# skbio.stats.composition.ancom¶

skbio.stats.composition.ancom(table, grouping, alpha=0.05, tau=0.02, theta=0.1, multiple_comparisons_correction='holm-bonferroni', significance_test=None, percentiles=(0.0, 25.0, 50.0, 75.0, 100.0))[source]

Performs a differential abundance test using ANCOM.

State: Experimental as of 0.4.1.

This is done by calculating pairwise log ratios between all features and performing a significance test to determine if there is a significant difference in feature ratios with respect to the variable of interest.

In an experiment with only two treatments, this tests the following hypothesis for feature $$i$$

$H_{0i}: \mathbb{E}[\ln(u_i^{(1)})] = \mathbb{E}[\ln(u_i^{(2)})]$

where $$u_i^{(1)}$$ is the mean abundance for feature $$i$$ in the first group and $$u_i^{(2)}$$ is the mean abundance for feature $$i$$ in the second group.

Parameters
• table (pd.DataFrame) – A 2D matrix of strictly positive values (i.e. counts or proportions) where the rows correspond to samples and the columns correspond to features.

• grouping (pd.Series) – Vector indicating the assignment of samples to groups. For example, these could be strings or integers denoting which group a sample belongs to. It must be the same length as the samples in table. The index must be the same on table and grouping but need not be in the same order.

• alpha (float, optional) – Significance level for each of the statistical tests. This can can be anywhere between 0 and 1 exclusive.

• tau (float, optional) – A constant used to determine an appropriate cutoff. A value close to zero indicates a conservative cutoff. This can can be anywhere between 0 and 1 exclusive.

• theta (float, optional) – Lower bound for the proportion for the W-statistic. If all W-statistics are lower than theta, then no features will be detected to be differentially significant. This can can be anywhere between 0 and 1 exclusive.

• multiple_comparisons_correction ({None, 'holm-bonferroni'}, optional) – The multiple comparison correction procedure to run. If None, then no multiple comparison correction procedure will be run. If ‘holm-boniferroni’ is specified, then the Holm-Boniferroni procedure 1 will be run.

• significance_test (function, optional) – A statistical significance function to test for significance between classes. This function must be able to accept at least two 1D array_like arguments of floats and returns a test statistic and a p-value. By default scipy.stats.f_oneway is used.

• percentiles (iterable of floats, optional) – Percentile abundances to return for each feature in each group. By default, will return the minimum, 25th percentile, median, 75th percentile, and maximum abundances for each feature in each group.

Returns

• pd.DataFrame – A table of features, their W-statistics and whether the null hypothesis is rejected.

”W” is the W-statistic, or number of features that a single feature is tested to be significantly different against.

”Reject null hypothesis” indicates if feature is differentially abundant across groups (True) or not (False).

• pd.DataFrame – A table of features and their percentile abundances in each group. If percentiles is empty, this will be an empty pd.DataFrame. The rows in this object will be features, and the columns will be a multi-index where the first index is the percentile, and the second index is the group.

Notes

The developers of this method recommend the following significance tests (2, Supplementary File 1, top of page 11): if there are 2 groups, use the standard parametric t-test (scipy.stats.ttest_ind) or non-parametric Wilcoxon rank sum test (scipy.stats.wilcoxon). If there are more than 2 groups, use parametric one-way ANOVA (scipy.stats.f_oneway) or nonparametric Kruskal-Wallis (scipy.stats.kruskal). Because one-way ANOVA is equivalent to the standard t-test when the number of groups is two, we default to scipy.stats.f_oneway here, which can be used when there are two or more groups. Users should refer to the documentation of these tests in SciPy to understand the assumptions made by each test.

This method cannot handle any zero counts as input, since the logarithm of zero cannot be computed. While this is an unsolved problem, many studies, including 2, have shown promising results by adding pseudocounts to all values in the matrix. In 2, a pseudocount of 0.001 was used, though the authors note that a pseudocount of 1.0 may also be useful. Zero counts can also be addressed using the multiplicative_replacement method.

References

1

Holm, S. “A simple sequentially rejective multiple test procedure”. Scandinavian Journal of Statistics (1979), 6.

2(1,2,3)

Mandal et al. “Analysis of composition of microbiomes: a novel method for studying microbial composition”, Microbial Ecology in Health & Disease, (2015), 26.

Examples

First import all of the necessary modules:

>>> from skbio.stats.composition import ancom
>>> import pandas as pd


Now let’s load in a DataFrame with 6 samples and 7 features (e.g., these may be bacterial OTUs):

>>> table = pd.DataFrame([[12, 11, 10, 10, 10, 10, 10],
...                       [9,  11, 12, 10, 10, 10, 10],
...                       [1,  11, 10, 11, 10, 5,  9],
...                       [22, 21, 9,  10, 10, 10, 10],
...                       [20, 22, 10, 10, 13, 10, 10],
...                       [23, 21, 14, 10, 10, 10, 10]],
...                      index=['s1', 's2', 's3', 's4', 's5', 's6'],
...                      columns=['b1', 'b2', 'b3', 'b4', 'b5', 'b6',
...                               'b7'])


Then create a grouping vector. In this example, there is a treatment group and a placebo group.

>>> grouping = pd.Series(['treatment', 'treatment', 'treatment',
...                       'placebo', 'placebo', 'placebo'],
...                      index=['s1', 's2', 's3', 's4', 's5', 's6'])


Now run ancom to determine if there are any features that are significantly different in abundance between the treatment and the placebo groups. The first DataFrame that is returned contains the ANCOM test results, and the second contains the percentile abundance data for each feature in each group.

>>> ancom_df, percentile_df = ancom(table, grouping)
>>> ancom_df['W']
b1    0
b2    4
b3    0
b4    1
b5    1
b6    0
b7    1
Name: W, dtype: int64


The W-statistic is the number of features that a single feature is tested to be significantly different against. In this scenario, b2 was detected to have significantly different abundances compared to four of the other features. To summarize the results from the W-statistic, let’s take a look at the results from the hypothesis test. The Reject null hypothesis column in the table indicates whether the null hypothesis was rejected, and that a feature was therefore observed to be differentially abundant across the groups.

>>> ancom_df['Reject null hypothesis']
b1    False
b2     True
b3    False
b4    False
b5    False
b6    False
b7    False
Name: Reject null hypothesis, dtype: bool


From this we can conclude that only b2 was significantly different in abundance between the treatment and the placebo. We still don’t know, for example, in which group b2 was more abundant. We therefore may next be interested in comparing the abundance of b2 across the two groups. We can do that using the second DataFrame that was returned. Here we compare the median (50th percentile) abundance of b2 in the treatment and placebo groups:

>>> percentile_df[50.0].loc['b2']
Group
placebo      21.0
treatment    11.0
Name: b2, dtype: float64


We can also look at a full five-number summary for b2 in the treatment and placebo groups:

>>> percentile_df.loc['b2']
Percentile  Group
0.0         placebo      21.0
25.0        placebo      21.0
50.0        placebo      21.0
75.0        placebo      21.5
100.0       placebo      22.0
0.0         treatment    11.0
25.0        treatment    11.0
50.0        treatment    11.0
75.0        treatment    11.0
100.0       treatment    11.0
Name: b2, dtype: float64


Taken together, these data tell us that b2 is present in significantly higher abundance in the placebo group samples than in the treatment group samples.