Final answer:
The study's expected improvement of 2 weeks in survival is not clinically significant considering the average 5-year survival rate and may not justify the costs and ethics of enrolling 20,000 patients. Furthermore, the ethical concern rises from using a placebo in life-threatening conditions where effective treatments are known.
Step-by-step explanation:
The primary problem with the pharmaceutical company's study design is that the expected survival improvement of 2 weeks is not clinically significant, especially when the average survival for the condition is 5 years. With such a small delta of improvement, enrolling 10,000 patients per arm to achieve statistical significance at an alpha error of p < 0.01 may not justify the resources, costs, and ethical considerations. Additionally, the use of a placebo instead of a standard of care in the control group may not be ethically acceptable, especially in cancer studies where a known effective treatment exists.
Phase III trialsshould be designed with both statistical and clinical significance in mind, ensuring that the benefits to patients are substantial and worth the potential risks of new treatments.