-stage sample size re-estimation based on a nuisance parameter: a review.

Abstract: Sample size calculations are important and difficult in clinical trails because they depend on the nuisance parameter and treatment effect. Recently, much attention has been focused on two-stage methods whereby the first stage constitutes an internal pilot study used to estimate parameters and revise the final sample size. This paper reviews two-stage methods based on estimation of nuisance parameters in either a continuous or dichotomous outcome setting.

An adaptive group sequential design for phase II/III clinical trials that select a single treatment from several.

Abstract: There is increasing interest in combining Phases II and III of clinical development into a single trial in which one of a small number of competing experimental treatments is ultimately selected and where a valid comparison is made between this treatment and the control treatment. Such a trial usually proceeds in stages, with the least promising experimental treatments dropped as soon as possible. In this paper we present a highly flexible design that uses adaptive group sequential methodology to monitor an order statistic. By using this approach, it is possible to design a trial which can have any number of stages, begins with any number of experimental treatments, and permits any number of these to continue at any stage. The test statistic used is based upon efficient scores, so the method can be easily applied to binary, ordinal, failure time, or normally distributed outcomes. The method is illustrated with an example, and simulations are conducted to investigate its type I error rate and power under a range of scenarios.

Two-sided tolerance intervals for balanced and unbalanced random effects models

Abstract: A procedure for constructing two-sided beta-content, gamma-confidence tolerance intervals is proposed for general random effects models, in both balanced and unbalanced data scenarios. The proposed intervals are based on the concept of effective sample size and modified large sample methods for constructing confidence bounds on functions of variance components. The performance of the proposed intervals is evaluated via simulation techniques. The results indicate that the proposed intervals generally maintain the nominal confidence and content levels. Application of the proposed procedure is illustrated with a one-fold nested design used to evaluate the performance of a quantitative bioanalytical method.

Measuring Parallelism, Linearity, and Relative Potency in Bioassay and Immunoassay Data

Abstract: There is often a need to determine parallelism or linearity between pairs of dose-response data sets for various biological applications This article describes a technique based on a modification of the well-known extra-sum-of-squares principle of statistical regression The standard extra-sum-of-squares method uses an F-distributed ratio as a statistic and an F-test based on this statistic as the parallelism test It is shown here that this metric does not directly measure the parallelism between the two curves and can often vary in opposition to actual parallelism To overcome this problem, a metric based on a chi-square test applied directly on the chi-square-distributed extra-sum-of-squares statistic is developed, which is shown to correspond directly to parallelism This parallelism metric does not suffer from the shortcomings of the conventional F-test-based metric, and is a more reliable and appropriate measure of parallelism The article also shows that the choice of curve model has a large effect on the sensitivity of either metric, and that using an asymmetric model, such as the asymmetric five-parameter logistic function, a generalization of the commonly used symmetric four-parameter logistic function, is necessary when working with asymmetric dose-response data The effect of noise, as well as the importance of correct weighting on the parallelism metrics and the relative potency, is also studied

A Note on Variance Estimation in Random Effects Meta-Regression

Abstract: For random effects meta-regression inference, variance estimation for the parameter estimates is discussed. Because estimated weights are used for meta-regression analysis in practice, the assumed or estimated covariance matrix used in meta-regression is not strictly correct, due to possible errors in estimating the weights. Therefore, this note investigates the use of a robust variance estimation approach for obtaining variances of the parameter estimates in random effects meta-regression inference. This method treats the assumed covariance matrix of the effect measure variables as a working covariance matrix. Using an example of meta-analysis data from clinical trials of a vaccine, the robust variance estimation approach is illustrated in comparison with two other methods of variance estimation. A simulation study is presented, comparing the three methods of variance estimation in terms of bias and coverage probability. We find that, despite the seeming suitability of the robust estimator for random effects meta-regression, the improved variance estimator of Knapp and Hartung (2003) yields the best performance among the three estimators, and thus may provide the best protection against errors in the estimated weights.

Subgroup Analyses in Randomized Clinical Trials: Statistical and Regulatory Issues

Abstract: Recently, two CPMP Points to Consider, one on adjustment for baseline covariates and the other on multiplicity issues in clinical trials, have included recommendations on the use of subgroup analysis for regulatory purposes. However, despite their regular use and regulatory attention, the validity and nature of subgroup analyses are still frequently questioned. This article provides guidance on when subgroup analyses can be done, when they should be done, and their interpretation. The validity of common regulatory claims based on subgroup analyses is then discussed.

Meta-analyses and adaptive group sequential designs in the clinical development process.

Abstract: The clinical development process can be viewed as a succession of trials, possibly overlapping in calendar time. The design of each trial may be influenced by results from previous studies and other currently proceeding trials, as well as by external information. Results from all of these trials must be considered together in order to assess the efficacy and safety of the proposed new treatment. Meta-analysis techniques provide a formal way of combining the information. We examine how such methods can be used in combining results from: (1) a collection of separate studies, (2) a sequence of studies in an organized development program, and (3) stages within a single study using a (possibly adaptive) group sequential design. We present two examples. The first example concerns the combining of results from a Phase IIb trial using several dose levels or treatment arms with those of the Phase III trial comparing the treatment selected in Phase IIb against a control. This enables a “seamless transition...

Sample Size Computation for Two-Sample Noninferiority Log-Rank Test

Abstract: When an experimental therapy is less extensive, less toxic, or less expensive than a standard therapy, we may want to prove that the former is not worse than the latter through a noninferiority trial. In this article, we discuss a modification of the log-rank test for noninferiority trials with survival endpoint and propose a sample size formula that can be used in designing such trials. Performance of our sample size formula is investigated through simulations. Our formula is applied to design a real clinical trial.

A multivariate test for similarity of two dissolution profiles

Abstract: A multivariate test of size α for assessing the similarity of two dissolution profiles is proposed. The inferential procedure is developed by using the approach for the common mean problem in a multivariate setup due to Halperin (1961). The performance of the proposed method is compared with Intersection Union Test as well as f 2 criterion recommended by the FDA through a simulation study. All the methods are illustrated with real examples.

A practical comparison of group-sequential and adaptive designs.

Abstract: Sequential methods provide a formal framework by which clinical trial data can be monitored as they accumulate. The results from interim analyses can be used either to modify the design of the remainder of the trial or to stop the trial as soon as sufficient evidence of either the presence or absence of a treatment effect is available. The circumstances under which the trial will be stopped with a claim of superiority for the experimental treatment, must, however, be determined in advance so as to control the overall type I error rate. One approach to calculating the stopping rule is the group-sequential method. A relatively recent alternative to group-sequential approaches is the adaptive design method. This latter approach provides considerable flexibility in changes to the design of a clinical trial at an interim point. However, a criticism is that the method by which evidence from different parts of the trial is combined means that a final comparison of treatments is not based on a sufficient statistic for the treatment difference, suggesting that the method may lack power. The aim of this paper is to compare two adaptive design approaches with the group-sequential approach. We first compare the form of the stopping boundaries obtained using the different methods. We then focus on a comparison of the power of the different trials when they are designed so as to be as similar as possible. We conclude that all methods acceptably control type I error rate and power when the sample size is modified based on a variance estimate, provided no interim analysis is so small that the asymptotic properties of the test statistic no longer hold. In the latter case, the group-sequential approach is to be preferred. Provided that asymptotic assumptions hold, the adaptive design approaches control the type I error rate even if the sample size is adjusted on the basis of an estimate of the treatment effect, showing that the adaptive designs allow more modifications than the group-sequential method.

Two-Stage Adaptive Design for Clinical Trials with Survival Data

Abstract: In long-term clinical trials we often need to monitor the patients’ enrollment, compliance, and treatment effect during the study. In this paper we take the conditional power approach and consider ...

Performance of a mixed effects logistic regression model for binary outcomes with unequal cluster size.

Abstract: When a clustered randomized controlled trial is considered at a design stage of a clinical trial, it is useful to consider the consequences of unequal cluster size (i.e., sample size per cluster). Furthermore, the assumption of independence of observations within cluster does not hold, of course, because the subjects share the same cluster. Moreover, when the clustered outcomes are binary, a mixed effect logistic regression model is applicable. This article compares the performance of a maximum likelihood estimation of the mixed effects logistic regression model with equal and unequal cluster sizes. This was evaluated in terms of type I error rate, power, bias, and standard error through computer simulations that varied treatment effect, number of clusters, and intracluster correlation coefficients. The results show that the performance of the mixed effects logistic regression model is very similar, regardless of inequality in cluster size. This is illustrated using data from the Prevention Of Suicide in Primary care Elderly: Collaborative Trial (PROSPECT) study.

The use of weighted Z-tests in medical research.

Abstract: Traditionally the un-weighted Z-tests, which follow the one-patient-one-vote principle, are standard for comparisons of treatment effects. We discuss two types of weighted Z-tests in this manuscript to incorporate data collected in two (or more) stages or in two (or more) regions. We use the type A weighted Z-test to exemplify the variance spending approach in the first part of this manuscript. This approach has been applied to sample size re-estimation. In the second part of the manuscript, we introduce the type B weighted Z-tests and apply them to the design of bridging studies. The weights in the type A weighted Z-tests are pre-determined, independent of the prior observed data, and controls alpha at the desired level. To the contrary, the weights in the type B weighted Z-tests may depend on the prior observed data; and the type I error rate for the bridging study is usually inflated to a level higher than that of a full-scale study. The choice of the weights provides a simple statistical framework for communication between the regulatory agency and the sponsor. The negotiation process may involve practical constrains and some characteristics of prior studies.

Mean particle diameters. From statistical definition to physical understanding.

Abstract: Mean particle diameters may be used to describe and to model physical, chemical, or physiological properties of products or materials containing dispersed phases. There are different notation systems for these mean diameters, which may cause much confusion. This equally applies to their nomenclature. This article introduces the Moment-Ratio definition system and evaluates briefly the ISO definition system. The ISO system appears to have serious drawbacks. Mean particle diameters can be estimated from histograms of size distributions by Summation (M-R system) and by Integration (ISO system) over the histogram intervals. Summation tends to be more accurate than Integration and is less sensitive to low values of the lower limit of size distributions. The Summation method equations are straightforward and generally applicable. The mathematical formulas of the Integration method are difficult to apply in daily practice, and their complexity may easily hide the physical background of a mean particle diameter. A coherent nomenclature system for denoting mean particle diameters is recommended. This nomenclature system does not contain any ambiguities and clearly conveys the physical meanings of mean particle diameters. This article deals also with an empirical method to select the proper type of mean diameter to describe a physical, chemical, or physiological property of a product or material containing dispersed phases. After calculation of the mean diameters from experimental data, the relationships between the product property and these mean diameters are investigated statistically. The selection method has been illustrated by two examples. The dataset of each example consists of a set of particle size distributions and the corresponding physical product properties that are influenced by the particle sizes. Hypotheses are formulated to explain the types of selected mean diameters. Sharing results from all over the world of applications of the developed selection method will lead to a buildup of knowledge of physical meanings and application areas of the types of mean particle diameters, which will support decision making in product development.

A Bayesian Approach on Sample Size Calculation for Comparing Means

Abstract: In clinical research, parameters required for sample size calculation are usually unknown. A typical approach is to use estimates from some pilot studies as the true parameters in the calculation. This approach, however, does not take into consideration sampling error. Thus, the resulting sample size could be misleading if the sampling error is substantial. As an alternative, we suggest a Bayesian approach with noninformative prior to reflect the uncertainty of the parameters induced by the sampling error. Based on the informative prior and data from pilot samples, the Bayesian estimators based on appropriate loss functions can be obtained. Then, the traditional sample size calculation procedure can be carried out using the Bayesian estimates instead of the frequentist estimates. The results indicate that the sample size obtained using the Bayesian approach differs from the traditional sample size obtained by a constant inflation factor, which is purely determined by the size of the pilot study. An example is given for illustration purposes.

A Hybrid Bayesian Adaptive Design for Dose Response Trials

Abstract: In recent years, the use of adaptive design methods based on accrued data of on-going trials have become very popular for dose response trials in early clinical development due to their flexibility (EMEA, 2002). In this paper, we developed a hybrid frequentist-Bayesian continual reassessment method (CRM) in conjunction with utility-adaptive randomization for clinical trial designs with multiple endpoints. The proposed hyperlogistic function family with multiple parameters gives users flexibility for probability modeling. CRM reassesses a dose-response relationship based on accrued data of the on-going trial, which allows investigators to make decisions based on a constantly updated dose-response model. The proposed utility-adaptive randomization for multiple-endpoint trials allows more patients to be assigned to superior treatment groups. The performance of the proposed method was examined in terms of its operating characteristics through computer simulations.

Inference for clinical trials with some protocol amendments.

Abstract: The use of adaptive methods in clinical development has become very popular in recent years due to its flexibility in modifying trial procedures and/or statistical procedures of on-going clinical trials. Modifications to trial procedures are usually documented by protocol amendments. However, the actual patient population after protocol amendments could deviate from the originally targeted patient population. In addition, protocol amendments made based on accrued data of the on-going trial may distort the sampling distribution of the statistic designed for the case of no protocol change. In this article, we model the population deviations due to protocol amendments using some covariates and study how to develop a valid statistical inference procedure. An example concerning an asthma trial is presented for illustration.

Maximum Likelihood Estimation in Survival Studies Under Progressive Interval Censoring with Random Removals

Abstract: Censoring occurs commonly in clinical trials. This article investigates a new censoring scheme, namely, Type II progressive interval censoring with random removals to cope with the setting that patients are examined at fixed regular intervals and dropouts may occur during the study period. We discuss the maximum likelihood estimation of the model parameters and derive the corresponding asymptotic variances when survival times are assumed to be Weibull distributed. An example is discussed to illustrate the application of the results under this censoring scheme.

A Comparison of Multiplicity Adjustment Strategies for Correlated Binary Endpoints

Abstract: Several Bonferroni-type adjustments have been proposed to control for family wise type I error among multiple tests. However, many of the approaches disregard the correlation among endpoints. This can result in a conservative hypothesis testing strategy. The James procedure is an alternative approach that accounts for multiplicity among correlated continuous endpoints. Here a simulation study compares four Bonferroni-type alpha-adjustments (Bonferroni, Dunn-Sidak, Holm, and Hochberg) and the James p-value adjustment when used for multiple correlated binary variables. These procedures provided adequate protection against familywise type I error for correlated binary endpoints, albeit, at times, in an overly cautious manner. That is, when correlations among endpoints exceed 0.60, the result is somewhat conservative for the approaches that do not account for those correlations. Among the adjustments examined, the James approach appears to be the uniformly preferred method. Analyses of data from a randomized controlled clinical trial of treatments for mania in bipolar disorder are used to illustrate the application of the multiplicity adjustments.

Analysis of Longitudinal Binary Data with Missing Data Due to Dropouts

Abstract: Longitudinal binary data from clinical trials with missing observations are frequently analyzed by using the Last Observation Carry Forward (LOCF) method for imputing missing values at a visit (e.g., the prospectively defined primary visit time point for analysis at the end of treatment period). Usually, to understand time trend in treatment response, analyses are also performed separately on data at intermediate time points. The objective of such analyses is to estimate the proportion of "response" at a time point and then to compare two treatment groups (e.g., drug vs. placebo) by testing for the difference in the two proportions of response. The commonly used methods are Fisher's exact test, chi-squared test, Cochran-Mantel-Haenszel test, and logistic regression. Analyses based on the Observed Cases (OC) data are usually also performed and compared with those obtained by LOCF. Another approach that is gaining popularity (after the introduction of PROC GENMOD by the SAS Institute) is to use the method of Generalized Estimating Equations (GEE) with a view to include all repeated observations in the analysis in a more comprehensive manner. It is now well recognized, however, that results obtained by these methods are susceptible to bias, depending on the "missing data mechanism." Of particular concern is the bias introduced by NMAR dropouts. Because there is no one method to satisfactorily handle dropouts in data analysis, consensus is gathering toward doing analyses by several methods (including methods to handle NMAR dropouts) to evaluate sensitivity of results to model assumptions. In this article, we demonstrate application of the following methods for handling dropouts in longitudinal binary data: Generalized Linear Mixture Models (GLMM) (for handling NMAR dropouts), Weighted GEE (for handling MAR dropouts), and GEE (MCAR dropouts). The results are also compared with those obtained by logistic regression (univariate) on both LOCF and OC data.

Adaptive statistical analysis following sample size modification based on interim review of effect size.

Abstract: In designing a comparative clinical trial, the required sample size is a function of the effect size, the value of which is unknown and at best may be estimated from historical data. Insufficiency in sample size as a result of overestimating the effect size can be destructive to the success of the clinical trial. Sample size re-estimation may need to be properly considered as a part of clinical trial planning. This paper is intended to give the motivations for the sample size re-estimation based partly on the effect size observed at an interim analysis and for a resulting simple adaptive test strategy. The performance of this adaptive design strategy is assessed by comparing it with a fixed maximum sample size design that is properly adjusted in anticipation of the possible sample size adjustment.

Tests for equivalence based on odds ratio for matched-pair design.

Abstract: Currently, methods for evaluation of equivalence under a matched-pair design use either difference in proportions or relative risk as measures of risk association. However, these measures of association are only for cross-sectional studies or prospective investigations, such as clinical trials and they cannot be applied to retrospective research such as case-control studies. As a result, under a matched-pair design, we propose the use of the conditional odds ratio for assessment of equivalence in both prospective and retrospective research. We suggest the use of the asymptotic confidence interval of the conditional odds ratio for evaluation of equivalence. In addition, a score test based on the restricted maximum likelihood estimator (RMLE) is derived to test the hypothesis of equivalence under a matched-pair design. On the other hand, a sample size formula is also provided. A simulation study was conducted to empirically investigate the size and power of the proposed procedures. Simulation results show that the score test not only adequately controls the Type I error but it can also provide sufficient power. A numerical example illustrates the proposed methods.

A Simple and Efficient Bias-Reduced Estimator of Response Probability Following a Group Sequential Phase II Trial

Abstract: A phase II clinical trial evaluating the rate of response of a new therapeutic treatment is often designed to have one or two interim analyses, allowing possible termination of the trial at an early stage if lack of treatment efficacy is evident. Due to the sequential nature of such a trial, the sample proportion yields biased estimation for the rate of response. In this paper we propose an estimator of response rate by subtracting the estimated bias directly from the sample proportion. The proposed estimator is simple, intuitive, and easy to compute. When the bias of the sample proportion is of concern to the investigators, the proposed estimator is an efficient alternative to other estimators in the literature in terms of bias and mean squared error.

Assessment of Equivalence Using a Concordance Correlation Coefficient in a Repeated Measurements Design

Abstract: Some assay validation studies are conducted to assess agreement between repeated, paired continuous data measured on the same subject with different measurement systems. The goal of these studies is to show that there is an acceptable level of agreement between the measurement systems. Equivalence testing is a reasonable approach in assay validation. In this article, we use an equivalence-testing criterion based on a decomposition of a concordance correlation coefficient proposed by Lin (1989, 1992). Using a variance components approach, we develop bounds for conducting statistical tests using the proposed equivalence criterion. We conduct a simulation study to assess the performance of the bounds. The criteria are the ability to maintain the stated test size and the simulated power of the tests using these bounds. Bounds that perform well for small sample size are preferred. We present a computational example to demonstrate the methods described in the article.

Class prediction in toxicogenomics.

Abstract: The intent of this article is to discuss some of the complexities of toxicogenomics data and the statistical design and analysis issues that arise in the course of conducting a toxicogenomics study. We also describe a procedure for classifying compounds into various hepatotoxicity classes based on gene expression data. The methodology involves first classifying a compound as toxic or nontoxic and subsequently classifying the toxic compounds into the hepatotoxicity classes, based on votes by binary classifiers. The binary classifiers are constructed by using genes selected to best elicit differences between the two classes. We show that the gene selection strategy improves the misclassification error rates and also delivers gene pathways that exhibit biological relevance.

Sample Size Calculation for Simulation-Based Multiple-Testing Procedures

Abstract: In this article, we present a simple method to calculate sample size and power for a simulation-based multiple testing procedure which gives a sharper critical value than the standard Bonferroni method. The method is especially useful when several highly correlated test statistics are involved in a multiple-testing procedure. The formula for sample size calculation will be useful in designing clinical trials with multiple endpoints or correlated outcomes. We illustrate our method with a quality-of-life study for patients with early stage prostate cancer. Our method can also be used for comparing multiple independent groups.

Two-stage adaptive designs with correlated test statistics.

Abstract: When performing a trial using an adaptive sequential design, it is usually assumed that the data for each stage come from different units; for example, patients. However, sometimes it is not possible to satisfy this condition or to check whether it is satisfied. In these cases, the test statistics and p-values of each stage may be dependent. In this paper we investigate the type I error of two-stage adaptive designs when the test statistics from the stages are assumed to be bivariate normal. Analytical considerations are performed under the restriction that the conditional error function is constant in the continuation region. We show that the decisions can become conservative as well as anticonservative, depending on the design parameters and on the sign of the correlation coefficient. Further, we discuss properties and advantages of this design and compare it with the Bauer-Kohne method.

Optimal Design for Dose Response Using Beta Distributed Responses

Abstract: 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 beta regression model. In this article, we explore locally optimal designs for this class of regression models, focusing mainly on minimization of the generalized variance of maximum likelihood estimators (D-optimality). Optimal designs and sensitivity to misspecification of model parameters are examined using a candidate points searching algorithm. Although formally the model assumes that the response is continuous, it provides a parsimonious approximation for ordinal data when there is a relatively large number of categories. The resulting estimators and optimal designs are simpler and may offer more ease in interpretation than those derived from models for ordered categorical outcomes. The proposed methods are applied to data from a clinical trial.