QC Calculations

This section details the parameters and calculations performed by AssayNet LIMS to obtain the allowable variance (control limit). This documentation focuses on replicates, but the calculations and parameters are the same for prep splits and prep QC samples. All parameters that define the control limits, except for the detection limit, are specified in the analysis code Q.C. Options category. For more information, see Set up QC Analysis Code Options.

The allowable variance is dynamic and varies based on sample concentration. At higher concentrations, the allowable variance is lower, resulting in tighter control limits, as stricter variance limits are required due to improved precision at these levels. Conversely, for lower concentrations and near the detection limit, the allowable variance increases to account for greater measurement uncertainty, allowing for more variance due to the higher susceptibility to variability at these levels.

For replicates, AssayNet LIMS only calculates one control limit. The high control limits serve as thresholds that determine whether the variance between the replicate and the original sample falls within the acceptable control limit. The calculated control limit at each sample concentration is displayed in QC control charts within the AssayNet LIMS Excel Add-in.

Method blank control limit is also defined within the analysis code Q.C. Options category, but its calculations and parameters differ from those for the QC samples described above. Additionally, control limits for other QC types, such as reference materials, client QC samples, and instrument control samples, are specified within their respective setup screens. For more detailed information on configuring control limits for these QC standards, see:

• Add and Set up Reference Material (CRMs)
• Add and Set up a Client QC Sample
• Add and Set up Instrument Control Samples

Calculation for the variance of replicates and prep split

AssayNet LIMS has two options to obtain the variance of duplicate samples; Std. Diff. and % RSD. The two calculations produce slightly different results for the duplicates' variance. The standard difference formula calculates the absolute percentage difference between the original and repeat assays. Below is the formula that AssayNet LIMS uses to calculate the standard difference.

The % RSD option provides insight into the variability of the data in proportion to its mean. Below is the formula AssayNet LIMS uses to calculate the % RSD:

Note: AssayNet LIMS calculates the two options for two replicates only.

Either option can be used depending on the desired level of detail or the client's QC requirements, but % RSD is typically preferred when precision and consistency across multiple measurements are critical.

Parameters for the calculation of the allowable variance at X concentration

• Detection limit (DL)—The minimum concentration of a substance that can be reliably detected by the method. Parameter is defined for each of the analyte schemes.
• Allowable variance at detection limit % (Dlvar)—This represents the maximum allowable percentage variance when the concentration is at the detection limit. If for example, a variance of 100% is allowed at the detection limit, this means that the results can vary significantly yet still be considered acceptable. For example, if the concentration is at the detection limit for the first sample and increases to 1 g/Mt for the second sample, a 100% variance is acceptable at the low detection limit.
• N—A multiplier that adjusts the allowable variance as concentrations increase. This parameter scales the detection limit to establish a new threshold for higher concentrations. For example, if N is set to 50 and the detection limit is 0.05 g/Mt, the high concentration limit will be calculated as 50 x 0.05 g/Mt, equating to 2.5 g/Mt. The allowable variance at this higher concentration can then be defined by the user, by setting the upper variance limit.
• Allowable variance at N times the low limit % (ULvar)—This upper limit variance parameter defines the maximum allowable variance when the high concentration limit is N times the detection limit.

How the dynamic variance formula was define

By analyzing extensive data for replicates, AssayNet developers observed that when plotting variance versus concentration, the data follows a logarithmic curve fit. Based on these findings, a formula was derived to calculate the dynamic variance at different concentrations. Below is the formula used by AssayNet LIMS to determine the control limit for any concentration:

Apply a client specific allowable variance value

When the control limit is calculated, it will directly reflect the value entered for both DLvar and ULvar, provided these parameters are set to the same value. In this case, the formula uses the specified percentage as a uniform control limit across all concentrations, making the allowable variance consistent regardless of sample concentration.

Alternative formula for the allowable variance

AssayNet LIMS users have an alternative method for calculating allowable variance through the formula . This approach utilizes an exponential curve fit for replicates analysis, where:

• a and b are user-defined parameters.
• M represents the absolute standard difference of the replicates.

This method does not incorporate the detection limit in its calculation parameters. Although the preferred method remains the standard logarithmic approach, this alternative provides flexibility for precision in specific scenarios where the exponential model is suitable.

Additional values calculated for replicates

To enhance quality assurance for replicate measurements, AssayNet LIMS calculates not only the high control limit but also the high warning limit and the high action limit. While the control limit is the primary threshold that determines whether the absolute percentage difference between replicates passes or fails, the additional limits provide further insight into the quality of the replicates. These limits act as early signals, allowing for proactive quality control measures before results reach the high control limit.

The high control limit is assumed to be 3 times standard deviation, so the other limits are calculated:

• The high warning limit is 1/3 of the high control limit.
• The high action limit is 2/3 of the high control limit.

The high warning limit and high action limit columns displays as column when loading the control charts within the Excel Add-in.

Prep QC variance calculation

The calculation parameters for prep QC follow the same approach as previously outlined. However, the variance calculation for prep QC differs from that used for replicates. In replicates, the Original and Repeat values represent the original sample and its duplicate. For prep QC, the variance specifically addresses potential cross-contamination (percent carry-over) based on the preceding sample in the preparation sheet.

To calculate this variance, both the prep QC sample and the preceding sample in the preparation sheet must be analyzed within the same instrument run. AssayNet uses the following formula to calculate the percent variance or percent carry-over:

Method blank calculation

For method blanks, only one user-input parameter is required: the N factor. This factor determines the allowable variance by setting a multiplier on the detection limit.

For example, if you want the allowable variance to be 20% above the detection limit, you would enter 1.2 as the value for N. This input means that the system will calculate the variance limit as 1.2 times the detection limit. By adjusting the N factor, users can easily control the tolerance level for method blanks, ensuring that it aligns with both detection sensitivity and the lab's quality assurance standards.

This single parameter approach makes it straightforward to manage the variance for method blanks.

For details on entering the parameters needed for these calculations, see Set up QC Analysis Code Options.