Instrumental variable estimation for compositional treatments

Abstract

Many scientific datasets are compositional in nature. Important biological examples include species abundances in ecology, cell-type compositions derived from single-cell sequencing data, and amplicon abundance data in microbiome research. Here, we provide a causal view on compositional data in an instrumental variable setting where the composition acts as the cause. First, we crisply articulate potential pitfalls for practitioners regarding the interpretation of compositional causes from the viewpoint of interventions and warn against attributing causal meaning to common summary statistics such as diversity indices in microbiome data analysis. We then advocate for and develop multivariate methods using statistical data transformations and regression techniques that take the special structure of the compositional sample space into account while still yielding scientifically interpretable results. In a comparative analysis on synthetic and real microbiome data we show the advantages and limitations of our proposal. We posit that our analysis provides a useful framework and guidance for valid and informative cause-effect estimation in the context of compositional data.

Keywords: Causality; Cause-effect estimation; Compositional data; Instrumental variable; Microbial diversity.

Fig. 1

The ternary plot shows an exemplary scenario with . The orange contour contains compositions for which the Simpson diversity is constant, while the blue contour shows compositions for which the Shannon diversity is constant. Shannon diversity changes along contours of Simpson diversity and vice versa.

Fig. 2

Cause-effect estimation of via an instrumental variable Z for compositional X.

Fig. 3

Visualization of a Setting A (): The left panel shows both a weak (left) and a strong (right) instrument, i.e. with the instrument value Z either barely influencing the the composition of the microbiome (left) or strongly impacting the composition of the microbiome (right). The right panel shows a discrepancy between the true causal effect and the observed effect which stems from a confounding factor.

Fig. 4

Boxplots of the results for setting B in Table 2 with . We show OOS MSE (left), recovery of non-zero coefficients (middle), and recovery of zero coefficients.

Fig. 5

We display OOS MSE and -MSE (for non-zero coefficients and where applicable) for our robustness checks. All results and further visualizations are in Supplementary Material S8.

Fig. 6

Taxonomic tree of the microbiome data at genus level. The influential log-ratios for both Only Second LC and ILR+LC are highlighted in black and blue, respectively.