Abstract
Estimating sample size and statistical power is an essential part of a good epidemiological study design. Closed-form formulas exist for simple hypothesis tests but not for advanced statistical methods designed for exposure mixture studies. Estimating power with Monte Carlo simulations is flexible and applicable to these methods. However, it is not straightforward to code a simulation for non-experienced programmers and is often hard for a researcher to manually specify multivariate associations among exposure mixtures to set up a simulation. To simplify this process, we present the R package mpower for power analysis of observational studies of environmental exposure mixtures involving recently developed mixtures analysis methods. The components within mpower are also versatile enough to accommodate any mixtures methods that will be developed in future. The package allows users to simulate realistic exposure data and mixed-typed covariates based on public dataset such as the National Health and Nutrition Examination Survey or other existing dataset from prior studies. Users can generate power curves to assess the trade-offs between sample size, effect size, and power of a design. This paper presents tutorials and examples of power analysis using mpower.
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Data Availability
Publicly available on Github (https://github.com/phuchonguyen/mpower).
Code Availability
Publicly available on Github (https://github.com/phuchonguyen/mpower).
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Funding
This work was partially supported by Grants R01ES027498 and R01ES028804 of the National Institute of Environmental Health Sciences of the United States National Institutes of Health.
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AHH devised and supervised the project. PHN developed the software, examples, and wrote the first draft of the manuscript. SME provided critical feedback and helped shape features of the software. All authors contributed to the final manuscript.
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Appendix A Estimated Signal-to-Noise Ratio as a Function of m
Appendix A Estimated Signal-to-Noise Ratio as a Function of m
We will estimate the SNR of the following data-generating process using different values for m:
The estimated SNR for the linear model example is unbiased but the standard error might be large with a small sample of simulated data. The red horizontal line is the ground truth SNR (Color figure online)
Since the predictors are independent standard normal distributions, and the noise variance is 1, we can calculate the true SNR as \([0.3^2(1) + 0.3^2(1)]/1 = 0.18\). Figure 7 shows the estimated SNR and 1000-bootstrap s.e. for m \(\in \{500, 5000, 50000, 10000, 200000\}\). A larger m results in a more precise estimate. When the mixture model is defined based on resampling, it may not be possible to choose a large m without duplicating observations and underestimating the signal.
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Nguyen, P.H., Herring, A.H. & Engel, S.M. Power Analysis of Exposure Mixture Studies Via Monte Carlo Simulations. Stat Biosci (2023). https://doi.org/10.1007/s12561-023-09385-7
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DOI: https://doi.org/10.1007/s12561-023-09385-7