Is there a survival analysis methodology that can model the time till event (death by x), given another event that can (assumption) trigger death on the days nearby it? I am thinking of a pregnancy, where the triggering event is giving birth, and the event of interest is death by prolapse, for instance. The prolapse can both occur before and after giving birth, being (assumptions) directly influenced by the triggering event and with increasing probability as one aproaches it from both sides.
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1$\begingroup$ In this situation, one might consider the triggering event to be conception rather than birth. Otherwise one gets into causality problems: if event A happens after event B, it’s hard to argue that A causes B. $\endgroup$– EdMCommented Apr 15, 2021 at 14:09
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$\begingroup$ @EdM That was my initial approach. But I have data of the sort I exemplified in the question, and cases begin to appear just after and increasing towards conception time. It seems rather obvious to me that it has some influence, and I find it interesting to try to tune my model to account for it, even If it is hard to assign causality. If there is a causality assumption in a survival analysis model that makes it unsuitable for this, any other suggested approach is welcomed. $\endgroup$– darubikCommented Apr 16, 2021 at 7:35
1 Answer
It isn't that birth several days later is "triggering" prolapse at an earlier time. It's that pregnancy (along with other biological factors) increases the probability both of prolapse and (obviously) of giving birth. That's confounding in its strict sense.* You don't want to set up a model in which giving birth per se is assumed to be the "cause" of prolapse and prolapse-associated death, when they are both due to something else (pregnancy) and both pregnancy and giving birth can lead to death from causes other than prolapse.
One way to approach this might be as a multi-state competing-risks model, in which you evaluate all states--prolapse
and gaveBirth
both separately and as a combined state (or 2 states, if you think that the order matters), pregnancy
(before prolapse
or gaveBirth
, as the starting state), and death--as a function of time from conception (or maybe from some later time to avoid pregnancies with early-term fetal losses). You model all the possible transitions among the states. If you are interested specifically in death due to prolapse, you might be primarily interested in the prolapse
→ death
and (prolapse + gaveBirth)
→ death
transitions, paying less attention to the gaveBirth
→ death
and pregnancy
→ death
transitions not involving prolapse. A vignette for the R survival
package outlines how to proceed with multi-state models.
*Hernán and Robins devote Chapter 7 and much of the rest of their Causal Inference book to problems arising from confounding.
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$\begingroup$ Exactly what I was looking for, thanks! $\endgroup$– darubikCommented Apr 18, 2021 at 17:18