A semi-parametric multiple imputation method for high-sparse, high-dimensional, compositional data

High sparsity (i.e., excessive zeros) in microbiome data, which are high-dimensional and compositional, is unavoidable and can significantly alter analysis results. However, efforts to address this high sparsity have been very limited because, in part, it is impossible to justify the validity of any such methods, as zeros in microbiome data arise from multiple sources (e.g., true absence, stochastic nature of sampling). The most common approach is to treat all zeros as structural zeros (i.e., true absence) or rounded zeros (i.e., undetected due to detection limit). However, this approach can underestimate the mean abundance while overestimating its variance because many zeros can arise from the stochastic nature of sampling and/or functional redundancy (i.e., different microbes can perform the same functions), thus losing power. In this manuscript, we argue that treating all zeros as missing values would not significantly alter analysis results if the proportion of structural zeros is similar for all taxa, and we propose a semi-parametric multiple imputation method for high-sparse, high-dimensional, compositional data. We demonstrate the merits of the proposed method and its beneficial effects on downstream analyses in extensive simulation studies. We reanalyzed a type II diabetes (T2D) dataset to determine differentially abundant species between T2D patients and non-diabetic controls.