Optimizing marine debris monitoring: balancing statistical power and test size in survey design

Conducting a power analysis is a best practice for designing long-term environmental monitoring programs so that trade-offs in survey design elements such as sample size and temporal revisits can be evaluated. However, these analyses are sensitive to a priori decisions about the underlying distribution of the data, appropriate model structure, and choice of trend test. Improper trend model specification and inappropriate trend tests can affect power estimates, leading to misguided choices of survey design elements, trend tests with inflated test size (i.e., increased probability of detecting a nonexistent trend), and management decisions based on misleading information.

In this simulation study, we conducted a power analysis to inform the design of a nationwide shoreline marine debris monitoring survey across 10 regional extents in the United States. Pilot data consisted of debris item counts having many zeros, transformed into item densities. We applied a generalized linear mixed model with a Tweedie conditional distribution to model simulated debris item density populations having known trend. We compared test size and power for three trend tests (Z-test, likelihood ratio test [LRT], and t-test), five levels of variance composition, five temporal revisit designs, and three levels of within-year replication for samples of 50 to 62 sites surveyed over an 11-year monitoring duration.

Test size and power were negatively affected when the year-to-year variation in debris item density was high. Revisit designs that included even a small panel of annually visited sites maintained test size close to the nominal level of 0.15. The LRT provided nominal trend test size in most cases except when the year-to-year variation in debris item density was high and in scenarios with sparse replication across years. In those cases, the LRT exhibited inflated test size and power, and the t-test provided a more conservative, but low power, test of trend. The LRT had slightly inflated test size when revisit designs without an annual panel of sites were used.

Our results demonstrate the importance of assessing both test size and power when assessing monitoring design choices to ensure that accurate trend inferences can be made.