I've sampled the influent and effluent of six wastewater treatment plants and analyzed for a large number of trace organic chemicals. There are many instances where the commercial lab conducting the analysis reports the concentration as not-detected (ND). This occurs most often for effluent samples, but occasionally for influent samples as well.
I am interested in determining the percent removal (i.e. [[Cx,inf - Cx,eff]/Cx,inf]*100) for each compound in each treatment plant, and then calculating measures of central tendency and dispersion for those removals across the six treatment plants.
Data reported as ND (censored data) obviously hinder the calculation of percent removal.
As a first approach, I replaced all values reported as ND with 0, but I am wondering if there is a better method.
The analytical lab reports all values below the Method Reporting Limit (MRL) as ND, though the raw data shows that in some cases there was no instrument response (i.e. raw value = 0.0), while in other cases the raw value is equal to some value below the Method Reporting Limit (MRL). It seems prudent to treat these cases differently when substituting values for censored data in order to calculate percent removals.
An obvious choice seems to be substituting 0 when there is no instrument response and substituting the MRL when there is a measured value below the MRL.
The substitution of MRL (vs. substituting 0) tends to yield more conservative percent removal values when NDs occur in the effluent, but can inflate percent removals when NDs occur for influent samples and always yields 0 percent removal when ND occurs in both the influent and effluent for a particular compound in a particular treatment plant.
Can anyone with experience calculating percent removals from censored data offer their advice?
The standard technique for data below the detectable limit is to assign them the mid-point value, so if the value is < 0.05 mg/l you assign it a value of 0.025 for assessing removals. If both inlet and outlet are below the detectable limit then I would suggest that you set the removal as 'not applicable'. All you can say is that the removal is somewhere between 0 and 100%.
The standard technique for data below the detectable limit is to assign them the mid-point value, so if the value is < 0.05 mg/l you assign it a value of 0.025 for assessing removals. If both inlet and outlet are below the detectable limit then I would suggest that you set the removal as 'not applicable'. All you can say is that the removal is somewhere between 0 and 100%.
There are a number of different ways to handle values below the method reporting limit, but they all have their pros and cons. Substituting a random number like 0 or 1/2 the MRL isn't a very logical approach because the numbers are arbitrary. In fact, zero is probably the only thing that you can be sure it isn't. (There is probably at least one molecule in the sample somewhere). Some books call this the "fabrication" approach. There is also MLE, which assumes a certain distribution in the data.
I'd say the best approach is to use nonparametric methods. They use these quite frequently in medical studies where one of the "endpoints" is censored, such as when someone dies during the study. Even when you have very few data points, you can use nonparametric procedures to estimate summary statistics and they don't assume any sort of distribution of the data.
I recommend the book by Dennis Helsel on the subject.
All that said, you can simply calculate percent removal and say "this treatment process removed >82%" and leave it at that. It depends on your audience, but most of the time you can use bins to summarize your data (e.g. these contaminants had >75% removal, these had >50% and these had
It's best to not substitute a value by using 1/2*DL (though it can be recommended when percentage of censored values are
- Badges
- Science method
- Similar topics
- Chemistry
- General Biochemistry
- Biochemical Techniques
- Analytical Chemistry