Researchers Find Study of Medical Marijuana Discouraged

New York Times article "Researchers Find Study of Medical Marijuana Discouraged" (January 18th, 2010) propagates a mistake in analyzing the impact of any drug on a population. In this case, the Times fails to report on possible treatment-response heterogeneity.

But there is no good evidence that legalizing the smoking of marijuana is needed to provide these effects. The Food and Drug Administration in 1985 approved Marinol, a prescription pill of marijuana’s active ingredient, T.H.C. Although a few small-scale studies done decades ago suggest that smoked marijuana may prove effective when Marinol does not, no conclusive research has confirmed this finding.

And Marinol is no panacea. There are at least three medicines that in most patients provide better relief from nausea and vomiting than Marinol, studies show.

Not all individuals are the same. Individuals have different reactions to different drugs. A drug may have phenomenal effects on twenty percent of the population it works on, while being no different than placebo for the other eighty percent.

Let's imagine a world in which each of the three medicines mentioned in the quote the Times exist, and marijuana is also a potential drug. Let us further imagine that there are four types of responders. Responders who respond to all three drugs but not marijuana, responders who respond only to Drug I and Drug III, responders who only respond to Drug I and Drug II, and responders who only respond to marijuana. This setup is displayed graphically below (click to enlarge), where a "1" denotes effective treatment, and a "0" denotes ineffective treatment.

From this we can see that, if we had a random sampling of all four people types in our drug testing  and assuming each is of equal size (unnecessary for the point, but convenient), then we should see that Drug I is "more effective for most of the population" than Drug II and Drug III, which are in turn "more effective for most of the population" than marijuana.

However, any discerning eye would see that keeping only the three "most effective" drugs offers no alternative for Person Type IV.  The Drug/Person-Type matrix is not of full rank--some individuals are left with nothing.  One might even notice that Drugs II and III are not even necessary, they are redundant, while marijuana is not.

In the above scenario, with treatment-response heterogeneity in the population, relative average effectiveness of a drug is not nearly as important as the population-specific average, and the existence of alternatives within population.