This analysis is concerned with the precision components of assay validation to estimate contributions due to assay variation, assay-to-assay variation, and ana-lyst-to-analyst variation. A single QC sample was prepared containing theoreti-cally 65 ng/mL of analyte. Five analysts were recruited for this study. Each analyst ran 5 aliquots of the sample on 4 assay runs. The data are available in the data set AssayVal1.CSV in the Phoenix examples directory.
The model
Import the linear mixed effects model data set:
1. Select File > Import or click the Import button. The Open File(s) dialog is displayed.
2. Navigate to the Phoenix examples directory, which by default is located at C:\Program
Files\Pharsight\Phoenix\applica-tion\Examples.
3. Select AssayVal1.CSV and click Open.
The Worksheet Import Options dialog is displayed. The dialog is used to assign options for how the data are imported and presented.
4. Click Finish. The data set is added to the project’s Data folder.
Units must be added to the Determination column before the data set can be used in a Linear Mixed Effects model.
5. Select AssayVal1 in the Data folder. The worksheet is displayed in the Grid tab in the right viewing panel.
• Use the Columns tab to modify columns in a worksheet. The Columns tab is located underneath the right viewing panel.
6. Select the Determination column header in the Columns box.
Insert the Linear Model:
1. Select the workflow in the Object Browser and then select Insert > NCA and Toolbox > Linear Mixed Effects.
The Linear Mixed Effects Model object is added to the workflow in the Object Browser.
Note: When multiple objects of the same type are added to a project they are num-bered sequentially. For example, the second Linear Mixed Effects Model object added to this project is called Linear Mixed Effects Model 1.
2. Map the data set AssayVal1 as the input source for the Linear Mixed Effects Model 1 object:
• Use the pointer to drag the AssayVal1 worksheet from the Data folder to the Linear Mixed Effects Model 1 object’s Main Mappings panel.
OR
• In the Linear Mixed Effects Model 1 Main Mappings panel click the Select source button to open the Select Object dialog.
• Select AssayVal1 and click Select.
The AssayVal1 data set is mapped to the Linear Mixed Effects Model 1 object.
3. Use the option buttons in the Main Mappings panel to map the data types to the following contexts:
• Map Analyst to the Classification context.
• Map Assay to the Classification context.
• Map Determination to the Dependent context.
4. Select the Variance Structure tab.
5. Drag Analyst from the Classification Variables box to the Random Effects field in the Random 1 tab, or type Analyst in the Random Effects field.
6. Click the Add Random button to add another Random effect.
7. Drag Assay from the Classification Variables box to the Random Effects field in the Random 2 tab, or type Assay in the Random Effects field.
8. Select the Estimates tab.
9. Select the Intercept Coefficient check box and type 1 in the Intercept Coef-ficient field.
10.Click the Execute button. The results are displayed in the Results tab.
Results
Statistical accuracy values are located in the Estimates worksheet.
The mean response is the intercept, which is estimated at 70.6 ng/mL with a 95%
confidence interval. The lower confidence interval is 65.97 and the upper confi-dence interval is 75.28. Since the theoretical analyte concentration of 65 ng/mL is not within the confidence interval, one can conclude that the bias is statistically significant. The method has a bias of approximately 5 ng/mL.
Select the Final Variance Parameters worksheet to view precision estimates and variance components.
Based on these results, most of the variation is coming from analyst-to-analyst variation and from within-assay variation. Assay-to-assay noise is quite small.
The units on the variances are (ng/mL).
Dependent Units Parameter Estimate
Determination ng/mL Var(Analyst)_11 7.807236
Determination ng/mL Var(Assay)_21 1.86966
Determination ng/mL Var(Residual) 9.9133
Re-execute the model with new data
Now fit the same model to the data in the data set AV3.CSV.
Re-run the model with a different data set:
1. Repeat steps 1. through 7. under Import the linear mixed effects model data set: on page 127 to import the data set AV3.CSV and add units to the Deter-mination column.
2. In the Workflow, right-click Linear Mixed Effects 1 and select Copy.
3. Right-click the Workflow object and select Paste.
A new Linear Mixed Effects object named Copy of Linear Mixed Effects 1 is added to the Workflow. The LinMix object copy contains the same settings as the original object.
4. Map the AV3 data set to Copy of Linear Mixed Effects 1. Do not change the data mappings in the Main Mappings panel.
5. Click the Execute button. The results are displayed in the Results tab.
The results are displayed in the Results tab.
The Final Variance Parameters worksheet contains the following variance com-ponents:
This table indicates that analyst to analyst variation is negative. Since variances can not be negative, it is customary to replace the value with 0. A negative vari-ance component indicates that the corresponding term should be removed from the model, which means that the contribution from that term is minimal compared to the contribution due to the other terms and it cannot be distinguished from the residual term.
From the variance components it is clear that the largest contribution to noise in the method is from run-to-run variation. Within-run variation also contributes to the noise. There is very little variation among analysts, indicating that the method is robust.
The Linear Mixed Effects object warns user about negative final variances.
• In the Results tab, select the Warnings and Errors text file.
Dependent Units Parameter Estimate
Determination ng/mL Var(Analyst)_11 -3.880848
Determination ng/mL Var(Assay)_21 26.42101
Determination ng/mL Var(Residual) 9.91625
The text file states: “Warning 11094: Negative final variance component.
Consider omitting this VC structure.”
Problems associated with a linear mixed effects model are written to this file during execution.
Note: It is not necessary to keep a project open after completing each chapter. This project is not required when working in the next chapter. To close a project right-click the project and select Close Project.