BMI prediction using the COMBO dataset

We first consider the COMBO data set and show how to predict Body Mass Index (BMI) from microbial genus abundances and two non-compositional covariates using “filtered_data”.

Import the package

import sys, os
from os.path import join, dirname, abspath

classo_dir = dirname(dirname(abspath("__file__")))
sys.path.append(classo_dir)
from classo import classo_problem, clr
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

Define how to read csv

def csv_to_np(file, begin=1, header=None):
    """Function to read a csv file and to create an ndarray with this

    Args:
        file (str): Name of csv file
        begin (int, optional): First colomn where it should read the matrix
        header (None or int, optional): Same parameter as in the function :func:`pandas.read_csv`

    Returns:
        ndarray : matrix of the csv file
    """
    tab1 = pd.read_csv(file, header=header)
    return np.array(tab1)[:, begin:]

Load microbiome and covariate data X

data_dir = join(classo_dir, "examples/COMBO_data")
X0 = csv_to_np(join(data_dir, "complete_data/GeneraCounts.csv"), begin=0).astype(float)
X_C = csv_to_np(join(data_dir, "CaloriData.csv"), begin=0).astype(float)
X_F = csv_to_np(join(data_dir, "FatData.csv"), begin=0).astype(float)

Load BMI measurements y

y = csv_to_np(join(data_dir, "BMI.csv"), begin=0).astype(float)[:, 0]
labels = csv_to_np(join(data_dir, "complete_data/GeneraPhylo.csv")).astype(str)[:, -1]

Normalize/transform data

y = y - np.mean(y)  # BMI data (n = 96)
X_C = X_C - np.mean(X_C, axis=0)  # Covariate data (Calorie)
X_F = X_F - np.mean(X_F, axis=0)  # Covariate data (Fat)
X0 = clr(X0, 1 / 2).T

Set up design matrix and zero-sum constraints for 45 genera

X = np.concatenate(
    (X0, X_C, X_F), axis=1
)  # Joint microbiome and covariate data and offset
label = np.concatenate([labels, np.array(["Calorie", "Fat"])])
C = np.ones((1, len(X[0])))
C[0, -1], C[0, -2] = 0.0, 0.0

Set up c-lassso problem

problem = classo_problem(X, y, C, label=label)
problem.formulation.intercept = True

Use stability selection with theoretical lambda [Combettes & Müller, 2020b]

problem.model_selection.StabSelparameters.method = "lam"
problem.model_selection.StabSelparameters.threshold_label = 0.5

Use formulation R3

problem.formulation.concomitant = True

problem.solve()
print(problem)
print(problem.solution)

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• 

Out:

FORMULATION: R3

MODEL SELECTION COMPUTED:
     Stability selection

STABILITY SELECTION PARAMETERS:
     numerical_method : Path-Alg
     method : lam
     B = 50
     q = 10
     percent_nS = 0.5
     threshold = 0.7
     lam = theoretical
     theoretical_lam = 0.2818


 STABILITY SELECTION :
   Selected variables :  intercept     Clostridium     Acidaminococcus
   Running time :  0.434s

Use formulation R4

problem.data.label = label
problem.formulation.huber = True
problem.formulation.concomitant = True

problem.solve()
print(problem)
print(problem.solution)

• 
• 

Out:

FORMULATION: R4

MODEL SELECTION COMPUTED:
     Stability selection

STABILITY SELECTION PARAMETERS:
     numerical_method : Path-Alg
     method : lam
     B = 50
     q = 10
     percent_nS = 0.5
     threshold = 0.7
     lam = theoretical
     theoretical_lam = 0.2818


 STABILITY SELECTION :
   Selected variables :  intercept     Clostridium     Acidaminococcus
   Running time :  0.658s

Use formulation R1 with ALO

ALO is implemented only for R1 without intercept for now.

problem.data.label = label
problem.formulation.intercept = False
problem.formulation.huber = False
problem.formulation.concomitant = False
problem.model_selection.ALO = True

problem.solve()
print(problem)
print(problem.solution)

• 
• 
• 
• 
• 

Out:

FORMULATION: R1

MODEL SELECTION COMPUTED:
     ALO
     Stability selection

ALO PARAMETERS:
     numerical_method : Path-Alg
     lamin = 0.001
     Nlam = 80


STABILITY SELECTION PARAMETERS:
     numerical_method : Path-Alg
     method : lam
     B = 50
     q = 10
     percent_nS = 0.5
     threshold = 0.7
     lam = theoretical
     theoretical_lam = 0.2818


 ALO COMPUTATION :
   Selected variables :   Alistipes     Clostridium     Acidaminococcus     Coprobacillus
   Running time :  0.157s

 STABILITY SELECTION :
   Selected variables :   Clostridium     Acidaminococcus
   Running time :  0.307s