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This story caught my eye for a different reason from the scientific fraud narrative.

What do we mean when we say that drug A is better than drug B ? Using "drug A" and "drug B" as names clashes with English grammar. In the interests of euphony, I've used a name generator and will call them Aproxin and Benzolax. Here are three different things that we might mean when we say that Aproxin is better than Benzolax because Aproxin works for 40% of patients, but Benzolax only works for 30%.

First meaning: Independent. Some lucky folk respond well to both 0.4 x 0.3 = 12%. Some patients (0.4 x 0.7 = 28%) only respond to Aproxin. Others (0.6 x 0.3 = 18%) only respond to Benzolax. Many (0.6 x 0.7 = 42%) benefit from neither.

Second meaning: Dominant. Hope that you are one of the 40% who respond to Aproxin. That forty percent splits into three quarters who also respond to Benzolax, and one quarter who don't respond to Benzolax. Notice the cunning with which I have contrived the numbers in my made up example. That is all of the 30% who respond to Benzolax accounted for. No-one responds to Benzolax and not to Aproxin. 60% of patients are out of luck. Obviously you try Aproxin first. If it doesn't help, give up. Benzolax has found itself in a context in which it is entirely useless.

Third meaning: Sequential. Weirdly, no-one responds to both drugs. You try Aproxin first. If it doesn't work, you move on to Benzolax. Notice how this messes with the numbers. If 40% respond to Aproxin, that leaves 60% moving on to Benzolax. Half of those who try Benzolax (under this treatment protocol) benefit. That is 50%, up from the 30% who benefited in the old days before Aproxin was discovered.

Notice how the discovery of Aproxin affects the sales of Benzolax. In the Dominant case, Benzolax becomes obsolete. In the Sequential case, a superficial reading/misunderstanding of the numbers makes it look as though the discovery of Aproxin makes Benzolax work better.

So how do you compare drugs? I've noticed that trials generally do a naive random assignment. You get numbers for the effectiveness of each drug as though the other drugs didn't exist. But how do the medicines relate? Independent? Dominant? Sequential? Not one of the extreme cases? The trials don't say. But it does matter for treatment.

At the heart of the article is STAR*D, Sequenced Treatment Alternatives to Relieve Depression https://ajp.psychiatryonline.org/doi/epdf/10.1176/ajp.2006.163.11.1905 Some-one has actually gone ahead and tried to measure what happens when you try drugs in sequence. They cheat which is the usual money grubbing of modern science. On the other hand, that are looking at the medically important comparison, which is progress.