Power and sample size analysis for longitudinal mixed models of health in populations exposed to environmental contaminants: a tutorial

Kylie K Harrall, Keith E Muller, Anne P Starling, Dana Dabelea, Kelsey E Barton, John L Adgate, Deborah H Glueck, Kylie K Harrall, Keith E Muller, Anne P Starling, Dana Dabelea, Kelsey E Barton, John L Adgate, Deborah H Glueck

Abstract

Background: When evaluating the impact of environmental exposures on human health, study designs often include a series of repeated measurements. The goal is to determine whether populations have different trajectories of the environmental exposure over time. Power analyses for longitudinal mixed models require multiple inputs, including clinically significant differences, standard deviations, and correlations of measurements. Further, methods for power analyses of longitudinal mixed models are complex and often challenging for the non-statistician. We discuss methods for extracting clinically relevant inputs from literature, and explain how to conduct a power analysis that appropriately accounts for longitudinal repeated measures. Finally, we provide careful recommendations for describing complex power analyses in a concise and clear manner.

Methods: For longitudinal studies of health outcomes from environmental exposures, we show how to [1] conduct a power analysis that aligns with the planned mixed model data analysis, [2] gather the inputs required for the power analysis, and [3] conduct repeated measures power analysis with a highly-cited, validated, free, point-and-click, web-based, open source software platform which was developed specifically for scientists.

Results: As an example, we describe the power analysis for a proposed study of repeated measures of per- and polyfluoroalkyl substances (PFAS) in human blood. We show how to align data analysis and power analysis plan to account for within-participant correlation across repeated measures. We illustrate how to perform a literature review to find inputs for the power analysis. We emphasize the need to examine the sensitivity of the power values by considering standard deviations and differences in means that are smaller and larger than the speculated, literature-based values. Finally, we provide an example power calculation and a summary checklist for describing power and sample size analysis.

Conclusions: This paper provides a detailed roadmap for conducting and describing power analyses for longitudinal studies of environmental exposures. It provides a template and checklist for those seeking to write power analyses for grant applications.

Keywords: Free software; General linear mixed model; Longitudinal study design; Persistent chemicals; Power analysis; Repeated measurements; Sample size.

Conflict of interest statement

The other authors declare they have no actual or potential competing financial interests.

© 2023. The Author(s).

Figures

Fig. 1
Fig. 1
A power analysis check-list
Fig. 2
Fig. 2
Power for time-by-group interaction, as a function of mean difference [(μ T1,A - μ T3,A) -(μ T1,C- μ T3,C)] and standard deviation of PFHxS. Data are back-transformed for interpretability. The standard deviation shown is 3.02 ng/mL. This mean difference is scaled by factors of 0.5, 1, 1.5, and 2 along the x-axis. The solid line shows how differences in the mean difference may affect power. Additionally, the two dashed lines show how the relationship between the mean difference and power changes when the standard deviation is smaller by half (1.51 ng/mL) or doubled in size (6.04 ng/mL)

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