Correlation vs Causation

Strong correlation (r ≈ 0.99):
  Ice cream sales and drowning rates (by month)
  
  Does ice cream cause drowning? No.
  Confounding variable: summer (warm weather → more swimming + more ice cream)
  
  Removing the confounder (season) eliminates the correlation.

1. Common cause (confounding):
   A → X and A → Y, so X correlates with Y
   Example: poverty → poor diet AND poor health → diet correlates with health
   (diet doesn't necessarily cause health outcomes directly; poverty drives both)

2. Reverse causation:
   Y causes X, not X causes Y
   Example: hospitalised patients have more medication use
   Correlation: medication ~ hospitalisation
   Reality: being sick causes both hospitalisation and medication, not vice versa

3. Coincidence (spurious correlation):
   No causal mechanism at all — just happened to correlate in this dataset
   Example: number of Nicolas Cage films per year correlates with pool drownings
   Reduces with more data / external validation

4. Selection bias:
   The way data was collected creates a correlation
   Example: Berkson's paradox — in hospitalised patients, two diseases may
   appear negatively correlated even if independent in the population

Correlation: patients on more medications have worse outcomes
  Naive interpretation: medications cause worse outcomes → prescribe less
  Reality: sicker patients receive more medications → confounding by illness severity
  Fix: control for comorbidity score (e.g., Charlson index)

Correlation: hospitals with more ICU beds have higher mortality rates
  Naive interpretation: ICU beds cause death
  Reality: sicker patients are referred to hospitals with more ICU capacity
  Fix: risk-adjust for case mix before comparing hospitals

Correlation: model trained on EHR data → high body mass index predicts cancer
  Naive interpretation: BMI causes cancer
  Reality: overweight patients may receive more cancer screening → detection bias
  BMI correlates with cancer diagnoses, not necessarily cancer incidence

Randomised Controlled Trial (RCT): gold standard
  Randomly assign subjects to treatment vs control
  Randomisation breaks all confounding

  Limitation: often impractical, expensive, or unethical in medicine

Instrumental Variables:
  Find a variable that affects X but has no direct effect on Y
  Use it to isolate causal variation in X
  Example: distance to hospital as instrument for treatment (affects treatment access
  but doesn't directly affect health outcome)

Difference-in-Differences:
  Compare before/after in treated group vs control group over same period
  Removes time-constant confounders

Propensity Score Matching:
  In observational data, match treated and untreated patients on confounders
  Then compare within matched pairs

# ML models learn correlations, not causation
# This has practical consequences:

# Example: A model predicts hospital readmission
# Feature: number_of_medications (highly correlated with readmission)
# 
# If a hospital reduces medications to lower predicted readmission:
#   → Model accuracy may drop (distribution shift)
#   → Patient outcomes may worsen (medications were there for a reason)
#   → The intervention acted on a correlated feature, not a causal mechanism

# Causal ML approaches:
# 1. Include domain knowledge: don't use features that are caused by the outcome
# 2. Structural causal models: explicit DAG of causal relationships
# 3. Counterfactual reasoning: "what would have happened if we hadn't intervened?"

# Detecting confounding in feature importance:
# If a feature is important in training but not in a different hospital's data:
#   → May be a confounder specific to that hospital's patient population

def check_feature_stability(
    model,
    X_site1: "pd.DataFrame",
    X_site2: "pd.DataFrame",
    feature_names: list[str],
) -> dict:
    """Compare feature importances across sites — instability suggests confounding."""
    import numpy as np
    imp1 = model.feature_importances_  # for tree models
    
    # Retrain on site2 (or use SHAP values at each site)
    return {
        "features": feature_names,
        "site1_importance": imp1.tolist(),
        "note": "High importance in site1 but not site2 = possible confounder",
    }

The standard way to establish causal effect of an ML system change:

  A/B test = randomised experiment in software
  Randomly assign users to control (A) or treatment (B)
  Measure outcome difference
  
  "The new RAG system increased user satisfaction by 12%"
  → This IS a causal claim (randomised assignment breaks confounding)

  "Users who clicked on recommendation X had higher engagement"
  → This is correlation (users who click on X may differ from those who don't)
  → Cannot claim X caused engagement without A/B test

Always design experiments for causal inference when making product decisions.
Always treat ML model outputs as correlational unless validated with an experiment.