## Simulating BLQ values in NONMEM

When simulation concentration-time data using NONMEM, there are times when you wish to include the censoring effect of BLQ measurements from your bioanalytical laboratory. It is very easy to implement this in your NONMEM control stream. Here is how I do it.

In the \$ERROR block , you will be adding your residual error to the prediction. The prediction is denoted F in NONMEM code. The individual prediction that is output as DV is denoted Y in NONMEM code. Let’s assume that the limit of quantitation is 0.1 ng/mL. The code to add at the end of your error code is the following:

Y=F + ERR(1)
IF(Y.LT.0.1) THEN
Y=0
ENDIF

The first line can vary depending on your specific residual error structure. The heavy lifting is done by the second line where the value Y is compared to the target value of 0.1 using the Fortran term for “less than” (LT). If the predicted value is less than the BLQ it will be replaced by the number zero. If the predicted value is greater than or equal to the BLQ, then the prediction does not change. You cannot assign text (eg BLQ) to the value of Y. Only numerical values are accepted. In my example I set it to zero; however, I could have assigned a value of -99999 also. Ether way I would extract these “BLQ” values from the simulated dataset before plotting the data.

## How to set your target limit of quantification

one of the key things to do during the transition from preclinical development studies to clinical development studies is to set the target for your drug assay limit of quantification (LOQ). I will outline a few considerations on that topic. Here are my main assumptions:

1. You are working with a drug that is intended for systemic delivery (not a local drug like topical dermatological or ophthalmic)
2. You have some exposure data from preclinical species
3. You have estimated a peak human exposure using some method (e.g. allometry)

To set your target LOQ, you use the expected peak human exposure. Let’s assume the following for our example:

Predicted Cmax = 250 ng/mL

You will need at least 5 half-lives after the peak occurs to accurately calculate the terminal elimination rate constant. You can calculate how much drug remains after 5 half-lives using the following equation:

$C_{remaining}=C_{max}*\frac{1}{2}^5$

$C_{remaining}=7.8125 ng/mL$

This gives a reasonable estimate for the LOQ. In this case, I would round down to 1 ng/mL as my initial target LOQ with a stretch goal of trying to achieve 0.1 ng/mL in case my human prediction was high.

That’s all there is to it!

## What to do with those BLQs!

BLQ values are like those pimples we used to get as teenagers. They often show up at the worst time and they always seem to be in the wrong place. (Is their really a “right” place for a pimple!?) Then what do you do with the pimple? Rub some alcohol on it, put other medication, squeeze the puss out? So many choices … which one will be the least noticeable, yet relieve the majority of the pain? Often we are faced with similar challenges with BLQ values in our data.

### What is BLQ?

BLQ stands for below the limit of quantification. Bioanalytical assays are validated within a pre-specified range. The lower end of that range is the “lower limit of quantification” or LLOQ. Concentration measurements below the LLOQ will have a percent coefficient of variation (%CV) of greater than 20%. That value of 20% was arbitrarily chosen as a cutoff for validated bioanalytical assays. Concentration measurements below the limit of quantification are then listed as BLQ (or BLOQ) in concentration-time datasets by laboratories.

### Why not report the actual measurement instead of BLQ?

Many pharmacokinetic scientists would agree with this position; and many bioanalytical scientists would disagree with this methodology. The two arguments are as follows:

In favor of using BLQ: If we cannot measure something with a specified degree of certainty, then we will have no confidence in what we measure. Therefore, if the variability around the measurement is > 20%, we consider that a measurement in which we have no confidence of the measure.

In favor of reporting extrapolated concentrations: All data contains some information. When we artificially create barriers, we introduce bias into the analysis. The uncertainty in the measurement can be accommodated using appropriate PK error models to reflect the lack of confidence in lower concentrations.

In a majority of regulatory agencies around the world, the currently accepted method is to use BLQ values in bioanalytical analysis. However, there is strong pressure to move toward reporting all data with associated variability. So, what do we do with BLQ values we have now?

### Set BLQ values to missing

Since no response information is provided with the BLQ one approach is to set all BLQ values to “missing”. When BLQ values occur at the end of the concentration-time profile, setting them to missing has the effect of truncating the AUC to the time of the last observed concentration. When BLQ values occur in between two observed concentrations, setting the BLQ value to missing has the effect of removing that time point from the AUC calculation. This can potentially overestimate the AUC as extrapolation occurs between the two observed data points, ignoring the intermediate BLQ value.

### Set BLQ values to zero

The approach endorsed by most regulatory agencies for the evaluation of bioequivalence data is to set all BLQ values to zero. The theory behind this approach is that since the concentration could not be measured accurately (i.e. within 20% CV) that there must be no drug present. This is a conservative approach that results in a potential for underestimation of the true AUC. However, it prevents overestimation of AUC that can occur as described in the “missing” section with intermediate BLQ values.

### Set BLQ values to 1/2 of the LLOQ

The third approach is to set all BLQ values to 1/2 of the LLOQ. This approach is based on the theory that all BLQ values must be between 0 and LLOQ. Assuming a normal distribution, the mean concentration would be the midpoint, or 1/2 of the LLOQ. Thus using that value as a replacement for BLQ provides an “average” estimate of the actual concentration. In some respects it is a middle ground between the “missing” and “zero” methods previously described. While that may seem beneficial, this method suffers from 2 key problems. First, concentration-time data is not normally distributed. It is lognormally distributed as described in another post. Thus using the average concentration of an incorrectly assumed distribution creates bias. The second problem is that drug elimination is known to follow exponential decline. When the 1/2 of LLOQ method is used, drug levels in the terminal portion of the concentration-time are flat. This results in overestimation of the terminal portion of the AUC.

### Which should I use?

My first recommendation is to use the actual response data along with the associated variability rather than using BLQ values. That said, you may have a difficult time convincing your bioanalytical laboratory to provide that information. Thus, if I am forced to use BLQ values, I prefer to use the “missing” method for most cases. The exception is to use the “zero” method when analyzing bioequivalence data submitted for generic products. I don’t recommend the “1/2 of LLOQ” method except when a regulator requests it.