## 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.

The dataset `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 `num_effects`

.

The columns in the modified dataset are:

Column | Description |
---|---|

`sex` | The gender of the individual |

`age` | The age of the individual |

`week` | The week of the drug testing |

`trx` | The treatment (Drug) and control (Placebo) groups |

`wbc` | The count of white blood cells |

`rbc` | The count of red blood cells |

`adverse_effects` | The presence of at least a single adverse effect |

`num_effects` | 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")
display(drug_safety)
```

```
# Create a count plot to show the number of adverse effects (num_effects) in the Drug and Placebo groups
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()
```

```
# get number of observations in each group
trx_num = drug_safety.groupby('trx')['adverse_effects'].value_counts()
# get number of total observations
trx_total = drug_safety.groupby('trx')['adverse_effects'].count()
# print pivot tables
print(trx_num)
print(trx_total)
# storing ztest required inputs in variables and printing
sux=[trx_num[('Drug', 'Yes')], trx_num[('Placebo', 'Yes')]]
cnts=[trx_total['Drug'], trx_total['Placebo']]
print(sux)
print(cnts)
```

```
# performing proportions ztest
two_samp_z_stat,two_samp_z_p_value = proportions_ztest(count=sux, nobs=cnts, alternative='two-sided')
# rounding result to 3 decimal places
two_samp_z_stat = two_samp_z_stat.round(decimals=3)
two_samp_z_p_value = two_samp_z_p_value.round(decimals=3)
# printing results
print(two_samp_z_stat)
print(two_samp_z_p_value)
```

```
# performing chi-square test of independence
expected, observed, stats = pingouin.chi2_independence(data=drug_safety,x='trx',y='num_effects')
stats = stats.round(3)
print(stats)
# storing p_value of the test
pearson_num_effect_trx = stats[stats['test'] == 'pearson']
print(pearson_num_effect_trx)
```

```
# visualizing distribution of age in the Drug and Placebo groups.
sns.histplot(data=drug_safety, x='age', hue='trx')
plt.show()
```

```
# subsetting ages of drug and placebo receivers
age_drug = drug_safety.loc[drug_safety["trx"] == "Drug", "age"]
age_placebo = drug_safety.loc[drug_safety["trx"] == "Placebo", "age"]
display(age_drug)
display(age_placebo)
```

```
# storing p-value in a variable
two_samp_ind_results = pingouin.mwu(age_drug, age_placebo).round(3)
display(two_ind_samp_results)
```