In antonvsdata/amp: Smoothing Metabolomics Analyses

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Statistics

This vignette provides an overview of the different statistical tests provided in the package. The first section discusses univariate tests, which are repeated for each feature.

Unless otherwise stated, all functions return separate data frames or other objects with the results. These can be then added to the object results using join_results(object, results)

Univariate functions

summary statistics and effect sizes

These functions provide summary statistics and effect sizes for all features:

Summary statistics (mean, sd, median, mad, quartiles): summary_statistics
Cohen's d: cohens_d
Fold changes between groups: fold_change

Hypothesis tests

These functions perform univariate hypothesis tests for each feature, report relevant statistics and correct the p-values using FDR correction. For features, where the model fails for some reason, all statistics are recorded as NA. NOTE setting all_features = FALSE does not prevent the tests on the flagged compounds, but only affects p-value correction, where flagged features are not included in the correction and thus do not have an FDR-corrected p-value. To prevent the testing of flagged features alltogether, use drop_flagged before the tests.

Formula interface

Many R functions for statistical tests use a so-called formula interface. For example, the function lm that is used for fitting linear models uses the formula interface, so when predicting the fuel consumption (mpg - miles per gallon) by the car weight (wt) in the inbuilt mtcars dataset, we would run:

lm(mpg ~ wt, data = mtcars)

For many of the univariate statistical test functions in this package use the formula interface, where the formula is provided as a character, with one special condition: the word "Feature" will get replaced at each iteration by the corresponding feature name. So for example, when testing if any of the features predict the difference between study groups, the formula would be: "Group ~ Feature". Or, when testing if group and time point affect metabolite levels, the formula could be "Feature ~ Group + Time + Group:Time", with the last term being an interaction term ("Feature ~ Group * Time" is equivalent).

Now that we know how the formula interface looks like, let's list the univariate statistical functions available:

linear models: perform_lm
linear mixed models: perform_lmer (uses lmer function from the lme4 package, with lmerTest package for p-values)
tests of equality of variance: perform_homoscedasticity_tests
Kruskal-Wallis test: perform_kruskal_wallis
Welch's ANOVA and Classic ANOVA: perform_oneway_anova
two-sample t-test (Welch or Student): perform_t_test

Functions not using the formula interface

Some functions do not use the formula interface. They include

pairwise t-tests: perform_pairwise_t_test
correlation tests between molecular features and/or phenotype variable: perform_correlation_tests
Area under curve computation: perform_auc

Model diagnostics

Model diagnostics visalizations are currently available for linear models and linear mixed models, see documenation of save_lm_diagnostic_plots.

Multivariate functions

Random forest

fit_rf fits a random forest predicting a column in the sample information (pData(obejct)) by the features
importance_rf extracts the feature importance in random forest prediction in a nice format