Differential regulation: ANCOVA for two groups

Differential regulation: ANCOVA for two groups#

This API example shows the functionality in the acore.differential_regulation module:

  • Analysis of Covariance (ANCOVA) for two groups

  • Effect of covariates is taken into account in the linear model

Then we can do the same for examples with three and more groups, where a omnibus analysis across groups is combined with posthoc anlysis for separate groups.

The functions are the same for both cases. The group1 and group2 columns give the posthoc comparison.

%pip install acore vuecore

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Note: you may need to restart the kernel to use updated packages.

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import dsp_pandas
import pandas as pd
import sklearn.impute
import vuecore.plots.basic.scatter

import acore.differential_regulation as ad

dsp_pandas.format.set_pandas_options(
    max_columns=9,
    max_colwidth=20,
)

BASE = (
    "https://raw.githubusercontent.com/Multiomics-Analytics-Group/acore/"
    "main/example_data/alzheimer_proteomics/"
)
# data is already preprocessed: log2, filtered
fname: str = "alzheimer_example_omics_and_clinic.csv"  # combined omics and meta data
covariates: list[str] = ["age", "male"]
group: str = "AD"
subject_col: str = "Sample ID"
drop_cols: list[str] = ["collection_site"]
factor_and_covars: list[str] = [group, *covariates]

Data loading#

Use combined dataset for ANCOVA analysis.

Hide code cell source

 
omics_and_meta = (
    pd.read_csv(f"{BASE}/{fname}", index_col=subject_col)
    .convert_dtypes()
    .dropna(subset=factor_and_covars)
    .drop(columns=drop_cols)
)
omics_and_meta
AD age male Q6UX72 ... Q9Y5I4 P55283 A1L4H1 Q7Z4T9
Sample ID
Sample_000 0 71 0 16.047 ... 17.187 17.422 15.542 19.331
Sample_001 1 77 1 14.457 ... 17.447 17.097 15.734 18.980
Sample_002 1 75 1 15.631 ... 17.410 17.752 15.824 19.326
Sample_003 1 72 0 16.204 ... 17.545 17.483 15.515 18.953
Sample_004 1 63 0 15.968 ... 17.297 17.172 15.334 18.651
... ... ... ... ... ... ... ... ... ...
Sample_205 1 69 0 15.262 ... 17.104 16.952 15.705 18.844
Sample_206 0 73 1 <NA> ... 17.109 18.056 15.282 18.686
Sample_207 0 71 0 15.463 ... 16.938 17.248 14.874 19.146
Sample_208 0 83 1 15.786 ... 17.155 16.353 15.471 16.853
Sample_209 0 63 0 15.691 ... 16.776 16.597 14.699 18.087

197 rows × 103 columns

Metadata here is of type integer. All floats are proteomics measurements.

Hide code cell source

 
omics_and_meta.dtypes.value_counts()

Float64   100
Int64       3
Name: count, dtype: int64

Hide code cell source

 
omics_and_meta[[group, *covariates]]
AD age male
Sample ID
Sample_000 0 71 0
Sample_001 1 77 1
Sample_002 1 75 1
Sample_003 1 72 0
Sample_004 1 63 0
... ... ... ...
Sample_205 1 69 0
Sample_206 0 73 1
Sample_207 0 71 0
Sample_208 0 83 1
Sample_209 0 63 0

197 rows × 3 columns

Impute missing values#

Currently the run_ancova function does not handle missing values for measurments which are not given.

Request implementation when necessary. We will therefore use acore imputation to impute missing values for the proteomics measurements.

# import acore.imputation_analysis

# acore.imputation_analysis.imputation_mixed_norm_KNN(
#     omics_and_meta,
#     index_cols=[group, *covariates],
#     group=group,
# )
omics_and_meta = pd.DataFrame(
    sklearn.impute.KNNImputer(n_neighbors=3).fit_transform(omics_and_meta),
    index=omics_and_meta.index,
    columns=omics_and_meta.columns,
)
omics_and_meta
AD age male Q6UX72 ... Q9Y5I4 P55283 A1L4H1 Q7Z4T9
Sample ID
Sample_000 0.000 71.000 0.000 16.047 ... 17.187 17.422 15.542 19.331
Sample_001 1.000 77.000 1.000 14.457 ... 17.447 17.097 15.734 18.980
Sample_002 1.000 75.000 1.000 15.631 ... 17.410 17.752 15.824 19.326
Sample_003 1.000 72.000 0.000 16.204 ... 17.545 17.483 15.515 18.953
Sample_004 1.000 63.000 0.000 15.968 ... 17.297 17.172 15.334 18.651
... ... ... ... ... ... ... ... ... ...
Sample_205 1.000 69.000 0.000 15.262 ... 17.104 16.952 15.705 18.844
Sample_206 0.000 73.000 1.000 16.111 ... 17.109 18.056 15.282 18.686
Sample_207 0.000 71.000 0.000 15.463 ... 16.938 17.248 14.874 19.146
Sample_208 0.000 83.000 1.000 15.786 ... 17.155 16.353 15.471 16.853
Sample_209 0.000 63.000 0.000 15.691 ... 16.776 16.597 14.699 18.087

197 rows × 103 columns

ANCOVA analysis for two groups#

If there is more than two groups, the code still runs, but then the results are to be interpreted as an omnibus test across groups. See for details pingouin.ancova documentation.

# omics_and_meta = omics_and_meta.astype(float)
# ? this is no needed for run_ancova (the regex where groups are joined)
ancova = (
    ad.run_ancova(
        omics_and_meta.astype({group: str}),  # ! target needs to be of type str
        # subject=subject_col, # not used
        drop_cols=[],
        group=group,  # needs to be a string
        covariates=covariates,
    )
    .set_index("identifier")
    .sort_values(by="posthoc padj")
)  # need to be floats?
ancova_acore = ancova
ancova
group1 group2 mean(group1) std(group1) ... rejected -log10 pvalue Method posthoc padj
identifier
P17174 0.0 1.0 19.100 0.411 ... True 6.170 One-way ancova 0.000
P01834 0.0 1.0 24.322 0.823 ... True 5.072 One-way ancova 0.000
P14174 0.0 1.0 18.069 0.729 ... True 5.217 One-way ancova 0.000
P08294 0.0 1.0 21.490 0.426 ... True 4.218 One-way ancova 0.002
P02787 0.0 1.0 26.596 0.271 ... True 3.715 One-way ancova 0.004
... ... ... ... ... ... ... ... ... ...
F5GY87 0.0 1.0 15.364 0.686 ... False 0.031 One-way ancova 0.969
H3BMA1 0.0 1.0 15.296 0.578 ... False 0.027 One-way ancova 0.969
E9PMI0 0.0 1.0 15.713 0.519 ... False 0.019 One-way ancova 0.977
P16870 0.0 1.0 19.588 0.320 ... False 0.003 One-way ancova 0.993
A0A286YFJ8 0.0 1.0 19.523 1.134 ... False 0.005 One-way ancova 0.993

100 rows × 22 columns

Inspect ANCOVA results#

  • summary statistics for each group

  • test results

  • t-test statistic, FDR correction method, etc.

View averages per protein group#

The first columns contain group averages for each group for the specific protein group

ancova.iloc[:, :6]
group1 group2 mean(group1) std(group1) mean(group2) std(group2)
identifier
P17174 0.0 1.0 19.100 0.411 19.492 0.534
P01834 0.0 1.0 24.322 0.823 23.712 0.736
P14174 0.0 1.0 18.069 0.729 18.648 0.645
P08294 0.0 1.0 21.490 0.426 21.205 0.293
P02787 0.0 1.0 26.596 0.271 26.405 0.327
... ... ... ... ... ... ...
F5GY87 0.0 1.0 15.364 0.686 15.484 0.717
H3BMA1 0.0 1.0 15.296 0.578 15.276 0.684
E9PMI0 0.0 1.0 15.713 0.519 15.763 0.393
P16870 0.0 1.0 19.588 0.320 19.617 0.373
A0A286YFJ8 0.0 1.0 19.523 1.134 19.449 1.059

100 rows × 6 columns

Test results#

The others contain the test results (based on a linear model) for each protein group (on each row). Some information is duplicated.

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regex_filter = "pval|padj|reject|post"
ancova.filter(regex=regex_filter)
posthoc T-Statistics posthoc pvalue pvalue padj rejected -log10 pvalue posthoc padj
identifier
P17174 5.138 0.000 0.000 0.000 True 6.170 0.000
P01834 -4.576 0.000 0.000 0.000 True 5.072 0.000
P14174 4.653 0.000 0.000 0.000 True 5.217 0.000
P08294 -4.101 0.000 0.000 0.002 True 4.218 0.002
P02787 -3.801 0.000 0.000 0.004 True 3.715 0.004
... ... ... ... ... ... ... ...
F5GY87 0.085 0.932 0.932 0.969 False 0.031 0.969
H3BMA1 0.075 0.940 0.940 0.969 False 0.027 0.969
E9PMI0 0.053 0.957 0.957 0.977 False 0.019 0.977
P16870 0.009 0.993 0.993 0.993 False 0.003 0.993
A0A286YFJ8 0.015 0.988 0.988 0.993 False 0.005 0.993

100 rows × 7 columns

Other information#

Hide code cell source

 
ancova.iloc[:, 6:].filter(regex=f"^(?!.*({regex_filter})).*$")
coef std err Conf. Int. Low Conf. Int. Upp. log2FC FC F-statistics correction Method
identifier
P17174 0.362 0.070 0.223 0.501 -0.392 0.762 26.401 FDR correction BH One-way ancova
P01834 -0.537 0.117 -0.769 -0.306 0.610 1.526 20.937 FDR correction BH One-way ancova
P14174 0.475 0.102 0.274 0.676 -0.579 0.669 21.652 FDR correction BH One-way ancova
P08294 -0.223 0.054 -0.330 -0.116 0.285 1.219 16.819 FDR correction BH One-way ancova
P02787 -0.170 0.045 -0.258 -0.082 0.191 1.142 14.451 FDR correction BH One-way ancova
... ... ... ... ... ... ... ... ... ...
F5GY87 0.009 0.103 -0.195 0.213 -0.120 0.920 0.007 FDR correction BH One-way ancova
H3BMA1 0.007 0.094 -0.178 0.192 0.020 1.014 0.006 FDR correction BH One-way ancova
E9PMI0 0.004 0.068 -0.131 0.138 -0.051 0.965 0.003 FDR correction BH One-way ancova
P16870 0.000 0.051 -0.101 0.102 -0.028 0.981 0.000 FDR correction BH One-way ancova
A0A286YFJ8 0.002 0.164 -0.322 0.327 0.074 1.053 0.000 FDR correction BH One-way ancova

100 rows × 9 columns

View Volcano plot of ANCOVA results#

  • p-value (unadjusted) using the -log10 transformation on the y-axis, using -log10 pvalue

  • fold change (FC) in the log2 space on the x-axis (2 means a fold change of 4, 1 a doubeling and -1 means a fold change of 0.5 and -2 of 0.25), using log2FC

  • significant features are colored in red using the reject column, which is True for significant features and False for non-significant features, and is calculated based on the padj column and a significance threshold (default 0.05)

scatter_plot_adv = vuecore.plots.basic.scatter.create_scatter_plot(
    data=ancova.reset_index(),
    x="log2FC",
    y="-log10 pvalue",
    color="rejected",
    title="Simple Volcano Plot",
    subtitle="Visualizing ANCOVA results",
    labels={
        "log2FC": "Log2 Fold Change",
        "-log10 pvalue": "-log10(p-value)",
        "rejected": "FDR corrected Significant",
        "identifier": "Protein Identifier",
    },
    hover_data=["identifier"],
    # currently does not work:
    # color_discrete_map={False: "#2166AC", True: "#B2182B"},  # Blue  # Red
    color_discrete_sequence=["red", "blue"],
    opacity=1,
    marker_line_width=1,
    marker_line_color="darkgray",
    width=800,
    height=600,
)
scatter_plot_adv