Re: Simulation Process and Independent Vs Paired Samples

duncan smith wrote:

In the model I'm dealing with there are competing risks. Once a treatment is introduced the patient might embark on a different series of transitions before death. Reducing the risk of transition from state X to state Y might result in a transition to state Z instead. I don't want the time spent in state Y (without treatment) to be correlated with the time spent in state Z (with treatment). (This violates the assumptions of the model.) Even in the case where there's only one possible transition I wouldn't use the same uniform random variate to generate the transition time, because that would imply that every patient would respond positively to the treatment (assuming it is on average effective). That's an assumption I'm not 100% happy with. I prefer the weaker assumption that the hazard is reduced in the same way for each patient, but that the times to transition in the treatment / non-treatment arms of the simulation are independent given the relevant hazard function.

I'll confess that I'm having a bit of trouble parsing this, since I don't have your model to look at. Let's say that Patient X enters the simulation and, at some point, you clone him, so that X continues on to get one treatment and X' gets a different treatment. If there is no medical reason to believe responses to the two treatments would be correlated, then there's no reason to use common random numbers in generating the treatment outcomes.

However, let's say that some characteristics of the patient (age, severity of illness, whether the patient is left-handed) affect both treatment outcomes in similar ways (such as increasing likelihood of transition to the next plane, as it were). If those characteristics are explicit parameters in the hazard function, you can attach them to the patient as attributes and, as each patient (or clone) moves through the model, plug them into the relevant functions. Perhaps not every common causal factor gets picked up as an attribute, though. That's an argument for using common random numbers (with different hazard functions) for patient X and clone X' ... but only when the random numbers are being used to generate outcomes where the common causal factors would indicate common "tendencies" (meaning toward the successful or unsuccessful side of the outcome distribution).

Disclaimer: I'm used to dealing with queueing models. There common random numbers are frequently appropriate. If I'm comparing two possible layouts for a fast food joint, and in simulating the first variant I manage to generate a customer who can't make up his mind and gums up the queue, I want a similar amount of dithering by that customer's clone in the second variant.

/Paul
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