Re: Simulation Process and Independent Vs Paired Samples

Paul Rubin wrote:
duncan smith wrote:


I'm in the process of writing simulation software that can generate paired values (patient histories). Basically, at some point in a patient's lifecourse, choices can be made regarding treatment. So a simulated patient can fork into separate simulations when such a point is reached (and fork again if more than one treatment is involved). The histories are identical up to the point different treatments can be applied.

One suggestion that was made to me was to use the same random numbers for each 'post-fork' simulation. I quickly dismissed that as it does introduce correlations that depend on the detailed implementation of the random variate generators.

Yes, that's the point; you want the correlations. With a bit of luck, the clones of the original patient entity produce outputs that are positively correlated, which allows you to do the ultimate comparisons with more power for a given sample size or smaller sample size for a given power. I don't see why you "quickly dismissed" this.


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 will note that the use of common random number streams does not guarantee that positive pairwise correlation, but sometimes it helps.

But it doesn't (to me) seem unreasonable for the pre-fork histories to be identical.

The simulation model basically models transitions between states, until eventually a patient dies. If a treatment is assumed to solely prolong the expected length of time spent in state X until transition to state Y, then there is an argument that the with / without treatment records should only differ in the length of time spent in state X. It has also been argued (not by me) that the same uniform random variate should be used to generate the length of time in state X (when using the inversion method of random variate generation). I can easily dismiss the latter as being unreasonable,

Why? Might not the random times to transition incorporate some factors that would be intrinsic to a patient (genetics, cardiovascular conditioning, ...) such that a patient who is, say, tougher than average would last longer with or without treatment than another patient who is weaker than average? The use of common random numbers is intended to "level the playing field" across decision alternatives.


Yes. Some of these factors are conditioned on, but after conditioning and adjusting the hazard for the treatment arm I generate independent random variates. The times might still be conditionally dependent, but there's no way of testing this, and I don't want to generate simulation results that seem to show that a treatment is effective for every patient that receives it. That's how the users would be likely to interpret it. I might introduce some additional dependence at some stage, but not "too much".

Duncan

although there is an implicit assumption (untestable in the real world) however I choose to generate the two times to transition. There are practical reasons why trying to pair records after a fork is difficult, because in most cases there are competing risks, and the effect of a treatment might be that a patient moves from state X to state Z, rather than state Y.

The point of pairing the records is simply to reduce the computational time necessary to give a given degree of confidence in model predictions; typically changes in life expectancy.

Correct.

Judicious pairing seems reasonable to me, if the question relates to the predicted effects on a particular cohort of patients (and not otherwise).

I'm not sure how relevant this is to the OP, but increasing the number of simulated cases will generally give as much power as you want.

Assuming you're patient (no pun intended).

/Paul
.

Relevant Pages

  • Re: Simulation Process and Independent Vs Paired Samples
    ... 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. ... 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. ... 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. ...
    (sci.stat.math)
  • Re: Simulation Process and Independent Vs Paired Samples
    ... sample t-test should be applied to the two samples differences (null ... If the simulation generates pairs of observations, and if the paired observations are correlated to each other, then the paired-difference t-test should be more accurate. ... Basically, at some point in a patient's lifecourse, choices can be made regarding treatment. ... So a simulated patient can fork into separate simulations when such a point is reached. ...
    (sci.stat.math)
  • Re: Simulation Process and Independent Vs Paired Samples
    ... So a simulated patient can fork into separate simulations when such a point is reached (and fork again if more than one treatment is involved). ... One suggestion that was made to me was to use the same random numbers for each 'post-fork' simulation. ...
    (sci.stat.math)
  • INSANE CURES: Still Crazy After All these Years
    ... "IT WAS A BRILLIANT CURE BUT WE'VE LOST THE PATIENT!" ... believed that stones in the head caused madness. ... Rush, a pioneer of early American psychiatry, recommended ... And as the short era of moral treatment introduced by Dr. Philippe ...
    (sci.med.psychobiology)
  • Re: PA needs help passing Lyme legislation
    ... records in terms of documenting diagnosis and treatment plan, ... to respond to patient emergencies, that kind of thing all within the ... > that it is YOUR perception that the hearings had to do with Lyme. ... owners of them early on before medicare prohibited doctor/owners of ...
    (sci.med.diseases.lyme)