Adaptive Sample Size Research Articles

Adaptive increase in sample size when interim results are promising: A practical guide with examples

This paper discusses the benefits and limitations of adaptive sample size re-estimation for phase 3 confirmatory clinical trials. Comparisons are made with more traditional fixed sample and group sequential designs. It is seen that the real benefit of the adaptive approach arises through the ability to invest sample size resources into the trial in stages. The trial starts with a small up-front sample size commitment. Additional sample size resources are committed to the trial only if promising results are obtained at an interim analysis. This strategy is shown through examples of actual trials, one in neurology and one in cardiology, to be more advantageous than the fixed sample or group sequential approaches in certain settings. A major factor that has generated controversy and inhibited more widespread use of these methods has been their reliance on non-standard tests and p-values for preserving the type-1 error. If, however, the sample size is only increased when interim results are promising, one can dispense with these non-standard methods of inference. Therefore, in the spirit of making adaptive increases in trial size more widely appealing and readily implementable we here define those promising circumstances in which a conventional final inference can be performed while preserving the overall type-1 error. Methodological, regulatory and operational issues are examined.

Estimation and Confidence Intervals for Two-Stage Sample-Size-Flexible Design with LSW Likelihood Approach

Adaptive sample size methods have been a popular topic in the field of clinical trials. There are a few basic requirements for the adaptive methods to be acceptable from the international regulatory viewpoint. All valid methods need to control the overall type-I error rate at the pre-specified level. The rule of the interim and final decisions needs to be explicit and clearly documentable. It is extremely desirable that the method employed also provides estimation of the treatment effect in addition to the significance test. In this paper we describe the point and confidence interval estimation for the likelihood approach of sample-size adaptive design proposed by Li et al. (Biostatistics 3:277–287, 2002, J. Biopharm. Stat. 15:707–718, 2005). We use the median unbiased estimator (Cox and Hinkley, Theoretical Statistics, p. 273, 1974) for estimating the treatment effect and demonstrate that the estimator has small mean squared error compared to the naive method, and that the confidence interval estimation has correct coverage probability.

Multivariate EWMA Control Chart with Adaptive Sample Sizes

Standard multivariate control charts usually employ fixed sample sizes at equal sampling intervals to monitor a process. In this study, a multivariate exponential weighted moving average (MEWMA) chart with adaptive sample sizes is investigated. Performance measure of the adaptive-sample-size MEWMA chart is obtained through a Markov chain approach. The performance of the adaptive-sample-size MEWMA chart is compared with the fixed-sample-size control chart in terms of steady-state average run length for different magnitude of shifts in the process mean. It is shown that the adaptive-sample-size chart is more efficient than the fixed-sample-size MEWMA control chart in detecting shifts in the process mean.

An adaptive noninferiority margin and sample size adjustment in covariate-adjustment regression model approach to noninferiority clinical trials

An adaptive noninferiority margin and sample size adjustment in covariate-adjustment regression model approach to noninferiority clinical trials

Optimal Filtering for Non-parametric Observation Models: Applications to Localization and SLAM

In this work we address the problem of optimal Bayesian filtering for dynamic systems with observation models that cannot be approximated properly as any parameterized distribution. In the context of mobile robots this problem arises in localization and simultaneous localization and mapping (SLAM) with occupancy grid maps. The lack of a parameterized observation model for these maps forces a sample-based representation, commonly through Monte Carlo methods for sequential filtering, also called particle filters. Our work is grounded on the demonstrated existence of an optimal proposal distribution for particle filters. However, this optimal distribution is not directly applicable to systems with non-parametric models. By integrating ideas from previous works on adaptive sample size, auxiliary particle filters, and rejection sampling, we derive a new particle filter algorithm that enables the usage of the optimal proposal to estimate the true posterior density of a non-parametric dynamic system. This new filter is better suited, both theoretically and in practice, than previous approximate methods for indoor and outdoor localization and SLAM, as confirmed by experiments with real robots.

Economic and economic statistical design of T 2 control chart with two adaptive sample sizes

The Hotelling's T 2 control chart, a direct analogue of the univariate Shewhart X¯ chart, is perhaps the most commonly used tool in industry for simultaneous monitoring of several quality characteristics. Recent studies have shown that using variable sampling size (VSS) schemes results in charts with more statistical power when detecting small to moderate shifts in the process mean vector. In this paper, we build a cost model of a VSS T 2 control chart for the economic and economic statistical design using the general model of Lorenzen and Vance [The economic design of control charts: A unified approach, Technometrics 28 (1986), pp. 3–11]. We optimize this model using a genetic algorithm approach. We also study the effects of the costs and operating parameters on the VSS T 2 parameters, and show, through an example, the advantage of economic design over statistical design for VSS T 2 charts, and measure the economic advantage of VSS sampling versus fixed sample size sampling.

Adaptive sample size and importance sampling in estimation-based local search for the probabilistic traveling salesman problem

The probabilistic traveling salesman problem is a paradigmatic example of a stochastic combinatorial optimization problem. For this problem, recently an estimation-based local search algorithm using delta evaluation has been proposed. In this paper, we adopt two well-known variance reduction procedures in the estimation-based local search algorithm: the first is an adaptive sampling procedure that selects the appropriate size of the sample to be used in Monte Carlo evaluation; the second is a procedure that adopts importance sampling to reduce the variance involved in the cost estimation. We investigate several possible strategies for applying these procedures to the given problem and we identify the most effective one. Experimental results show that a particular heuristic customization of the two procedures increases significantly the effectiveness of the estimation-based local search.

Optimizing Trial Design

Despite substantial progress in the prevention of cardiovascular disease and its ischemic complications, it remains the single largest killer in the United States. New treatment options are needed, particularly to respond to the challenges of an aging population and rising rates of obesity and diabetes. Development of novel therapeutic strategies for the management of acute cardiovascular disease is especially challenging. Specific problems include relatively low event rates, diverse patient populations, lack of reliable surrogate end points, and small treatment effects subject to substantial uncertainty. Because the clinical development process is enormously expensive and time consuming, there is considerable interest in statistical methods that use accumulating data from a clinical trial to inform and modify its design. Such redesign might include changes in target sample size and even changes in the target population. This article discusses developments in adaptive design of interest to cardiovascular research. To illustrate the methods we discuss, we focus on the development of novel therapies for the management of acute coronary syndromes. However, the ideas we discuss have much wider application. We begin by discussing the traditional approach to determination of a fixed sample size for a clinical trial. We then describe group sequential designs and the benefit they provide in the conduct of trials. In the section on Adaptive Sample Size Reestimation, we discuss designs that are adaptive in the sense that they allow an adjustment of the target sample size based on the accumulating data from the trial. In the section on Adaptive Sample Size Reestimation With Enrichment, we discuss enrichment designs that shift the focus to a patient subgroup when the accumulating data suggest greatest benefit for that subgroup. Additional details about population enrichment are provided in the online-only Data Supplement. We consider therapies intended to reduce the risk of acute ischemic complications in …

Bayesian np control charts with adaptive sample size for finite production runs

AbstractThe design of a control chart requires the specification of three decision variables, namely the sample size, n, the sampling interval, h, and the action limit under which the process must be stopped for potential repair. In this paper, the Bayesian attribute control chart, namely the np chart for short run production, using a variable sample size is discussed. In a simulated experiment, optimal solutions of the static np chart, the basic Bayesian np chart, and the Bayesian scheme with adaptive sample size are presented. Results of the empirical study show that varying the sample size leads to more cost savings compared with the other two approaches. In order to detect how the input parameters affect decision variables, a regression analysis is conducted. It is obtained that the benefits of using the basic Bayesian np chart and the Bayesian chart with adaptive sample size instead of the static scheme are affected by the length of the production run. Copyright © 2008 John Wiley & Sons, Ltd.

Hotelling’s T 2 control chart with two adaptive sample sizes

Some quality control schemes have been developed when several related quality characteristics are to be monitored. The familiar multivariate process monitoring and control procedure is the Hotelling’s T 2 control chart for monitoring the mean vector of the process. It is a direct analog of the univariate shewhart \({\bar{x}}\) chart. As in the case of univariate, the ARL improvements are very important particularly for small process shifts. In this paper, we study the T 2 control chart with two-state adaptive sample size, when the shift in the process mean does not occur at the beginning but at some random time in the future. Further, the occurrence time of the shift is assumed to be exponentially distributed random variable.

Adaptive control schemes for two dependent process steps

The article considers the statistical adaptive process control for two dependent process steps. We construct adaptive sample size and sampling interval (ASSI) Z X ¯ and Z e ¯ control charts to monitor the quality variables produced by the first process step and the second process step at the end of the second process step and effectively distinguish which process step is out-of-control. The performance of the proposed ASSI control charts is measured by adjusted average time to signal (AATS) using Markov chain approach. An example of automobile braking system shows the application and performance of the proposed ASSI Z X ¯ and Z e ¯ control charts in detecting shifts in process mean. Furthermore, the performance of the ASSI Z X ¯ and Z e ¯ control charts and the nonadaptive sample size and sampling interval Z X ¯ and Z e ¯ control charts are compared by some numerical analysis results. It demonstrates that the former is much faster than the latter in detecting small shifts in mean.

Performance of adaptive sample size adjustment with respect to stopping criteria and time of interim analysis

The benefit of adjusting the sample size in clinical trials on the basis of treatment effects observed in interim analysis has been the subject of several recent papers. Different conclusions were drawn about the usefulness of this approach for gaining power or saving sample size, because of differences in trial design and setting. We examined the benefit of sample size adjustment in relation to trial design parameters such as 'time of interim analysis' and 'choice of stopping criteria'. We compared the adaptive weighted inverse normal method with classical group sequential methods for the most common and for optimal stopping criteria in early, half-time and late interim analyses. We found that reacting to interim data might significantly reduce average sample size in some situations, while classical approaches can out-perform the adaptive designs under other circumstances. We characterized these situations with respect to time of interim analysis and choice of stopping criteria.

A nonparametric repeated significance test with adaptive target sample size

In this article a general result is derived that, along with a functional central limit theorem for a sequence of statistics, can be employed in developing a nonparametric repeated significance test with adaptive target sample size. This method is used in deriving a repeated significance test with adaptive target sample size for the shift model. The repeated significance test is based on a functional central limit theorem for a sequence of partial sums of truncated observations. Based on numerical results presented in this article one can conclude that this nonparametric sequential test performs quite well.

Adaptive, group sequential and decision theoretic approaches to sample size determination

This paper presents two adaptive methods for sample size re-estimation within a unified group sequential framework. The conceptual and practical distinction between these adaptive modifications and more traditional sample size changes due to revised estimates of nuisance parameters is highlighted. The motivation for the adaptive designs is discussed. Having established that adaptive sample size modifications can be made without inflating the type 1 error, the paper concludes with a novel decision theoretic approach for determining the magnitude of the sample size modification.

Multivariate double sampling |S| charts for controlling process variability

A new multivariate statistical process variability control scheme, the multivariate double sampling (MDS) |S| control chart scheme for controlling shifts in a variance–covariance matrix, is proposed. An MDS |S| chart is a double-stage extension of a single-stage control chart based on the sample generalized variance. The statistical efficiency in terms of average run length of the MDS |S| charts is compared with that of traditional and adaptive sample size control charts based on the sample generalized variance for a bivariate case. The results of the comparison show that the MDS |S| charts provide a significant improvement in efficiency for detecting shifts of any range over these schemes. The performance of the MDS |S| charts in terms of detecting power is also compared with that of the modified likelihood ratio test, the sum of standardized variances for principal components charts and a decomposition procedure. The results of the comparison show that for certain out-of-control situations, the performance of the MDS |S| chart is among those of the best schemes.

Optimal Design of the Adaptive Sample Size and Sampling Interval np Control Chart

AbstractRecent research has shown that the adaptive control charts are quicker than the traditional static charts in detecting process shifts. This paper develops the algorithm for the optimization designs of the adaptive np control charts for monitoring the process fraction non‐conforming p. It includes the variable sample size chart, the variable sampling interval chart, and the variable sample size and sampling interval chart. The performance of the adaptive np charts is measured by the average time to signal under the steady‐state mode, which allows the shift in p to occur at any time, even during the sampling inspection. By studying the performance of the adaptive np charts systematically, it is found that they do improve effectiveness significantly, especially for detecting small or moderate process shifts. Copyright © 2004 John Wiley & Sons, Ltd.

S29.3: Risks and benefits of adaptive sample size adjustments

S29.3: Risks and benefits of adaptive sample size adjustments

Neuroprotection Is Unlikely to Be Effective in Humans Using Current Trial Designs: An Opposing View

To summarize recent neuroprotective trials, there has been no useful balance of benefit over risk.1 It is premature to shoot the messenger without evidence either that the results have been misleading or that we have missed trends. Confirmatory trials and/or meta-analysis support the validity of the results, and similar designs have successfully revealed the risks and benefits of thrombolysis. Trial designs have been imperfect, but the message is accurate: the drugs or doses we tried were inadequate. We need safer and better drugs, we need to know when and how to use them, and we need to maximize the efficiency of our trials. All are possible with current designs.2 Originally, limited efficacy data from a single laboratory and an acceptable toxicity profile were sufficient to proceed to clinical development. Choice of dose range, the optimal duration of therapy, patient subgroup selection, and the likely extent of benefit were all reserved for testing in clinical trials. The misplaced optimism of such an approach is now recognized, however, and guidance on preclinical testing has been elaborated.3 Rigorous external scrutiny of preclinical data now occurs in the more informed companies,4 and clinical development is deferred pending resolution of any deficiencies. This is the first role of the (now mandatory) trial steering committee. The drug classes under investigation are evolving, and new approaches are still being discovered. Glutamate antagonists have been widely studied.1 While effective in small animal models, their short time window in the laboratory, failure to protect …

A comparison of methods for adaptive sample size adjustment

In fixed sample size designs, precise knowledge about the magnitude of the outcome variable's variance in the planning phase of a clinical trial is mandatory for an adequate sample size determination. Wittes and Brittain introduced the internal pilot study design that allows recalculation of the sample size during an ongoing trial using the estimated variance obtained from an interim analysis. However, this procedure requires the unblinding of the treatment code. Since unblinding of an ongoing trial should be avoided whenever possible, there should be some benefit of this design compared with blinded sample size recalculation procedures to justify the unveiling of the treatment code. In this paper, we compare several sample size recalculation procedures with and without unblinding. The simulation results indicate that the procedures behave similarly. In particular, breaking of the blind is not required for an efficient sample size adjustment. We also compare these pure sample size adaptation procedures with study designs which additionally allow for early stopping. Evaluation of the cumulative distribution function of the resulting sample sizes shows that the option for early stopping may lead to lower expectation but generally to a higher variability. The procedures are illustrated by an example of a trial in the treatment of depression.

GENERALIZED VARIANCE CHART DESIGN WITH ADAPTIVE SAMPLE SIZES. THE BIVARIATE CASE

Multivariate Statistical Quality Control has recently become a basic tool in process control. Various control charting procedures have been proposed when several quality characteristics are to be monitored simultaneously, for example, the mean and covariance matrix of a multivariate quality measurement. On the other hand, it has been showed that many of the charts usually employed are not powerful enough to detect small changes in the process. The use of adaptive sample size is one of the methods that offers the best results to increase the power. The present work shows the design of the Generalized Variance Chart |S| with adaptive sample size to control processes defined by two quality characteristics, comparing the power of this new chart versus the |S| chart with fixed sample size.