Hypothesis Testing in Healthcare: Drug Safety
A pharmaceutical company GlobalXYZ has just completed a randomized controlled drug trial. To promote transparency and reproducibility of the drug's outcome, they (GlobalXYZ) have presented the dataset to your organization, a non-profit that focuses primarily on drug safety.
The dataset provided contained five adverse effects, demographic data, vital signs, etc. Your organization is primarily interested in the drug's adverse reactions. It wants to know if the adverse reactions, if any, are of significant proportions. It has asked you to explore and answer some questions from the data.
drug_safety.csv was obtained from Hbiostat courtesy of the Vanderbilt University Department of Biostatistics. It contained five adverse effects: headache, abdominal pain, dyspepsia, upper respiratory infection, chronic obstructive airway disease (COAD), demographic data, vital signs, lab measures, etc. The ratio of drug observations to placebo observations is 2 to 1.
For this project, the dataset has been modified to reflect the presence and absence of adverse effects
adverse_effects and the number of adverse effects in a single individual
The columns in the modified dataset are:
|The gender of the individual|
|The age of the individual|
|The week of the drug testing|
|The treatment (Drug) and control (Placebo) groups|
|The count of white blood cells|
|The count of red blood cells|
|The presence of at least a single adverse effect|
|The number of adverse effects experienced by a single individual|
The original dataset can be found here
# Import packages import numpy as np import pandas as pd from scipy.stats import norm from statsmodels.stats.proportion import proportions_ztest import pingouin import seaborn as sns import matplotlib.pyplot as plt # Load the dataset drug_safety = pd.read_csv("drug_safety.csv") # The distribution of adverse effects plot_num_eff = sns.countplot(data = drug_safety, x = 'num_effects', hue = 'trx') plt.xlabel('Number of Adverse Effects') plt.title("Distribution of the Number of Effects Between the Groups") plt.show() # Two samples proportions z test adverse_effects_by_trx = drug_safety.groupby('trx').adverse_effects.value_counts() adverse_effects_by_trx_total = adverse_effects_by_trx.groupby('trx').sum() two_samp_z_stat, two_samp_z_p_value = proportions_ztest(count = [adverse_effects_by_trx['Drug']['Yes'], adverse_effects_by_trx['Placebo']['Yes']], nobs = [adverse_effects_by_trx_total['Drug'], adverse_effects_by_trx_total['Placebo']]) two_samp_z_stat = round(two_samp_z_stat, 3) two_samp_z_p_value = round(two_samp_z_p_value, 3) # Association between adverse effects and the groups expected, observed, stats = pingouin.chi2_independence(data = drug_safety, x = 'num_effects', y = 'trx') pearson_num_effect_trx = stats[stats['test'] == 'pearson'].round(3) # Distribution of age in the Drug and Placebo groups sns.histplot(data = drug_safety[drug_safety['trx'] == "Drug"], x = 'age', bins = 30) plt.xlabel("Age (years)") plt.ylabel('Frequency') plt.title('Distribution of age in the Drug group') plt.show() sns.histplot(data = drug_safety[drug_safety['trx'] == "Placebo"], x = 'age', bins = 30) plt.xlabel("Age (years)") plt.ylabel('Frequency') plt.title('Distribution of age in the Placebo group') plt.show() # Significant difference between the ages of both groups age_drug = drug_safety.loc[drug_safety['trx'] == 'Drug', 'age'] age_placebo = drug_safety.loc[drug_safety['trx'] == 'Placebo', 'age'] #Performing a two-sided independent-samples t-test ttest = pingouin.ttest(age_drug, age_placebo) # Performing a Mann-Whitney U test two_samp_ind_results = pingouin.mwu(age_drug, age_placebo).round(3) print(pearson_num_effect_trx) print(ttest) print(two_samp_ind_results)