Bayesian reanalysis of EMPACT-MI

import pymc3 as pm

import numpy as np

import arviz as az

# Empagliflozin after Acute Myocardial Infarction 24 https://www.nejm.org/doi/full/10.1056/NEJMoa2314051

log_or = np.log(0.9)

log_or_lower = np.log(0.76)

log_or_upper = np.log(1.06)

# The scale for the Cauchy distribution

cauchy_scale = 0.707

# Model setup

with pm.Model() as model:

  # Prior distribution for the log-OR

    log_or_prior = pm.Cauchy("log_OR", alpha=0, beta=cauchy_scale)

    # Likelihood (normal approximation of the distribution of log-OR)

    se_log_or = (log_or_upper - log_or_lower) / 3.92

    likelihood = pm.Normal("likelihood", mu=log_or_prior, sigma=se_log_or, observed=np.array([log_or]))

    # Sample from the posterior distribution

    trace = pm.sample(500000, cores=1, tune=150000, chains=4)

# Convert log-OR samples to HR samples

hr_samples = np.exp(trace["log_OR"])

# Calculate the posterior probability that HR < 1

post_prob_hr_less_than_1 = np.mean(hr_samples < 1)

# Print the posterior probability

print("Posterior probability that HR < 1:", post_prob_hr_less_than_1)

# Calculate the 95% HDI

hdi_95 = az.hdi(trace, hdi_prob=0.95)

# Print the 95% HDI

print("95% HDI:")

print("Lower bound:", hdi_95["log_OR"][0])

print("Upper bound:", hdi_95["log_OR"][1])

# Calculate convergence diagnostics

summary = az.summary(trace, kind='diagnostics')

print(summary)

az.plot_trace(trace)

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