Abstract
BackgroundEstimating the required sample size and statistical power for a study is an integral part of study design. For standard designs, power equations provide an efficient solution to the problem, but they are unavailable for many complex study designs that arise in practice. For such complex study designs, computer simulation is a useful alternative for estimating study power. Although this approach is well known among statisticians, in our experience many epidemiologists and social scientists are unfamiliar with the technique. This article aims to address this knowledge gap.MethodsWe review an approach to estimate study power for individual- or cluster-randomized designs using computer simulation. This flexible approach arises naturally from the model used to derive conventional power equations, but extends those methods to accommodate arbitrarily complex designs. The method is universally applicable to a broad range of designs and outcomes, and we present the material in a way that is approachable for quantitative, applied researchers. We illustrate the method using two examples (one simple, one complex) based on sanitation and nutritional interventions to improve child growth.ResultsWe first show how simulation reproduces conventional power estimates for simple randomized designs over a broad range of sample scenarios to familiarize the reader with the approach. We then demonstrate how to extend the simulation approach to more complex designs. Finally, we discuss extensions to the examples in the article, and provide computer code to efficiently run the example simulations in both R and Stata.ConclusionsSimulation methods offer a flexible option to estimate statistical power for standard and non-traditional study designs and parameters of interest. The approach we have described is universally applicable for evaluating study designs used in epidemiologic and social science research.
Highlights
Estimating the required sample size and statistical power for a study is an integral part of study design
Where b is the Type II error rate, F is the normal cumulative distribution function, c is the number of clusters per arm, n is the number of individuals per cluster, d is the mean difference between treatment groups, s2 is the variance of the outcome, Za/2 is the quantile of the standard normal distribution associated with a Type I error rate of a, and r is the intraclass correlation coefficient (ICC)
We have demonstrated with practical examples how to use computer simulation to estimate study design power based on an assumed mixed model data generating distribution for the outcomes, which is identical to the distribution assumed for conventional power equations [1]
Summary
Estimating the required sample size and statistical power for a study is an integral part of study design. Feiveson [16] presents an applied, general overview of estimating power by simulation using Stata software, but the article is not indexed in major databases, and has only been cited twice in applied research [17,18] To our knowledge, this is the first published application of this approach that outlines the method using the data generating models that are both the foundation of traditional power calculations and familiar to quantitative epidemiologists. Our goal with this article is to motivate and demonstrate with concrete examples how to use simulation techniques to estimate design power in a way that quantitative, applied epidemiologists can use in practice We believe this approach has the potential for widespread application because the setting in which we have applied it is similar to that found in many studies
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