Efficient and flexible simulation-based sample size determination for clinical trials with multiple design parameters

Abstract

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, often 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 a sample size determination problem involving complex clustering structures, two primary endpoints and small sample considerations.

Power Analysis for the Wald, LR, Score, and Gradient Tests in a Marginal Maximum Likelihood Framework: Applications in IRT

“…It must be expected that the results are more prone to error with smaller sample sizes and larger effect sizes; however, we note that the dependence on the sample size also applies to the statistics under a true null hypothesis. To avoid this problem, one can use simulation-based approaches (Wilson et al, 2020). The main disadvantage of these are that for sample size planning, in particular, a high computational load can be expected to approximate the relationship between sample size and power.…”

Sample Size Planning for Complex Study Designs: A Tutorial for the mlpwr Package

“…We also use one in the package mlpwr to focus computational resources on finding promising design parameter sets. Wilson et al (2020) use surrogate modeling in the context of a clinical trial. They apply a multilevel model and consider multiple study design dimensions.…”

“…The package closes two gaps in the literature by providing an implementation for multiple design parameters and allowing for the consideration of costs during the optimization. If cost information is available, our approach enables a more efficient search compared to the approach by Wilson et al (2020), where a selection by cost can be performed after some suitable design parameter sets are identified. Since optimization of power is a very specific use case of surrogate modeling, the mlpwr package provides a specifically tailored interface on top of its own implementation of surrogate modeling.…”

Power analysis for the Wald, LR, score, and gradient tests in a marginal maximum likelihood framework: Applications in IRT

“…It must be expected that the results are more prone to error with smaller sample sizes and larger effect sizes; however, we note that the dependence on the sample size also applies to the statistics under a true null hypothesis. To avoid this problem, one can use simulation-based approaches (e.g., Wilson et al, 2020). The main disadvantage of these are that for sample size planning, in particular, a high computational load can be expected to approximate the relationship between sample size and power.…”