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When a treatment is very powerful or very weak, statistics are not necessary. Before penicillin, most people with pneumonia died; after it, most lived. Statistics are redundant here.
It is in the moderate range of strength of effect, where the majority of good medical ideas lie, that statistics are most needed. The usual progression starts with an effect described in a few cases. It intrigues others enough to repeat the study, perhaps in a larger sample. If the effect is robust and useful, it gets tested many times, from many directions. If it withstands such testing and is important, it is tested in a giant sample of thousands of patients. Then it becomes a minimum standard of care, applied to the entire population of such patients. Examples of such giant studies include the treatment of mild and moderate hypertension, the association of smoking with lung cancer, and cholesterol level and
Behar D. FastPro: Software for MetaAnalysis by the Confidence Profile Method. JAMA. 1992;268(15):2109. doi:10.1001/jama.1992.03490150163049