Measurement uncertainty

When entering confidence intervals only the program responses with a message box

The message shouldnot be in red as it is not a critical error. It results in 5.3% confidence C95%>OEL

Taking the point estimators, result in a higher 13.3% confidence that C95%>OEL. What is the logic ? For such a large sample (n=18) one expect no influence of measurement uncertainty.

Hello Theo,

A couple of ideas :

  • the higher risk without interval censorship appears due to the higher estimated GSD when you replaced [a-b] with (a+b)/2.

  • I think it is discussed in another area of the forum (link) and in a small report I wrote, but using the interval censorship capability of IHSTAT_Bayes is not meant to be used as a way to model measurement error. Measurement error is usually modelled as a gaussian distribution centered on the point estimate. Interval censorship on the other hand, considers nothing is know within the interval, and is influenced by where the interval is compared to the overall exposure distribution. This might have caused the change in numbers. I see the interval censoring approach useful for detected but not quantified results, or for when there was too much chemical in the second section of the tube.

  • Thanks for the tip on the error, indeed it shoulnd be shown as critical.


Hello Theo, It does not, in our mind at least. It is just a showcase of the capabilities of the engine.

Ah another curcumstance where interval censorship is useful, which I had forgotten to mention, and we might say example 3 illustrates that : when you calculate a 8h TWA from 2 samples, one of which is non quantified, what you know about the 8h value is actually a range. E.g. for 2 4-hour samples : <10 and 20 correspond to [10-15].

This and the other cases mentionned above are what interval censorhip is intended for.

Ok thanks for this additional information
What I understood from you earlier respons is that IHStat-Bayes replaces [a-b] with (a+b)/2
As Non-quantified means no knowledge at all, not even <LoD, the range should be [10-20]

When seeking the influence of CV=30%, you can use something like MC on the gaussian distribitions around the point estimators

Hello Theo, as additional info : Our measurement error model (algorithms available and public but not yet implemented in expostats) is the following :

True exposure(i) = lognormal(GM, GSD).

Oberved exposure(i) = normal( true exposure(i) , measuement error CV).

For my example, I beg to differ, a lab will report <LOQ, so we can assume the true value was anywhere between 0 and LOQ (0 and 10 in my example). so the TWA anywhere between (0+20)/2 and (10+20)/2, no ?

I would appriciate if the example I used in IHStat-Bayes can be processed.
Sometimes a lab repports ‘nothing’ as the sample was corrupt, disappeared or whatever. So for 2 4-hour samples : unknown and 20 correspond to [10-saturation concentration ] :grinning:.

can you clarify please ? not sure I understand

See the first message on this subject
Below the point estimators from AIHA 2015 annex V. You may use CV 30%.
But if I can do it myself with the available and public algorithms, please forward them.

OK I understand, algorithms are presented in this report, and available here, but they might be a tad difficult to navigate. You could try the Csharp prototype or I can run the analysis for you but it’ll take a few days :). Main impact I can predict is a smaller GSD but overall small differences ( as shown by previous authors).

Some results.

First without error, then with 30% error. For each case, screenshot of input, then output of the C# prototype.

No error

With 30% error CV (no bias)

As Grzebyk et al. showed, the “mistake” caused by not considering measurement error in the analysis corresponds to an overestimation of variability, seen in GSD and P95 estimates.

This C# prototype looks quite mature !
And the result is as expected: for N=18 the influence of a Variation Coefficient (%)=30 on Exceedance (%) is minimal

This example from the AIHA 2015 strategy Annex V (Paul Hewett) page 442 refers to Heptane with an OELV of 400,which will give more illustrative exceedance and critical percentage - overexposure risk (%) values than the current 100%

How can I get this application running on W11 system? Or do you have a link?
I would like to see what happens with samples of size N= 3, 4 and 5


Hello Theo, the link I provided above :

Should provide enough information to run the prototype easily (I did it myself yesterday) : downlowd the repository on your PC, then run one of the mentionned files (there is a windows security warning to bypass)


Thanks Jerome, I will give it a try!

The Readme instruction is quite different from what you should do

So donot :

  • Download the code (by clicking the green “Clone or download” button)
  • Open the folder containing the code
  • Click the green “Code” button, in the upper right corner
  • Click Download ZIP

It works

Excellent, thanks for the practical instructions :slight_smile:

FYI the mathematical models underlying the prototype are described in the IRSST report, and an extensive validation effort (additional to what was described in the report but no yet published) was conducted to verify that all platforms (C#, R, JAGS, Javascript) yield the same results for the same data.