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I have a longitudinal data including 4 follow-ups and the individuals are old. My event of interest is if happening of ability fall and I am also looking for competing risk of death. But the problem is that when I check there is no competing risk of death which is kind of strange. Individuals may have missing values. I am considering Age as time in my analysis therefore; I check if "age at death" is after "age at inclusion" and before or equal to "age at exclusion". Or if "age at death" is same as "age at exclusion". And, of course inclusion and exclusions are specific for each person. Something might be wrong, or any other advice? thanks.

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A competing risk analysis, with death as the competing risk, tries to answer the question "What is a risk of a fall that precedes death?". It is the clause "that precedes death" that makes the quantity being estimated very hard to interpret. In most cases it is better to conceptualize the problem as a state transitions, some of the transitions being from a "no fall" state to "fall" or from "fall" to "death". You can treat fall an death as ordered categories and use an ordinal longitudinal state transition model, e.g., Markov proportional odds model.

Once you get estimates from a Markov model you can get transition probabilities as well as state occupancy probabilities such as $\Pr($death or fall at 2 years). What makes interpretation clear is that these are unconditional probabilities with respect to mortality. More information may be found at https://www.fharrell.com/talk/cmstat/ and https://hbiostat.org/proj/covid19.

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