Generally when I receive or obtain an analysis below LOQ, I use the LOQ as the result for any analysis, included a statistical analysis. But I'm interested in opinion of others.

Yes, I also do same. I used the value with symbol. ex, my LOQ is 0.03 mg/kg, I used it as a

Below detection limit can be replaced by half of the Limit of Detection (LOD) values of the instrument for statistical analysis.

Karishma,

Do you have a reference for this approach? Half the LOD seems to be a riskious approach that can alter the statistical analysis. I'm interested in reading the theory for this approach.

Thanks

Emanuele

Hi all, Thanks for your comments.

I have since come across this text (link attached).

Based on these,

"there are many intuitive practices for selecting the value for analysis when the response is below the LOQ. Some analysts use 0, others use the LOD itself, and still others split the difference and use half of the LOD. Finally, some analysts regard such a case as indeterminate and so leave the value missing. These ad hoc approaches unfortunately do not address the central problem but instead introduce bias in any estimates, such as model parameters. A missing value reduces the sample size and, therefore, the power of the analysis, as if nothing is known about the response when, in fact, there is information available. Using 0 biases your estimates downward, using the LOD biases your estimates upward. Using half the LOD might average out the bias, if you are optimistic and tend to be lucky. Isn’t there a better way? Isn’t there a rigorous approach based on statistical theory that

eliminates this bias and allows you to use all of the data?"

I am still interested to hear your opinion on the best approach in handling these kind of data

http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0CCgQFjAA&url=http%3A%2F%2Fwww.mwsug.org%2Fproceedings%2F2013%2FJM%2FMWSUG-2013-JM01.pdf&ei=QjZnU_zxAoXH7AbphIF4&usg=AFQjCNEy2nX7YjNAnY3bvVXIL_PQi7rvGQ&sig2=LNy48Oq2vcNjRAa8ghZnNA&bvm=bv.65788261,d.ZGU

I am attaching herewith an article to treat BDL data in statistical analysis. Half of BDL is often used in statistical analysis if less than half of your data set have BDL values and your data set is log normally distributed.

Karishma,

Thanks for this invaluable contribution and interesting approach of dealing with

I would analyse the data 3 ways, 1 setting the

In Statistical Analysis, If the data is not in our desired way, We have to apply the data preprocessing techniques to form appropriate data.

Apply different different  preprocessing methods and then analyse them. It will be a better approac and I think It will be very Helpful to You. 

The approach recommended by Horwitz is to use the value of the data as is, including any negative signs present. This avoids the somewhat arbitrary approaches of using the LOQ or 1/2*LOQ.

Karishma, what if my distribution is non-normal and I am using non-parametric tests? I was always inclined to not use the value (since the value is undetermined, you dont know what is the value), but now I also have the doubt about how to treat the data on my statistical software. Should I determine these values as missing values or should I just leave them blank? Is there any difference actually between the two ways? 

Hi,

great tanks for all.

However, when obtained values are above the higher limit of quantification ? what should we do ?

Best.

If a data set contains a variable whose values sometimes fall below a detection limit DL, it is an extremely bad idea to simply replace these censored values with 0, DL, or DL/2 in order to perform a statistical analysis. There are a few problems with doing so, but bias in the resulting model estimates is the most glaring. If a statistician is available to spend time building an appropriate model, several techniques based on likelihood approaches have been proposed (multiple imputation, Bayesian, maximum likelihood). These approaches generally will reduce or eliminate bias with careful modeling (assuming that the data below the DL does not follow a different pattern than the data above the DL). If a statistician is not available, the best strategy is often simply to conduct a "complete case" analysis. In this type of analysis, any observation units with a variable value below a detection limit are ignored for the purpose of statistical analyses. In the context of regression models, the resulting model estimates will be unbiased, though "throwing out" some of the data means the model estimates will be less precise. For some analyses, such as estimating a mean for a variable, complete case methods are not a good idea.

Dear Radhouene Doggui,

In the case of >ULOQ (upper limit of quantification) the situation appears to be much simplier. If you dilute your sample, you will finally fall into the range of quantification. By multiplying your result by the diluting factor, you will succeed.

Thank you Michal,

The problem is that the samples volume are not enough to realize again the analysis by operating a dilution.

So, is there any statistically approach to resolve these values >ULOQ ?

Or simply to conduct a "complete case" analysis and thus to ignore for these values ?

For all these questions, I guess that answers could be find in Helsel book

Article Nondetects and Data Analysis: Statistics for Censored Enviro...

There is an R-package related to these approaches :

https://cran.r-project.org/web/packages/NADA/index.html

"NADAforR_Examples.pdf" could be found on the web and give some ... examples.

Thank you Dominique Soudant for your valuable answer.

Have you a link for stata software package ?

Best.

is there any statistically approach to resolve values >ULOQ ?

Thanks

This document by US-EPA is helpful

https://www.epa.gov/sites/production/files/2015-08/documents/g9s-final.pdf

@ Mohamed Shamrukh: Thank you.

Dear All,

There is a usefull paper from Senn et al (Article The ghosts of departed quantities: Approaches to dealing wit...

Hi, did anyone find an answer for what to substitute for values that are >ULOQ? The publications suggested on this thread are helpful, but only seem to deal with

There are number of ways to solve the problem of values below detection limits, here I list some of them:

1- Substitute value of LOD/2 for all of them.

2- If you want to use the substitution, it is better to substitute LOD/sqrt(2) (to consider for the variance as well).

3- Impute the values below detection limits using multiple imputation.

4- More advance statistical approach is to use the mixture model. A binomial model for below detection limit and a log-normal model for above detection model data.

Hope it helps.