Simpson’s Paradox: A Causal Inference Challenge
by Yildiz Culcu
The Medical Treatment Paradox
You're the lead researcher at a major hospital analyzing a new treatment for a chronic condition. Here's the aggregated data from two hospitals over one year:
| Hospital | Treatment Group | Success Rate | Total Patients |
|---|---|---|---|
| Hospital A | New Treatment | 60% | 200 |
| Hospital A | Standard Treatment | 70% | 100 |
| Hospital B | New Treatment | 90% | 100 |
| Hospital B | Standard Treatment | 95% | 200 |
Additional Information:
- • Hospital A typically treats more severe cases
- • Hospital B specializes in early-stage interventions
- • Patient assignment to treatments was not randomized
- • Treatment costs are identical
The Challenge
As the lead researcher, you need to make a recommendation about which treatment should be the standard protocol. Consider these questions:
- When combining all data from both hospitals, you find that the new treatment appears to have a higher overall success rate than the standard treatment. However, in each individual hospital, the standard treatment performs better. Can you explain this apparent contradiction?
- If you had to make a causal claim about treatment effectiveness, what additional information would you need?
- Design an experiment that would help resolve this paradox and provide a clear answer about which treatment is actually more effective.
- How would you explain this situation to hospital administrators who need to make a policy decision?
Before looking at the solution, try to:
- Calculate the overall success rates for both treatments
- Identify potential confounding variables
- Draw a causal diagram
- Consider how selection bias might affect the results
