The microbiome OTU table for all samples was used to calculate the Shannon diversity index. Samples were rarefied to 1000 reads per sample before statistical analysis. Diversity calculations were done using the vegan package in the R statistical software. Regressions between diversity measures and WinCF variables were carried out using Pearson’s r. The RF algorithm was used to develop both a classification and linear model of both the metabolome and microbiome data based on the linear variables of the capillary columns and by sample type. RF analyses were carried out using the randomForest package in R with 5000 trees. Variable importance plots were used to identify OTUs and metabolites that were most correlated to the linear variables.

A generalized linear mixed-effects model (GLMM) was applied to model the relationship between bacterial sequence counts (at the genus level) as the dependent variable and pH and depth as the independent variables. The GLMM model accounts for non-normal distribution of data and to assign a random effect to individual (patient), as data were gathered over time on the same individuals with differing microbial sputum profiles. To model metabolite intensity as the dependent variable and pH and depth variables as independent, a standard linear mixed-effects model (LMM) was used. The R packages MASS and nlme were used to perform the modeling.

Balance trees were used to assess the effect of the gradients and gas production on the WinCF model microbiome at the taxonomic level of genera. Balances represent the log ratios of groups of microbes mitigating many of the issues associated with compositionally (19). The 16S rRNA gene sequencing data from the pH experiment were used to help develop the balance tree method and have been previously published (19). Here, we have built two trees, one to characterize the pH gradient, where microbes are split according to where they are most abundant along the pH gradient and another to characterize effects of the oxygen gradient. Balances were computed from these trees via the isometric log-ratio transformation using Gneiss (19). Two different LMMs were run on these balances to test for differences in pH and depth while accounting for the patient-specific differences.

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