I have three clinics that are testing for Zika virus. We know the proportion of positives aggregated across all clinics, i.e., the first clinic has identified 20% of all positives across the three clinics, the second 30% and the third 50%. Now we know there are 100 new cases but these proportions change with respect to previous cases, i.e., they are now 10% 50% and 40%. Is there a distribution that can tell me if these proportions are significantly different than would be expected given the original proportions? I have run a Monte Carlo simulation to figure this out, but I was wondering if there was a distribution that describes this.
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$\begingroup$ If you know nothing about the volumes, then you can't simulate this with Monte Carlo either. $\endgroup$– AksakalCommented Jun 27, 2016 at 18:05
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$\begingroup$ Thanks for you comment. However, I think if we make an assumption that the relative volumes are constant it is ok. $\endgroup$– jtamCommented Jun 27, 2016 at 20:56
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$\begingroup$ It's not enough. You'd need an assumption of what are these relative volumes. $\endgroup$– AksakalCommented Jun 27, 2016 at 21:10
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$\begingroup$ Indeed. I can do this with another assumption: that the relative volume of patients is equal to the relative number of positives. $\endgroup$– jtamCommented Jun 27, 2016 at 21:15
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$\begingroup$ So, maybe you can add these assumptions to your question, then it'll be more realistic to come up with the distribution. Otherwise your question has too many degrees of freedom to suggest a sensible answer. $\endgroup$– AksakalCommented Jun 27, 2016 at 21:19
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I think I figured this out: multinomial distribution!
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$\begingroup$ This is being automatically flagged as low quality, probably because it is so short. I recognize that this is your question, & you think this is the answer, but at present it is more of a comment than an answer by our standards. Can you expand on it? $\endgroup$ Commented Jun 29, 2016 at 17:50