Addressing erroneous scale assumptions in microbe and gene set enrichment analysis.

By applying Differential Set Analysis (DSA) to sequence count data, researchers can determine whether groups of microbes or genes are differentially enriched. Yet sequence count data suffer from a scale limitation: these data lack information about the scale (i.e., size) of the biological system under study, leading some authors to call these data compositional (i.e., proportional). In this article, we show that commonly used DSA methods that rely on normalization make strong, implicit assumptions about the unmeasured system scale. We show that even small errors in these scale assumptions can lead to positive predictive values as low as 9%. To address this problem, we take three novel approaches. First, we introduce a sensitivity analysis framework to identify when modeling results are robust to such errors and when they are suspect. Unlike standard benchmarking studies, this framework does not require ground-truth knowledge and can therefore be applied to both simulated and real data. Second, we introduce a statistical test that provably controls Type-I error at a nominal rate despite errors in scale assumptions. Finally, we discuss how the impact of scale limitations depends on a researcher's scientific goals and provide tools that researchers can use to evaluate whether their goals are at risk from erroneous scale assumptions. Overall, the goal of this article is to catalyze future research into the impact of scale limitations in analyses of sequence count data; to illustrate that scale limitations can lead to inferential errors in practice; yet to also show that rigorous and reproducible scale reliant inference is possible if done carefully.