Unit conversion from disease case to physician consultation

[patrick_at]

Hi everyone,

I have a problem with units in my simulation model. Basically the idea is that disease cases of patients who consult one doctor are of unit [case]. A case can need one ore more consultations. For every consultation there should be a probability that it is the last consultation, or that a further consultation at the same doctor is required, or that a referral to another physician is made. I have two stocks for cases: In the first level cases are until the patient has his first consultation (because the time would be the normal waiting time at the physician), in the second the patient is until his case ends or he gets a referral (here there could be different times between follow-up visits than the normal waiting time for the first visit).
First I worked with waiting times and had choosen the unit [month]. In the equations for the rates of cases (unit [case/month]) I used something like:
ProbablilityOfReferral/waitingTime*Cases of units [dmnl/month*case]

That worked, but when I wanted to calculate how many consultations a doctor had, from cases and the waiting time between cases, I had of course no unit with [consultation]!

I can solve that when I use consultationsPerMonthAndCase (unit [consultation/(month*case)]) instead of waitingTime. But the inverse (to use it in the equation above instead of waitingTime) would have units [case*month/consultation] which don't make sense for me. However, by multiplying instead of dividing in the equation it works for the follow-up cases. Still it is a bit strange for me, as waitingTime between consultations is an obvious variable, but I cannot use it anymore (not unless I would use another variable with value 1 and unit [case/consultation] but this seems very artificial). Furthermore, I do not know if consultationsPerMonthAndCase is a good variable for cases until there first consultation (clearly, they should lead to only one consultation as long as they are in the first level).

All in all I'm a bit confused about these unit issues and wondering if you would come up with better solutions or if I'm on the wrong track.

Thank you and kind regards
Patrick

[Administrator]

Is your model in Vensim? If yes, can you upload it as it would be far easier to work directly with the model.

But if it helps, try and keep things simple. The units for any model parameter should be the same as in reality. For example, the rate for how quickly cases "appear" should be "cases/month" (which is the same as DMNL * case/month). I'd expect you to have a stock of cases awaiting consultation (units:case) and then the rate at which this is drained would be case/month. To convert this to consultation/month, you need to create a constant called "consultation per case", multiply case/month with consultation/case and you get consultation/month. It could well be that each case needs more than one consultation, constant you introduce to convert case/month to consultation/month will take care of this.

Units are so important in model building just as a simple but very effective model check. I still cannot believe why some people choose not to bother implementing them.

[patrick_at]

Yes, the model is implemented in Vensim, however with German variable names. Thank you very much for your reply, I decided to follow your advice and use the constant for converting cases into consultations. Actually from new cases there follows one consultation, and a proportion of cases has follow ups with an average number of consultations, so there are two "consultation per case" constants.

I also think that units are a helpful tool for checking model equations, and as demonstrated here they force you to think if you're mixing up the right things (and if anything is missing).

[Administrator]

I also think that units are a helpful tool for checking model equations, and as demonstrated here they force you to think if you're mixing up the right things (and if anything is missing).

I wish others would realise their importance. In my opinion, they are absolutely vital. I will not even look at results from a model unless it passes the units check.