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I'm trying to compare the effect of two treatments on the time to fracture healing, and came across a study that does the following:

They compared effect of treatment A vs treatment B on fracture healing by reporting the mean time until fracture healing post-surgery. However the follow up times were uneven (1.5 months, 3 months, 6 months, 1 year), same follow up times for both treatment groups.

Is it valid or meaningful to calculate a mean time to event if the observation points are not evenly spaced?

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  • $\begingroup$ Suppose there was a an additional time of 50 years. However most ppl have the healing event after a year or two. This massive jump will skew your results. You should look into interval censoring, which will gracefully solve your original problem. $\endgroup$
    – Cam.Davidson.Pilon
    Oct 28, 2019 at 23:26

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Apologies in advance: my answer relies on more of a semantic argument than a mathematical one.

Suppose the patient had to wear a cast until the doctor could certify that they'd healed, which can only be done in the doctor's office in an appointment. In this world, doctor's appointments are restricted to follow that uneven spacing after a surgery. So a cast's duration in months has support $\{1.5, 3, 6, 12\}$. The variable of interest is no longer "time to fracture healing", but rather "time till the patient gets to take off that itchy cast".

In this case, the mean time to event becomes quite meaningful. If I were a doctor, I'd want to be able to tell the patient how long they should expect to have to wear that darn cast.

I think the reason why I find this so much easier to swallow is that it sidesteps the question of "what if the fracture actually healed sometime between observation points?" which sort of captures why I was initially hesitant.

Anyway, that's why I think it's appropriate. I hope this makes sense!

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