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  1. I have a population of 300 cases. It's split in three sub-populations 50, 50 and 200 in size.

  2. I have developed three (different) models resulting in a score variable which rank orders each of the sub-populations separately. The score-ranges for all three segments are different... 40 to 240, 20-410 and 4 to 600. Within each sub-population, higher score means higher level of toxicity i.e. level of risk. Score are not comparable at the moment (that's what I'm trying to achieve).

  3. I know (a priori) that the absolute level of toxicity for first sub population is highest, average for middle sub-population and lowest for the third sub-population.

What I'm trying to achieve is single rating scale. Ideally, I should be rescale each score variables to reflect my a priori knowledge.... first population should have highest scores, then second and then third... something like this

range A      from 40 to 240     to       600 to 1000
range B      from 20 to 410     to       400 to 700
range C      from 4 to 600      to       0   to 500

NOTE: I intentionally allowed for overlaps

Im currently stuck... I know its more art than science, and I will appreciate any ideas you may have.

Thanks

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Do you have the toxicity numbers (true values)? If so, why arent you simply doing a regression? If not, how are you able to rank within each group? – reisner Jul 5 '11 at 21:13
That's funny: questions about toxicity deal with objective, observable fact and due to their potential importance, ought (IMHO) to be addressed using science. If possible, "art" should not enter the picture. – whuber♦ Jul 5 '11 at 21:28
good point ;)....but I don't have any data on mortality. I know from theory that three groups have different mortality... there are actually various previous works suggesting different percentages... the only thing they have in common is that A is highest, B is the middle and C is the lowest.... – user333 Jul 5 '11 at 21:35
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Why not leave it at that? Do you really need a numerical score? Sometimes the ranking is good enough for decision-making, whereas providing a number can mislead whoever doesn't read the fine print into using the value quantitatively, a use that is not supported by the theory. – whuber♦ Jul 5 '11 at 22:15
I know. The idea is to look at the master score and focus on areas where both models can produce the score (overlaping areas) and then to use expert judgement to fine tune boundaries. For example, I want to look at cases who score 500 by model A and compare with cases who score 400 on model B. – user333 Jul 6 '11 at 7:20
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