But you already have a control which is a statistic called "survival rate after x years". If you beat it with a large enough treatment group, then you can prove it works.
If you don't control who gets the treatment, who gets a placebo, and who gets the current state of the art treatment, you cannot really exclude your results are biased. There are some ideas about how to reason with observational data but your conclusion are still weaker as with experimental data.
If you don't control who gets the treatment, who gets a placebo, and who gets the current state of the art treatment, you cannot really exclude your results are biased. There are some ideas about how to reason with observational data but your conclusion are still weaker as with experimental data.