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Register a new userEfficient and flexible simulation-based sample size determination for clinical trials with multiple design parameters
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Duncan Wilson
Publication date
2019
fields
Mathematical Statistics
and research's language is
English
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Simulation offers a simple and flexible way to estimate the power of a clinical trial when analytic formulae are not available. The computational burden of using simulation has, however, restricted its application to only the simplest of sample size determination problems, minimising a single parameter (the overall sample size) subject to power being above a target level. We describe a general framework for solving simulation-based sample size determination problems with several design parameters over which to optimise and several conflicting criteria to be minimised. The method is based on an established global optimisation algorithm widely used in the design and analysis of computer experiments, using a non-parametric regression model as an approximation of the true underlying power function. The method is flexible, can be used for almost any problem for which power can be estimated using simulation, and can be implemented using existing statistical software packages. We illustrate its application to three increasingly complicated sample size determination problems involving complex clustering structures, co-primary endpoints, and small sample considerations.
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A central goal in designing clinical trials is to find the test that maximizes power (or equivalently minimizes required sample size) for finding a true research hypothesis subject to the constraint of type I error. When there is more than one test, such as in clinical trials with multiple endpoints, the issues of optimal design and optimal policies become more complex. In this paper we address the question of how such optimal tests should be defined and how they can be found. We review different notions of power and how they relate to study goals, and also consider the requirements of type I error control and the nature of the policies. This leads us to formulate the optimal policy problem as an explicit optimization problem with objective and constraints which describe its specific desiderata. We describe a complete solution for deriving optimal policies for two hypotheses, which have desired monotonicity properties, and are computationally simple. For some of the optimization formulations this yields optimal policies that are identical to existing policies, such as Hommels procedure or the procedure of Bittman et al. (2009), while for others it yields completely novel and more powerful policies than existing ones. We demonstrate the nature of our novel policies and their improved power extensively in simulation and on the APEX study (Cohen et al., 2016).
Phase III randomized clinical trials play a monumentally critical role in the evaluation of new medical products. Because of the intrinsic nature of uncertainty embedded in our capability in assessing the efficacy of a medical product, interpretation of trial results relies on statistical principles to control the error of false positives below desirable level. The well-established statistical hypothesis testing procedure suffers from two major limitations, namely, the lack of flexibility in the thresholds to claim success and the lack of capability of controlling the total number of false positives that could be yielded by the large volume of trials. We propose two general theoretical frameworks based on the conventional frequentist paradigm and Bayesian perspectives, which offer realistic, flexible and effective solutions to these limitations. Our methods are based on the distribution of the effect sizes of the population of trials of interest. The estimation of this distribution is practically feasible as clinicaltrials.gov provides a centralized data repository with unbiased coverage of clinical trials. We provide a detailed development of the two frameworks with numerical results obtained for industry sponsored Phase III randomized clinical trials.
We propose BaySize, a sample size calculator for phase I clinical trials using Bayesian models. BaySize applies the concept of effect size in dose finding, assuming the MTD is defined based on an equivalence interval. Leveraging a decision framework that involves composite hypotheses, BaySize utilizes two prior distributions, the fitting prior (for model fitting) and sampling prior (for data generation), to conduct sample size calculation under desirable statistical power. Look-up tables are generated to facilitate practical applications. To our knowledge, BaySize is the first sample size tool that can be applied to a broad range of phase I trial designs.
The development of a new diagnostic test ideally follows a sequence of stages which, amongst other aims, evaluate technical performance. This includes an analytical validity study, a diagnostic accuracy study and an interventional clinical utility study. Current approaches to the design and analysis of the diagnostic accuracy study can suffer from prohibitively large sample sizes and interval estimates with undesirable properties. In this paper, we propose a novel Bayesian approach which takes advantage of information available from the analytical validity stage. We utilise assurance to calculate the required sample size based on the target width of a posterior probability interval and can choose to use or disregard the data from the analytical validity study when subsequently inferring measures of test accuracy. Sensitivity analyses are performed to assess the robustness of the proposed sample size to the choice of prior, and prior-data conflict is evaluated by comparing the data to the prior predictive distributions. We illustrate the proposed approach using a motivating real-life application involving a diagnostic test for ventilator associated pneumonia. Finally, we compare the properties of the proposed approach against commonly used alternatives. The results show that by making better use of existing data from earlier studies, the assurance-based approach can not only reduce the required sample size when compared to alternatives, but can also produce more reliable sample sizes for diagnostic accuracy studies.
Manufacturers are required to demonstrate products meet reliability targets. A typical way to achieve this is with reliability demonstration tests (RDTs), in which a number of products are put on test and the test is passed if a target reliability is achieved. There are various methods for determining the sample size for RDTs, typically based on the power of a hypothesis test following the RDT or risk criteria. Bayesian risk criteria approaches can conflate the choice of sample size and the analysis to be undertaken once the test has been conducted and rely on the specification of somewhat artificial acceptable and rejectable reliability levels. In this paper we offer an alternative approach to sample size determination based on the idea of assurance. This approach chooses the sample size to answer provide a certain probability that the RDT will result in a successful outcome. It separates the design and analysis of the RDT, allowing different priors for each. We develop the assurance approach for sample size calculations in RDTs for binomial and Weibull likelihoods and propose appropriate prior distributions for the design and analysis of the test. In each case, we illustrate the approach with an example based on real data.
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