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### Type-Specific Hazards

The classification of events into different types is often somewhat arbitrary and may vary according to the specific goals of the analysis. I’ll have more to say about that later. For now, let’s suppose that the events we are interested in are deaths, and we have classified them into five types according to cause: heart disease, cancer, stroke, accident, and a residual category that we’ll call other. Let’s assign the numbers 1 through 5, respectively, to these death types. For each type of death, we are going to define a separate hazard function that we’ll call a type-specific or cause-specific hazard.

As before, let Ti be a random variable denoting the time of death for person i. Now let Ji be a random variable denoting ...

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