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Module 6: Calculate Concentrations

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Note: Although this software and accompanying documentation is dated 2004-2005, it is still valid in 2014. Questions can be sent to CDC-INFO.

Introduction

This module facilitates calculating antibody concentrations from patient serum samples and quality control samples. These concentrations may be arbitrarily assigned units (e.g., antibody units/ml), or mass values (e.g., µg/ml). A diagram used to illustrate the concentration calculations is shown in Figure 17. In this diagram, the absorbance is plotted on the logit-log scale to simplify the example. ELISA for Windows performs the actual calculations using the results of the more accurate four parameter logistic-log fit.

Figure 17 displays a rather idealized standard curve bracketed by two twofold serially diluted patient serum samples or unknown curves. For the purposes of this example, assume the antibody concentration of the standard reference serum (the calibration factor) is 135.8 micrograms/ml (µg/ml), and that the standard was initially diluted 1/100 with six subsequent twofold serial dilutions. This would lead to standard point 1 containing 1.358 µg/ml, point 2 containing 0.679 µg/ml, etc. The sample from Patient 1 was initially diluted 1/400 and that from Patient 2 was initially diluted at 1/25.


Figure 17. Diagram illustrating antibody concentration calculation for patient unknowns.

Figure 17. Diagram illustrating antibody concentration calculation for patient unknowns.

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ELISA for Windows uses the following formula to calculate antibody concentration:

Image reads: concentration equals interpolated dilution from standard curve divided by actual dilution of sample multiplied by calibration factor.

The calculated concentration for Patient 1, using the third point on the patient curve would be:

33.95 ug/ml equals 0.0025 divided by 0.01 multiplied by 135.8

Alternatively, the calculated antibody concentration for patient 2, using the sixth point on the patient curve would be:

54.20 ug/ml equals 0.0003125 divided by 0.000078125 multiplied by 135.8

The optical densities and dilutions corresponding to patient and quality control samples are located in the file.UNK (patient serum samples or unknowns), and file.QC (quality control samples), where file is the root file name associated with the collection of samples.

The user must perform parameter estimation (Module 4) prior to entering this module. This module will access the coefficient data file to determine which fitting techniques were chosen during parameter estimation and only offer these for antibody concentration calculations. Thus, if only the robust fit were selected in Module 4, the user would not have the option of selecting unweighted least squares for calculation purposes. ELISA for Windows, also offers a nonparametric fit, the three point cubic spline, as an additional option which is always available for selection. If there were any plates in a standards data file where the solution did not converge to a stable set of parameter estimates after processing the data with Module 4, then the spline fit, again, will be the only option available for these plates.

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Opening Menu Dialog

This module is entered from the main menu (Figure 3) and begins by displaying a standards data file selection dialog window. If the user enters this module directly after estimating the logistic-log parameters (Module 4), ELISA for Windows will insert a file name in the file name box which corresponds to the .DAT or .STD file just processed. This is offered as a convenience to the user in an attempt to eliminate repetitive entry of file names. This file is selected by clicking on OK. The user may also select a different file from the file list box.

After a standards data file has been chosen, the dialog window in Figure 18 appears.

The window displays the standards data file name along with the number of plates contained in the file. Initially, the window is set to plate 1, unknown 1. The number of unknowns within each plate is also listed. Users may then select the plate and unknown for antibody concentration calculations. When a new plate number is entered in the plate number field, ELISA for Windows will interrogate the unknowns data file to determine how many unknowns are contained on that plate and display this in the dialog window. This information is updated when the plate number field is exited.

When the user exits the plate number field, ELISA for Windows also interrogates the coefficient file associated with the standards data file and determines which types of fit should be made available for selection. Fits which were not used during parameter estimation (Module 4) will be suppressed as options in the type of fit option box. As mentioned earlier, the spline fit will be the only choice allowed for those plates where the solution did not converge during parameter estimation.

Users may analyze an entire plate of serum samples or an entire file of plates without returning to the dialog window. In these cases, the parameters set initially (type of fit, calibration factor, etc) will apply for the entire plate or file. By default, when either of these two options are selected, the program will save the results to a report file and not display them on screen.

The construction of the report is designed using the choices in the 'Select computation parameters' box. Serum samples and quality control samples may be estimated alone or together depending on which boxes are checked. If a particular plate does not contain serum samples or quality control samples, these check boxes will be suppressed. If both boxes are checked, the QC samples will follow the serum samples in the output file described later. Next, the calibration factor must be entered ELISA for Windows will not exit this dialog window without a number specified for this quantity. If a calibration factor is not needed, enter 1 in this box.

The user may elect to save the results of the subsequent calculations to a report file by checking the 'Save report to file (.RPT)' box. This output file will remain in effect and open throughout the procedure, that is, until the user exits the module and returns to the main menu. ELISA for Windows will annotate the output with the comment lines contained in the file.LBL file. An additional title for the report may be entered in the dialog window.

The user also has the option of storing a distilled version of the output to a summary file which has an assigned .SUM extension. The summary file is an abridged version of the report file. This file abstracts pertinent information about each plate, unknown, and QC sample, eliminating much of the detail included in the report file. This file contains the overall mean for each unknown, excluding the dilution-specific information. However, dilution means are recorded for quality control samples. The report file is cumulative in nature. Each result is appended to the end of this file. The summary file is updated in that information is revised as users censor optical densities and recalculate results.

If the user selected the option to save the results to a report file, an output file selection dialog window will now appear. ELISA for Windows will suggest file.RPT, where file is the root name of the standards data file. If this file already exists, it will be appended with information from the current session. If the user elects to analyze an entire plate or file of plates, the output will be stored in this file. If the user selects one serum sample, the results will be displayed on screen where they may be stored to file by clicking on the 'Save report to file' option button. If a single plate or an entire file is selected for processing, the opening dialog window for this module will reappear after the current round of processing has finished.

computer screen shot: Calculate Antibody Concentrations

Figure 18. Dialog window for Module 6 - Calculate Concentrations.

If the user selected the option to save the results to a summary file, an output file selection dialog window will appear next. ELISA for Windows will suggest file.SUM, where file is the root name of the standards data file. If this file already exists, it will be updated with information from the current session. Recording summary results is automatic–it is not necessary to click on a save-to-file button as is the case with the report file. If the user elected to analyze an entire plate or file of plates, the output will be stored in this file. If the user selected one unknown, the results will be displayed on screen and recorded in the summary file. If optical densities are subsequently censored and the unknown recalculated, the summary file will be automatically updated to reflect the revised mean, standard deviation and CV.

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Calculation Parameters

ELISA for Windows contains a feature that allows users to pre-screen optical densities which are included in mean, standard deviation, and CV calculations. This gives an investigator a wide degree of latitude in eliminating observations that would normally be excluded from these calculations without examining each unknown in detail. This is meant as a time-saving device which will facilitate analysis of large numbers of plates in high-volume laboratories. Trying different options and different combinations of options will enable the user to arrive at optimized settings for a given experimental design.

Clicking on the 'SetParams' button will open a new window offering these different options. This window is diagramed in Figure 19.

The 'Set Calculation Parameters' screen offers a number of choices for censoring optical densities. Users may select as many options as desired. A particular optical density will be eliminated from subsequent calculations if it is excluded by any one condition. Essentially, all selected conditions are chained with 'OR' logic.

The first block allows users to enter minimum and maximum OD filters. In this instance, all optical densities below the minimum or above the maximum OD filter settings will be censored.

The next option is a check box which will censor all optical densities which fall outside the range of the standard's optical densities which is listed within parentheses.

The next box allows the user to enter a CV filter. This will effectively exclude from overall mean calculations all ODs for a particular dilution where the within dilution CV is above this selected setting. Enter the number as a percentage, i.e., a number between 1 and 100.

The following box allows users to screen optical densities based on the asymptotes of the fitted standard curve. If the spline fit was selected on the previous screen, this box will be disabled. ODs will be censored if they fall below the lower or above the upper asymptote settings. For reference, the asymptotes are listed in the section title. When a percentage is entered, upon tabbing out of the box or clicking on another option, the program will calculate what the OD filter setting will be and echos this out in the gray area in the right side of the box. For example, if the upper asymptote for the standard curve is 3.5 and the user wishes to include only those unknown ODs that fall within 95% of the upper asymptote of the standard curve fit, then 5.0 would be entered in the 'Include values __ % below the upper asymptote' box. This would set the upper asymptote OD filter at 3.5 - (3.5 × 0.05) = 3.325 and all unknown ODs greater than this value will be censored. If the user wishes to use the values of the asymptotes themselves then enter 0.0 in both the lower and upper asymptote text boxes. This is unnecessary, however, as it is impossible to calculate concentrations for ODs that fall outside the range of the asymptotes. The program will flag these situations automatically as non calculable (N/C - see below).

Figure 19. Dialog window for optical density filter setting.

Figure 19. Dialog window for optical density filter setting.

The next box works in the same was the asymptotes box using the range of the standard optical densities in place of the bracketing asymptotes. As with the asymptotes, the values for the minimum and maximum standard OD are listed in the box title. When a percentage is entered, the newly defined filter is calculated and listed in the gray area in the right side of the box. All OD's below the minimum filter or above the maximum filter will be censored. The final censoring criteria is a check box which instructs the program to exclude all optical densities within a specific dilution if any one of them is censored using any one of the other options.

Click on 'Set and Exit' to save the filter settings and apply them to subsequent analyses. They will stay in place until the module is exited to the main menu or they may be erased by clicking on the 'Reset and Exit' button.

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Results Window

Figure 20 displays a typical screen displaying the results from this module. A complete listing is provided in Appendix A.

The header comments record the one line title statement if entered by the user in the opening dialog window (Figure 18). Also included are: the file name, the date and time the report was generated, the type of fit, and the four coefficients from the four parameter logistic-log function (which, of course, are missing if the spline fit was chosen in the dialog window, Figure 18). Note that the present parameterization of the logistic-log function determines the lower asymptote of the sigmoidal curve be defined as the sum of the first two coefficients. The upper asymptote is equal to the first coefficient. This is all to say that it is impossible to calculate concentrations for optical densities from patient unknowns or quality control samples which fall below the lower asymptote or above the upper asymptote as seen in Figure 21. The range of calculable values is listed in the report just under the coefficients. The report also lists the range of the dilutions for the standard reference serum. Next, the calibration factor is listed. If any optical density filters were set to automatically exclude ODs based on predetermined criteria. They will be detailed next. Each criteria will be followed by a letter in parentheses which is used to annotate the line listing for the report.

The body of the report begins with listing the plate and serum sample number selected by the user. It includes a listing of the sample number, and the optical densities which are grouped into blocks of serum samples as specified by the template used to abstract the original data. The dilutions corresponding to the optical densities are also detailed. The average optical density and concentration are given for each group of replicate samples in the serum sample series. ELISA for Windows considers all samples with the same dilution as members of a replicate series. If the serum sample did not contain a replicate sample, these averages would simply amount to the single OD and concentration. The report also lists the standard deviation and the coefficient of variation (CV) for the replicates. The CV is defined as:

(std.dev./average concentration) × 100.0.

If the serum sample does not contain a replicate sample the standard deviation and coefficient of variation are set equal to 0.0.

Referring to Figure 20, the 'N/C' designation in the right margin beside the second sample stands for Non Calculable. The optical densities for line number 2 is outside the range of permissible ODs as detailed in the header comments to the report. The descriptive statistics for the dilution containing this sample has been adjusted to reflect the absence of one calculated concentration value. If a plate is formatted that includes several replicates and only one or two ODs fell out of the range of permissible values, these statistics would still be calculated, using the subset of acceptable optical densities. The two entries for dilution 50 illustrate this, where line number 2 was excluded from the calculations. The average concentration for the pair is simply the value for the remaining line number in the replicate series. Figure 21 illustrates the primary cause for N/C conditions - the observed optical densities fall above or below the upper or lower, respectively, asymptotes for the standard curve.

Figure 20. Sample output from Module 6 - Calculate Concentrations.

Figure 20. Sample output from Module 6 - Calculate Concentrations.

Line numbers 3, 5, and 8 are excluded from the summary calculations due to a user defined filtering criteria–their optical densities fell above the preset level of 3.700. The last line lists the grand average concentration, standard deviation, and CV over all calculable samples within the unknown series. Refer to page 53 for a sample of a complete listing. Typically, the window used to display the results will not be large enough to frame the entire listing. There are horizontal and vertical scroll bars on the bottom and right side of the window, respectively. It should be noted that users may edit the contents of the output window. Comments may be added to further annotate the output. Several rudimentary Micro-soft Word operations will work in these windows. For example, text may be marked by clicking the left mouse key and dragging the cursor through the target text or pressing the shift key while moving the cursor through the text with the cursor control keys. Once text is marked it may be deleted, moved, etc.

Figure 21. Logistic-log plot showing areas of antibody concentration unestimability.

Figure 21. Logistic-log plot showing areas of antibody concentration unestimability.

The options available to the user at this stage appear at the bottom of the output window, beneath the horizontal scroll bar. If the user elected to save the results to a file, the option to save the results will be active and the output file name will be listed underneath the option button. Results will not be saved unless the 'Save Results to File' button is clicked. This allows the user to censor optical densities at will, using many steps and examining intervening results before deciding which set to actually save to the results file. If the user did not select the save file option in the opening dialog window for this module, the 'Save Report to File' option in the output screen will be suppressed. The user may also send the contents of the output window directly to the printer. In either case, all additional comments added to the output window will be included during the save and print operations. If the user elects to create a summary file, this will be indicated on the results screen. Results will be recorded automatically when the program returns to the previous screen (clicking the Return button). In this case the last round of calculations represents the results which will be recorded. If the summary file already contains an entry for the particular plate and unknown, it will be over-written by the present results. This is contrary to the results file where all results are appended to the end of an existing file. Previous results are never over-written.

The first line of options under the results window provides the flexibility of manually calculating antibody concentrations for optical densities not included in the unknowns file. After the optical density and dilution are entered in their respective boxes, clicking the Calc Concentration button will yield the concentration. Dilutions may be entered as the actual decimal number or the reciprocal equivalent (e.g., 0.0033333, 3.333E-3, or 300).

Another option gives the user the ability to include and/or exclude one or more data points and recalculate replicate and overall means, standard deviations, and CVs.

This option is displayed as:

<Exclude> [   ]

<Include> [   ]

The user may enter a single line number, several line numbers or a range of line numbers within the total range of line for the serum sample series (in the present example, this would be 1-14, listed in the first column of the output window). Single line numbers must be separated with a comma (,); a range of line numbers is indicated by using a hyphen (-); spaces are optional. Thus

1, 5, 7, 9 - 11, 15

would indicate the operation involves samples 1, 5, 7, 9, 10, 11, and 15.

Once a series of line numbers has been entered, clicking on Exclude or Include will mark those sample numbers for exclusion or inclusion from subsequent calculations. 'Ex' and 'In' will appear between the line number and the optical density to remind the user which sample numbers are to be excluded and included, respectively, from the next round of calculations. This operation may be repeated until just the desired samples are finally included in the summary statistics. To effect these final calculations, click the left mouse button on the Recalculate button. This will revise the output window, excluding/ including all previously marked samples. The notation 'Cen' will appear in the extreme right margin, indicating all samples that have been censured. Excluded samples may be re-included using the Include box. Note that the 'Ex' and 'In' markers will appear temporarily, that is, they disappear after recalculation. Lastly, if the user attempts to include samples that have been automatically censured because they are out of range of permissible optical densities (N/C samples) , ELISA for Windows will ignore these and continue to exclude them. In this case, the 'N/C' notation will remain in the right margin. Optical densities that were censored due to preset filters may be re-included with the Include function. They will re-enter the summary statistics after clicking on Recalculate.

Additional user comments added to the output window will be lost after recalculation.

Figure 20 displays the result of censuring line number 7. Again, this technique works in a toggle fashion. That is, the user may experiment with deleting and reentering specimens to observe the effect on the calculations of the descriptive statistics. If the user desired to reclaim sample number 7, simply entering 7 in the Include box, clicking on Include and then Recalculate would include the sample back into the calculations of means, standard deviations and CVs upon recalculation. Samples 3, 5, and 8 were censured due to preset filtering criteria–their optical densities fell above 3.700. They may also be re-included in the summary calculations using the Include function.

Users must experiment with these different features to achieve the final desired results. Once the selected line numbers have been censured, the user may record the results by saving them to a file or printing them. In this fashion, users may record their results at any point in the analysis stage. Alternatively, users may record results at the start of the process to retain a record of the unknown before any data were censured, and then record the output again after all relevant points have been deleted from statistics calculations.

If, in the opening dialog window, the user selects both serum sample and quality control samples to be included in the report, they will both appear in the output window with the QC report following the unknown listing (see page 53 for a sample listing). In this case, each will have its own set of descriptive statistics. While the preset filters will operate on both types of samples, the user will only be allowed to include/exclude line numbers from the serum sample series using the Recalculate function in the Report window. It will not be possible to manually censor samples in the QC part of the report. If it is necessary to exclude one or more samples from the QC block, then select only the QC option for the type of calculations in the opening dialog window (Figure 18).

Clicking on Exit will return the program to the initial dialog window (Figure 18).

A sample summary file is displayed in Figure 22. This file is mainly intended for export into other statistical analysis programs. However, it also serves as a useful compressed listing of results for each unknown and quality control sample in a file containing many plates. This file is grouped by plate and contains information pertinent to each plate. Plates are numbered sequentially. The header or comment lines which precede each plate are prefixed with a period (.) In column 1, followed by the plate number. This will help programmers extract these lines from the following data to facilitate data analysis. Each serum sample is represented by one line which contains the overall summary statistics. Each quality control sample contains as many lines as there are unique dilutions for each sample. The dilution is listed for the QC samples and is indicated as combined for the unknowns as their results are summarized over all dilutions.

Upon exiting this module ELISA for Windows returns to the main menu (Figure 3).

Figure 22. Sample summary (SUM) file.

Figure 22. Sample summary (SUM) file.

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