simpsons_paradox.png

# ===========================================================================
# MODULE 15 · Causal Inference (Simpson's Paradox)
# ===========================================================================
print("[15] Kausale Inferenz (Simpson's Paradox) ...")

np.random.seed(42)
n_patients = 100

# Mild group: low dose, high health score
dose_mild = np.random.normal(3.0, 0.8, n_patients)
health_mild = 65 + 4 * dose_mild + np.random.normal(0, 4.0, n_patients)

# Severe group: high dose, low health score
dose_severe = np.random.normal(8.0, 0.8, n_patients)
health_severe = 20 + 4 * dose_severe + np.random.normal(0, 4.0, n_patients)

# Combined data
all_dose = np.concatenate([dose_mild, dose_severe])
all_health = np.concatenate([health_mild, health_severe])

fig, ax = plt.subplots(figsize=(8, 4.8))

# Scatter plots
ax.scatter(dose_mild, health_mild, color=PRIMARY, alpha=0.6, label="Mild erkrankt (Leichte Fälle)")
ax.scatter(dose_severe, health_severe, color=EVENT, alpha=0.6, label="Schwer erkrankt (Kritische Fälle)")

# Regressions for subgroups (True causal positive effect)
slope_m, intercept_m = np.polyfit(dose_mild, health_mild, 1)
ax.plot(np.linspace(1, 5, 50), slope_m * np.linspace(1, 5, 50) + intercept_m, color=PRIMARY, linewidth=2)

slope_s, intercept_s = np.polyfit(dose_severe, health_severe, 1)
ax.plot(np.linspace(6, 10, 50), slope_s * np.linspace(6, 10, 50) + intercept_s, color=EVENT, linewidth=2)

# Overall regression (Confounded negative slope)
slope_all, intercept_all = np.polyfit(all_dose, all_health, 1)
ax.plot(np.linspace(1, 10, 100), slope_all * np.linspace(1, 10, 100) + intercept_all, color=SECONDARY, linestyle="--", linewidth=2.5, label="Crude Assoziation (Gesamtgruppe)")

ax.text(2.0, 46, "Lokaler Effekt:\nPositive Assoziation (+)", color=PRIMARY, fontsize=9.5, fontweight="semibold")
ax.text(6.8, 62, "Crude Assoziation:\nNegative Assoziation (-)", color=SECONDARY, fontsize=9.5, fontweight="semibold")

ax.set_xlabel("Therapie-Dosis (Dose)")
ax.set_ylabel("Gesundheits-Score (Health Score)")
ax.set_title("Simpson-Paradoxon: Confounding in der Praxis\n(Subgruppen vs. Gesamtassoziation)")
ax.legend(loc="upper right")
ax.grid(True, linestyle=":", alpha=0.6)

(ASSETS / "15-kausale-inferenz" / "assets").mkdir(parents=True, exist_ok=True)
save(fig, ASSETS / "15-kausale-inferenz" / "assets" / "simpsons_paradox.png")