Hey Jérôme, me again

I posted this else where but didn’t get a strong answer one way or the other. Keen on your thoughts.

ACGIH suggests summing the concentration / OEL ratios for additive mixtures:

Σ Cn/OELn > 1 = Unacceptable

Σ Cn/OELn < 1 = Acceptable

I wondered if there is any statistical issue with modelling the summed ratio, in addition to individual contaminate analysis. I had two initial thoughts (remember, I’m still self teaching stats - doesn’t come naturally yet!).

- Calculate the sum ratio and treat it like any other analysis with an OEL of 1.

To trial this, I simulated a dataset of 25 samples, each with two chemicals. Both chemical’s were sampled from a log-normal distribution. Sigma of the Chemical 2 distribution was x0.2 chemical 1. I think you would expect exposures to be highly correlated like that - say the chemical source is the same process.

The chemical 1, chemical 2, and summed ratios samples were all log-normal (pretty much).

Correlation chem1 ~ chem 2 = .90 as expected.

If you were using exceedance fraction as your measure for acceptability - it would go from good to bad.

Does that make sense? Is there a better way of attacking this problem? Seems like this would be very important for larger and larger mixtures.

- Model chem1, chem2 … chemN is an GLM

y = ß° + ß1X1 + ß2X2 … + Bi + e

Kind of treat each chemical like a ‘exposure determinant’.

But it feels weird because I think the chemicals would be fixed effects given you would know exactly what the results are, unlikely say the effect of an LEV system being off or on.

Also because you’d expect X1 (chemical 1) ~ X2 (chemical 2) to be highly correlated in most cases, this LM does work so well?

As you can tell, I’m a bit confused. Any help would be greatly appreciated as always.

John