Is There Any Theoretical Justification for Randomized Contrial Trials in Cancer Research?

No.

There is no theoretical justification for using randomized control trials to test the effectiveness of treatments for cancer in humans.

Donald Rubin

To be clear, the question is not whether it is good to have careful studies or to do replicable analysis.  Those things are good.  The question here is whether randomizing treatment assignment provides any information over and above some other treatment assignment mechanisms.  To be even more clear, the question is not whether randomized control trials are justified in general.  The question is whether they are justified in measuring survival in cancer research.

When justifying the use of randomized control trials statisticians generally point to Harvard's Donald Rubin and his seminal paper "Estimating Causal Effects of Treatments from Randomized and Nonrandomized Studies."  In the paper, Rubin states that "...given the choice between a randomized study and an equivalent nonrandomized study, one should choose the data from the experiment..."

Why?

Rubin says that we should be interested in the causal effect of some treatment.  If we were interested in the causal effect on survival of a new drug, Rubin would define that to be the difference between a patient's survival on the new drug and a patient's survival on the alternative treatment (perhaps the standard of care).  I have no problem with that definition.

But Rubin notes that this difference, the causal effect, cannot be observed.

Houston we have a problem.

So what to do.

This is where the rabbit goes into the hat.  Watch carefully.

Rubin states that instead of the causal effect (which is not observed) we should instead be interested in the "typical" causal effect.  OK.  I'm with you.  Typical sounds reasonable. 

Rubin then states that an "obvious" definition of "typical" is the average difference.  Perhaps.  Rubin then points out that due to the linearity of averages, the average difference is equal to the difference in the average outcome for each treatment.  Further, due to the unconfounded nature of ideal randomized control trials, the average outcome of each treatment arm is an unbiased estimate of the average outcome of each treatment.  

Bob's your uncle.

If we are willing to concede that the average causal effect is the appropriate measure, then that information is provided by an ideal randomized control trial.

Why is cancer different from every other night?

I'm glad you asked, youngest imaginary blog reader.

Cancer is different from every other night because in cancer, people die.  Actually, the statistical problem is caused by them not dying.  Because people don't die we have a censoring problem and we are unable to measure the average survival from each trial arm.  No average, therefore no difference in averages, therefore no average difference, therefore no typical difference, and therefore no dice.