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The question is whether prenatal diagnosis of a congenital condition shortens the time to surgical intervention. The condition is one that is obvious at birth, but not necessarily in utero, and once diagnosed requires transfer to one of a handful of institutions that are capable of surgically intervening.

All data is retrospective.

The time interval starts with birth and ends with the initial surgical intervention. The categorical variable will be prenatal diagnosis status.

There are a handful of individuals for which we do not know the date of initial surgical intervention due to incomplete records (We do know that the event was reached, however).

I am having trouble deciding whether this situation is an appropriate application of survival analysis.

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This phenomenon doesn't sound obviously suited for survival analysis methods, in my opinion. If you were looking how long a child lives after birth with this condition, then it would be one thing. In your case the date of surgery seems to be defined by preparedness of the hospital, or something like that, because once a child is born you know it needs a surgery (given it has this condition).

You seem to imply that if you have a good prenatal diagnosis, this may tell the hospital to prepare for a surgery before birth, and hence shorten the time to surgery.

In this case I'd start with the simplest ANOVA. Get two samples: one with pre-natal diag, and the other without it. Look at average surgery times.

You have an issue with missing data. Try to identify whether the data is missing at random. You can start with ignoring if it's missing at random. Look at the prelim results, this may give you more ideas.

Next, think of how to deal with missing data.

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Survival analysis is badly named since it can be used to analyze data with any variable that is elapsed time to some one-time event. The event does not need to be death. Analyzing time until surgery is fine with survival analysis. The tricky parts will be figuring out how to deal with unknown dates of surgery and with kids (if any) who die before getting surgery.

Survival analysis is also called failure analysis. But again this name is misleading, as sometimes (as in this example) the event is a good thing (life saving surgery) not a "failure".

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Your stated question reduces to: does an earlier diagnosis of an in utero condition lead to earlier treatment? In this setting, you could analyze the freedom from or provision of surgery as the outcome of interest using time to event methods. However, it would seem highly likely that diagnosis would result in transfer or therapy. If the interval between birth and transfer or therapy is short and you have few subjects lost to followup, survival methods may not differ much from logistic methods.

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