Question about combining hazard ratios - Maybe Simpson's paradox?

I’m reviewing an article, and can’t give details but here is the situation, and it’s got me puzzled

Patients were divided into 4 categories (call them A B C and D), which were exhaustive and exclusive. Adjusted hazard ratios were computed for these four groups for all patients and for two subgroups of patients (call them Lung and Heart). The two subgroups were also exhaustive and exclusive. For the full sample, the hazard ratios for B C and D (compared to A) were 5.08, 4.39, and 1.81. For the lung group, they were 1.15, 1.16 and 1.07. For the heart group they were 2.55, 1.69 and 1.28. That is, they were lower for both subgroups than for the whole population. The lung group and heart group are not the same size; from the info provided, it’s not clear whether A B C and D are equally divided across heart and lung groups.

So …. This seems like Simpson’s paradox. But I’ve not seen that term used for survival analysis. I don’t see why it could NOT be so applied.

My feeling here is to suggest that heart and lung should ONLY be presented separately, but I’m not completely sure.

(Excuse me if I am missing something obvious – dealing with some family health problems and not sleeping that well)

Thanks for any insights or thoughts

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2 Answers

Strictly, Simpson's paradox refers to a reversal in the direction of effect, which hasn't happened here as all the hazard ratios are above 1, so I'd refer to this by the more general term confounding. You can certainly have confounding in survival analysis. I agree it appears sensible to only present the heart and lung results separately.

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Thank you Onestop –  Peter Flom Feb 12 '11 at 12:46

Yes. It is certainly possible that this is due to something like Simpson's paradox. If the data looked like $$\begin{array}{rrrrrr} \textit{Organ}&\textit{Outcome}&A&B&C&D\\ \textrm{Lung}&\textrm{Bad}&371&2727&2374&418\\ \textrm{Lung}&\textrm{Good}&556&3199&2740&558\\ \textrm{Heart}&\textrm{Bad}&214&245&195&273\\ \textrm{Heart}&\textrm{Good}&8859&3828&4691&8752\\ \end{array}$$ then I think you would get something like your hazard ratios (if that means ratios of bad outcomes/totals fractions). Many other patterns of numbers would too.

If you are reviewing the article, it seems reasonable to ask for the underlying numbers to be presented. If they look anything like mine, then it does seem a little strange to add Lung and Heart numbers without a good reason.

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