When a Hazard Ratio Is Too Good

A study of people with psoriasis found those taking a GLP-1 had 78% lower all-cause mortality than those on other diabetes and obesity drugs.^[1] It is the third such figure we have read this month, and a fourth has since turned up in a study of seizure recurrence. ★ And the confounding this argument rests on has now been measured rather than inferred: people with a mental health diagnosis have roughly a quarter the odds of being prescribed one of these drugs and half again the odds of being put on insulin — a quarter as likely to be offered it. ★ For the constructive counterpart — an observational study reporting effects just as large that does deserve trust, and the specific techniques that earn it — see how to trust an observational study. Nothing in medicine reliably cuts all-cause mortality by three quarters — not statins, not blood pressure treatment, not smoking cessation. When a number looks like that, it is usually telling you about the patients rather than the drug.

The pattern, three times over

Each appeared in a real journal, with matching, adjustment and sensitivity analyses. None is fraudulent. And a drug that genuinely produced any of those effects would be the most important medicine of the century, which is a useful sanity check on its own.

Ask what a true effect of this size would mean. If the answer is “the greatest advance in the history of medicine”, look at the comparison group.

What produces numbers like this

One mechanism explains all three: the people who receive a newer, more expensive, more demanding drug are not like the people who do not.

1. They are well enough to be prescribed it. Clinicians do not start a weight-loss drug in someone acutely unwell, frail, or approaching end of life. Those patients stay in the comparison group and die at the rate very sick people die.
2. They are engaged with care. Getting and staying on one of these drugs requires appointments, prescriptions, prior authorizations and money. That selects for people already doing better on every axis.
3. The comparator is often a marker of severity. Insulin marks advanced diabetes. “Other antiobesity drugs” can mark people who failed or could not tolerate the newer option.

None of that is measurable in a claims database, so no amount of statistical adjustment removes it. Matching equalizes what was recorded, and what predicts death most strongly — frailty, functional status, whether someone is quietly dying — is largely not recorded.

The tell inside this particular study

The psoriasis paper reports something its authors treat as a finding and which reads more naturally as a warning: the risk reductions were markedly higher in people with psoriasis than in cohorts with obesity or diabetes but without it.^[1]

A biological story could be told about that — psoriasis is inflammatory, these drugs reduce inflammatory markers. But there is a duller explanation. In a population with more comorbidity, prescribing is more selective, so the gap between who gets the newer drug and who does not grows wider. A differential that tracks how sick the population is, rather than tracking anything about the disease mechanism, is the signature of confounding rather than of biology.

Which rows to believe in the same study

This is the part that matters, because the answer is not “ignore the paper”. The same study reports figures that are entirely plausible.

• Major adverse cardiac events, HR 0.561. Consistent in size and direction with randomized cardiovascular outcome trials. Believable.
• Alcohol abuse 0.346 and substance abuse 0.510. Larger, but consistent with a randomized trial in alcohol use disorder and with national cohort data on substance use. Worth taking seriously.
• No increase in typical adverse drug events. A null in a large sample, which is the kind of finding observational data handles well.
• All-cause mortality 0.219. Not believable as a drug effect, for the reasons above.

The rule, portable

1. Find the comparison group before the result. Lower than what?
2. Distrust hazard ratios below about 0.5 in non-randomized data. They usually describe who was prescribed the drug.
3. Check whether the effect survives a fair comparator. In the breast cancer study it vanished entirely against a modern one.
4. Weight specific outcomes above all-cause mortality in observational work.
5. Ask what a real effect that size would mean. Usually the answer settles it.

Applied across this month’s reading, that rule keeps the cardiovascular findings, the infection findings and the psychiatric findings — and discards three mortality figures. That is not skepticism about the drugs. It is the difference between evidence and arithmetic about who gets prescribed them.