Bayesian Sample Size Determination Research Articles

Bayesian clinical trial design using historical data that inform the treatment effect.

We consider the problem of Bayesian sample size determination for a clinical trial in the presence of historical data that inform the treatment effect. Our broadly applicable, simulation-based methodology provides a framework for calibrating the informativeness of a prior while simultaneously identifying the minimum sample size required for a new trial such that the overall design has appropriate power to detect a non-null treatment effect and reasonable type I error control. We develop a comprehensive strategy for eliciting null and alternative sampling prior distributions which are used to define Bayesian generalizations of the traditional notions of type I error control and power. Bayesian type I error control requires that a weighted-average type I error rate not exceed a prespecified threshold. We develop a procedure for generating an appropriately sized Bayesian hypothesis test using a simple partial-borrowing power prior which summarizes the fraction of information borrowed from the historical trial. We present results from simulation studies that demonstrate that a hypothesis test procedure based on this simple power prior is as efficient as those based on more complicated meta-analytic priors, such as normalized power priors or robust mixture priors, when all are held to precise type I error control requirements. We demonstrate our methodology using a real data set to design a follow-up clinical trial with time-to-event endpoint for an investigational treatment in high-risk melanoma.

Bayesian sample size determination for a Phase III clinical trial with diluted treatment effect

ABSTRACTWhen Phase III treatment effect is diluted from what was observed from Phase II results, we propose to determine the Bayesian sample size for a Phase III clinical trial based on the normal, uniform, and truncated normal prior distributions of the treatment effects on an interval, which starts from an acceptable treatment effect to the observed treatment effect from Phase II. After incorporating the prior information of the treatment effects, the Bayesian sample size is the number of patients of the Phase III trial for a given Bayesian Predictive Power (BPP) or Bayesian Historical Predictive Power (BHPP). After that, the numerical simulations are carried out to determine the Bayesian sample size for the Phase III clinical trial. In particular, there exists a hook phenomenon for the BHPP when the number of patients of the Phase II trial equals 70 assuming the normal, uniform, or truncated normal treatment effect. Moreover, we add some sensitivity analysis of the Bayesian sample size about the parameters in the simulations. Finally, we determine the Bayesian sample size (number of events or deaths) of the Phase III trial for a fixed power, Bayesian Historical Power (BHP), and BHPP in the axitinib example.

Bayesian sample size determination for cost-effectiveness studies with censored data.

Cost-effectiveness models are commonly utilized to determine the combined clinical and economic impact of one treatment compared to another. However, most methods for sample size determination of cost-effectiveness studies assume fully observed costs and effectiveness outcomes, which presents challenges for survival-based studies in which censoring exists. We propose a Bayesian method for the design and analysis of cost-effectiveness data in which costs and effectiveness may be censored, and the sample size is approximated for both power and assurance. We explore two parametric models and demonstrate the flexibility of the approach to accommodate a variety of modifications to study assumptions.

Bayesian sample size determination for product retesting after design change in Poisson distributed data

Many times, a design is changed after product validation testing in the real world. It occurs more frequently in the engineering field, which will create a problem of retesting the product with the original product specification without consideration of the degree and significance of the design change. As far as cost and resources are concerned, we have to find the minimum sample size for retesting the product. In this paper, we present a Bayesian method for determining sample size for retesting the redesigned product in Poisson distributed data via success-based testing prior. Numerical results of sample size for retesting the redesigned product are given. An example of paper pulp is provided.

Bayesian sample size determination for product retesting after design change in Poisson distributed data

Many times, a design is changed after product validation testing in the real world. It occurs more frequently in the engineering field, which will create a problem of retesting the product with the original product specification without consideration of the degree and significance of the design change. As far as cost and resources are concerned, we have to find the minimum sample size for retesting the product. In this paper, we present a Bayesian method for determining sample size for retesting the redesigned product in Poisson distributed data via success-based testing prior. Numerical results of sample size for retesting the redesigned product are given. An example of paper pulp is provided.

Bayesian assurance and sample size determination in the process validation life-cycle

ABSTRACTValidation of pharmaceutical manufacturing processes is a regulatory requirement and plays a key role in the assurance of drug quality, safety, and efficacy. The FDA guidance on process validation recommends a life-cycle approach which involves process design, qualification, and verification. The European Medicines Agency makes similar recommendations. The main purpose of process validation is to establish scientific evidence that a process is capable of consistently delivering a quality product. A major challenge faced by manufacturers is the determination of the number of batches to be used for the qualification stage. In this article, we present a Bayesian assurance and sample size determination approach where prior process knowledge and data are used to determine the number of batches. An example is presented in which potency uniformity data is evaluated using a process capability metric. By using the posterior predictive distribution, we simulate qualification data and make a decision on the number of batches required for a desired level of assurance.

Bayesian Sample Size Determination in Two-Sample Poisson Models

Bayesian Sample Size Determination in Two-Sample Poisson Models

Bayesian Sample Size Determination in Two-Sample Poisson Models

Sample size determination is a vital part of clinical studies where cost and safety concerns lead to greater importance of not using more subjects and resources than are required. The Bayesian approach to sample size determination has the advantages of being able to use prior data and expert opinion to possibly reduce the total sample size while also acknowledging all uncertainty at the design stage. We apply a Bayesian decision theoretic approach to the problem of comparing two Poisson rates and find the required sample size to obtain a desired power while controlling the Type I error rate.

Contrast of Bayesian and Classical Sample Size Determination

Sample size determination is a prerequisite for statistical surveys. A comprehensive overview of the Bayesian approach for computation of the sample size, and a comparison with classical approaches, is presented. Two surveys are taken as example to illustrate the accuracy and efficiency of each approach, and to make recommendations about which method is preferred. The Bayesian approach of sample size determination may require fewer subjects if proper prior information is available.

Bayesian-frequentist sample size determination: a game of two priors

Experimental design represents the typical context in which the interplay between Bayesian and frequentist methodology is natural and useful. Before the data are observed, it is licit and unavoidable even for a Bayesian statistician to take into account sample variability for the evaluation of statistical procedures and for decision making. At the same time, design planning fatally involves a number of pre-experimental choices that even a frequentist statistician is forced to make, preferably by exploiting external sources of knowledge. In this paper we discuss this mutual exchange between Bayesian and frequentist methodology, with specific focus on the primary crucial aspect of experimental designs, that is sample size determination (SSD). We review this topic by highlighting how the interplay between two prior distributions helps in managing the close relationship between the two approaches. Although the distinction between decisional and performance-based methods for Bayesian SSD is discussed, the main interest of this article is on the latter. We propose a general framework that includes several performance-based methods as special cases and thus makes the comparison of their characteristics easier. Finally, we extend the overview to robust methods for Bayesian SSD that allow to deal with the critical issue of sensitivity to prior elicitation. Illustrative examples are provided for normal models.

Bayesian sequential meta‐analysis design in evaluating cardiovascular risk in a new antidiabetic drug development program

Recently, the Center for Drug Evaluation and Research at the Food and Drug Administration released a guidance that makes recommendations about how to demonstrate that a new antidiabetic therapy to treat type 2 diabetes is not associated with an unacceptable increase in cardiovascular risk. One of the recommendations from the guidance is that phases II and III trials should be appropriately designed and conducted so that a meta-analysis can be performed. In addition, the guidance implies that a sequential meta-analysis strategy could be adopted. That is, the initial meta-analysis could aim at demonstrating the upper bound of a 95% confidence interval (CI) for the estimated hazard ratio to be < 1.8 for the purpose of enabling a new drug application or a biologics license application. Subsequently after the marketing authorization, a final meta-analysis would need to show the upper bound to be < 1.3. In this context, we develop a new Bayesian sequential meta-analysis approach using survival regression models to assess whether the size of a clinical development program is adequate to evaluate a particular safety endpoint. We propose a Bayesian sample size determination methodology for sequential meta-analysis clinical trial design with a focus on controlling the familywise type I error rate and power. We use the partial borrowing power prior to incorporate the historical survival meta-data into the Bayesian design. We examine various properties of the proposed methodology, and simulation-based computational algorithms are developed to generate predictive data at various interim analyses, sample from the posterior distributions, and compute various quantities such as the power and the type I error in the Bayesian sequential meta-analysis trial design. We apply the proposed methodology to the design of a hypothetical antidiabetic drug development program for evaluating cardiovascular risk.

Bayesian Sample Size Determination for Case-Control Studies When Exposure May be Misclassified

Odds ratios are frequently used for estimating the effect of an exposure on the probability of disease in case-control studies. In planning such studies, methods for sample size determination are required to ensure sufficient accuracy in estimating odds ratios once the data are collected. Often, the exposure used in epidemiologic studies is not perfectly ascertained. This can arise from recall bias, the use of a proxy exposure measurement, uncertain work exposure history, and laboratory or other errors. The resulting misclassification can have large impacts on the accuracy and precision of estimators, and specialized estimation techniques have been developed to adjust for these biases. However, much less work has been done to account for the anticipated decrease in the precision of estimators at the design stage. Here, we develop methods for sample size determination for odds ratios in the presence of exposure misclassification by using several interval-based Bayesian criteria. By using a series of prototypical examples, we compare sample size requirements after adjustment for misclassification with those required when this problem is ignored. We illustrate the methods by planning a case-control study of the effect of late introduction of peanut to the diet of children to the subsequent development of peanut allergy.

Bayesian Sample Size Determination for a Clinical Trial with Correlated Continuous and Binary Outcomes

In clinical trials, multiple outcomes are often collected in order to simultaneously assess effectiveness and safety. We develop a Bayesian procedure for determining the required sample size in a regression model where a continuous efficacy variable and a binary safety variable are observed. The sample size determination procedure is simulation based. The model accounts for correlation between the two variables. Through examples we demonstrate that savings in total sample size are possible when the correlation between these two variables is sufficiently high.

Bayesian Sample-size Determination for Medical Decision Making

Bayesian Sample-size Determination for Medical Decision Making

On the Limiting Behavior of the “Probability of Claiming Superiority” in a Bayesian Context

In the context of Bayesian sample size determination in clinical trials, a quantity of interest is the marginal probability that the posterior probability of an alternative hypothesis of interest exceeds a specified threshold. This marginal probability is the same as “average power”; that is, the average of the power function with respect to the prior distribution when using a test based on a Bayesian rejection region. We give conditions under which this marginal probability (or average power) converges to the prior probability of the alternative hypothesis as the sample size increases. This same large sample behavior also holds for the average power of a (frequentist) consistent test. We also examine the limiting behavior of “conditional average power”; that is, power averaged with respect to the prior distribution conditional on the alternative hypothesis being true.

Bayesian sample size determination for the bounded linex loss function

In this paper, we discuss optimum sample size determination for a bounded linex loss function (blinex). The linex loss function is often used when losses are asymmetric, but it has the disadvantage that it can only be used if the moment-generating function of the posterior distribution exists. Blinex loss has the advantage that it can always be calculated. Also many authors have argued that a bounded loss function is to be preferred. We have obtained the optimum sample size for a number of distributions when the cost of sampling is linear. The form of the posterior risk function does not allow an analytical solution so simulation is necessary.

Bayesian sample size determination for binary regression with a misclassified covariate and no gold standard

Covariate misclassification is a common problem in epidemiology, genetics, and other biomedical areas. Because this form of misclassification is known to bias estimators, accounting for it at the design stage is of high importance. In this paper, we extend on previous work applied to response misclassification by developing a Bayesian approach to sample size determination for a covariate misclassification model with no gold standard. Our procedure considers both conditionally independent tests and tests in which dependence exists between classifiers. We specifically consider a Bayesian power criterion for the sample size determination scheme, and we demonstrate the improvement in model power for our dual classifier approach compared to a naïve single classifier approach.

Bayesian Sample Size Determination Using Linex Loss and Linear Cost

Sample size determination (SSD) is an important issue to consider when estimating any parameter. A number of researchers have studied the Bayesian SSD problem. One group considered utility (or loss) functions and cost functions in their SSD problem and the others did not. Among the former, most of the SSD problems are based on symmetric squared error (SE) loss function. On the other hand, in a situation when under estimation is more serious than overestimation or vice versa, then an asymmetric loss function should be used. In such a situation how many samples do we need to take to estimate the parameter under study? In this article, we consider sample size using the asymmetric linex loss function and a linear cost function for various distributions. We compare the sample size obtained from this asymmetric loss function with the sample size from the symmetric SE loss function. We also consider the situation where it is not worth sampling due to high sampling cost or strong prior information.

Bayesian Meta‐Experimental Design: Evaluating Cardiovascular Risk in New Antidiabetic Therapies to Treat Type 2 Diabetes

Recent guidance from the Food and Drug Administration for the evaluation of new therapies in the treatment of type 2 diabetes (T2DM) calls for a program-wide meta-analysis of cardiovascular (CV) outcomes. In this context, we develop a new Bayesian meta-analysis approach using survival regression models to assess whether the size of a clinical development program is adequate to evaluate a particular safety endpoint. We propose a Bayesian sample size determination methodology for meta-analysis clinical trial design with a focus on controlling the type I error and power. We also propose the partial borrowing power prior to incorporate the historical survival meta data into the statistical design. Various properties of the proposed methodology are examined and an efficient Markov chain Monte Carlo sampling algorithm is developed to sample from the posterior distributions. In addition, we develop a simulation-based algorithm for computing various quantities, such as the power and the type I error in the Bayesian meta-analysis trial design. The proposed methodology is applied to the design of a phase 2/3 development program including a noninferiority clinical trial for CV risk assessment in T2DM studies.

Bayesian sample size determination for inspection of general corrosion of process components

A Bayesian approach-based method is proposed for calculating the minimum size of a sample to assess, with a specified precision, the integrity of process components suffering from general corrosion. The proposed method ensures that the error in the posterior estimate of the mean does not exceed a pre-defined acceptable margin of error at a specified confidence level. An analytical formula to estimate the sample size is introduced. The sample size obtained using the proposed method is smaller than a sample size obtained using the classical method with same confidence level. This reduces sampling inspection cost without affecting the precision of the estimate.