Is this a competing risks scenario, or just multiple events? Background
I have some car and motorcycle insurance claims data, and I'd like to do a time-to-event analysis on it. Specifically, I'd like to use a semi-parametric method such as a Cox model to regress an outcome Y on a binary X variable and account for another 3 covariates C. X is another binary 1/0 variable, while the 3 covariates C are a mix of factor and continuous numeric variables.
While structured as a 1/0 binary variable, my outcome actually maps to three different events of interest. In other words, a policyholder (identified by a unique claim_id) will be marked Y=1 in my dataset if they have any of 3 different events (say for the sake of argument that these are a cracked axle, a smashed rear windshield, or a blown head gasket).
Further, policyholders can have multiple events in this data. Some people won't have any, obviously, but others will have both a cracked axle and a blown head gasket at different time. This leads to within-subject correlation, which'll need to be accounted for.
The Problem
I'm wondering if I have a "competing risks" situation on my hands but I can't quite tell.
Now, I've seen the notion of competing risks explained using this analogy: if one's study outcome is death, but study subjects can get the outcome from, say, poisoning or heart attack or falling off a cliff, then you have competing risks and need to deal with them. In my study, though, I don't have an exactly analogous situation: it's not that you can get to the same event in n different ways; it's that there are n different events grouped into one big y=1 or y=0.
Elsewhere, I've seen competing risks described like so:
Competing risks are said to be present when a patient is at risk of more than one mutually exclusive event, such as death from different causes, and the occurrence of one of these will prevent any other event from ever happening. (Gichangi & Vach, 2005)
This doesn't quite apply either, as my events aren't mutually exclusive, and having e.g. a blown head gasket wouldn't prevent a policyholder from having a smashed rear windshield.
Progress so far
I'm still getting my data ready for analysis, but my plan so far has been to use an extended version of the Cox Proportional Hazards model that accounts for shared frailty. This latter bit will (I hope) deal with the multiple events I mentioned above.
But I'm still unsure about competing risks. I'm leaning toward "no", but I want to be more certain.  Any thoughts?

No. The key aspect of competing risks is that one event stops you seeing the others. You just have multiple event types.
