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Suppose I am a company eager to get at the (causal) effect between age and the event of contract termination. However, people can also die instead of actively terminating a contract. This seems like a classic competing events scenario to me. Similar to, e.g., death from cancer vs death from stroke.

As I am no expert on survival analysis, the following may be wrong. To my mind, this scenario looks similar to a mediation case.

Let $A$ be age at baseline, $D_t$ death, and $Y_t$ contract termination.

The DAG would look like this to me: $A_t \rightarrow D_t \rightarrow Y_t$ and $A_t \rightarrow Y_t$. Then you also have $A \rightarrow D_{t+1} \rightarrow Y_{t+1}$ and $A \rightarrow Y_{t+1}$. Note that I think its safe to assume that there is no arrow between $Y_t$ and $D_t+1$.

Is there any way I could get at the age effect in, say, a classic cox model? I would treat death as censored in this case I suppose (i.e time to event Y, treating death as 0). What are the implications of this?

From a first hunch, this may (let's neglect all parametric assumptions here) correspond to some sort of total effect, potentially masking the (natural) direct effect, right? And perhaps this is not too bad in the case of the company versus the cancer and stroke case?

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As the R "Multi-state models and competing risks" vignette says in Section 2.2:

A common mistake with competing risks is to use the Kaplan-Meier separately on each event type while treating other event types as censored.

Thus you would not treat death time as a censoring time if you view death (and associated contract termination) and contract termination for other causes as competing risks. Section 3 of the vignette outlines the procedure for successful joint modeling, with a detailed example of 2 competing risks including age as a covariate modeled separately for each risk.

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  • $\begingroup$ Thanks for the hint! I will try to wrap my head around this from a causal perspective in the next few days. Might add to the question or add a comment. $\endgroup$
    – persephone
    Apr 25, 2022 at 14:43
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    $\begingroup$ @persephone Hernán and Robins discuss causal modeling with competing risks, in particular in Chapter 17. $\endgroup$
    – EdM
    Apr 25, 2022 at 15:04

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