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I am observing N devices over a period of time $[0,T]$ and counting the number of certain events $y_j$, for each device, during that period of time. I also have some specifications $x_j$ for each device (explanatory variables). I was thinking of conducting Poisson regression on these data. However, I realized that some devices fail before the observation period ends.

Is it still valid to use Poisson regression? Can I include a dummy variable that indicates whether the device failed or not?

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  • $\begingroup$ what do you mean events $Y_j$? is it a fail? If there is a fail then it is impossible that event $Y_j$ will happen I would not include those fails at all. For example you should not include dead people in your survival analysis. $\endgroup$ – Deep North May 4 '17 at 10:19
  • $\begingroup$ @DeepNorth No, $Y_j$ is not a fail. It is basically another non-fatal phenomenon. $\endgroup$ – Possum May 4 '17 at 10:27
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There are two situations here:

  1. You know when each device failed, so you know the total time it was functioning. Then you have, for each device a variable $OT_i$ (observation time $i$) that you use use (after logging) as an offset in the Poisson regression. See Offset in Poisson regression Or, if you know the OT only approximately, that could still be a useful approximation.

  2. You do not know, even approximately, when the device failed. Then the situation is more difficult, and we would need (much) more details and context for advice.

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