Reading the plate object

The basic functionality of the PvSTATEM package is reading raw MBA data. To present the package’s functionalities, we use a sample dataset from the Covid OISE study, which is pre-loaded into the package. You might want to replace these variables with paths to your files on your local disk. Firstly, let us load the dataset as the plate object.

library(PvSTATEM)

plate_filepath <- system.file("extdata", "CovidOISExPONTENT.csv", package = "PvSTATEM", mustWork = TRUE) # get the filepath of the csv dataset

layout_filepath <- system.file("extdata", "CovidOISExPONTENT_layout.xlsx", package = "PvSTATEM", mustWork = TRUE)


plate <- read_luminex_data(plate_filepath, layout_filepath) # read the data
#> Reading Luminex data from: C:/Users/tymot/AppData/Local/Temp/Rtmpk1YQco/Rinst523856934c41/PvSTATEM/extdata/CovidOISExPONTENT.csv
#> using format xPONENT
#> 
#> New plate object has been created with name: CovidOISExPONTENT!
#> 
plate
#> Plate with 96 samples and 30 analytes

Processing the whole plate

Once we have loaded the plate object we may process it using the function process_plate. This function fits a model to each analyte using the standard curve samples and computes the dilutions for each analyte using the corresponding model. The computed dilutions are then saved to a CSV file.

tmp_dir <- tempdir(check = TRUE)
test_output_path <- file.path(tmp_dir, "output.csv")
process_plate(plate, output_path = test_output_path)
#> Fitting the models and computing the dilutions for each analyte
#> Saving the computed dilutions to a CSV file located in: 'C:\Users\tymot\AppData\Local\Temp\RtmpOU19fF/output.csv'

Quality control and normalization details

Apart from the process_plate function, the package provides a set of functions that allow for more detailed and advanced quality control and normalization of the data.

Plate summary and details

After the plate is successfully loaded, we can look at some basic information about it.

plate$summary()
#> Summary of the plate with name 'CovidOISExPONTENT':
#> Total number of samples: 96
#> Number of blank samples: 1
#> Number of standard curve samples: 11
#> Number of positive control samples: 0
#> Number of negative control samples: 0
#> Number of test samples: 84
#> Number of analytes: 30
plate$summary(include_names = TRUE) # more detailed summary
#> Summary of the plate with name 'CovidOISExPONTENT':
#> Total number of samples: 96
#> Number of blank samples: 1
#> Number of standard curve samples: 11
#> Sample names: '1/50', '1/100', '1/200', '1/400', '1/800', '1/1600', '1/3200', '1/6400', '1/12800', '1/25600', '1/102400'
#> Number of positive control samples: 0
#> Number of negative control samples: 0
#> Number of test samples: 84
#> Number of analytes: 30
plate$sample_names
#>  [1] "B"              "1/50"           "1/100"          "1/200"         
#>  [5] "1/400"          "1/800"          "1/1600"         "1/3200"        
#>  [9] "1/6400"         "1/12800"        "1/25600"        "1/102400"      
#> [13] "CO-F-226-01-CF" "CO-F-263-02-KC" "CO-F-080-02-TV" "CO-F-215-01-BA"
#> [17] "CO-H-SD-039-BC" "CO-H-RD-053-MO" "CO-F-030-01-LA" "CO-F-204-01-TC"
#> [21] "CO-F-009-01-CS" "CO-F-156-02-GB" "CO-F-402-03-DE" "CO-H-SK-021-BC"
#> [25] "CO-F-226-02-CM" "CO-F-266-01-LC" "CO-F-080-03-TA" "CO-F-215-02-BN"
#> [29] "CO-H-SD-042-DD" "CO-H-RK-002-BA" "CO-F-031-01-LD" "CO-F-204-02-TT"
#> [33] "CO-F-021-03-DF" "CO-F-156-03-GN" "CO-F-402-04-DR" "CO-H-SK-023-DC"
#> [37] "CO-F-226-03-CG" "CO-F-272-01-DF" "CO-F-080-04-TM" "CO-F-215-03-BA"
#> [41] "CO-H-SK-004-GA" "CO-H-RK-004-WN" "CO-F-112-01-CN" "CO-F-220-01-VV"
#> [45] "CO-F-028-01-PJ" "CO-F-214-01-SP" "CO-F-402-05-DS" "CO-H-SK-029-LC"
#> [49] "CO-F-234-01-LC" "CO-F-310-01-DC" "CO-F-082-01-OF" "CO-F-299-01-CS"
#> [53] "CO-H-SK-006-MS" "CO-H-RK-007-CJ" "CO-F-180-01-PN" "CO-F-243-01-BL"
#> [57] "CO-F-124-01-SV" "CO-F-237-01-LE" "CO-H-SD-002-WL" "CO-H-SK-030-MJ"
#> [61] "CO-F-234-02-LS" "CO-F-311-01-PC" "CO-F-089-01-DP" "CO-F-325-01-LN"
#> [65] "CO-H-SK-011-CC" "CO-H-RK-009-MB" "CO-F-180-02-DM" "CO-F-243-02-SH"
#> [69] "CO-F-134-01-MK" "CO-F-281-01-BV" "CO-H-SD-013-LV" "CO-H-SK-031-CP"
#> [73] "CO-F-260-01-GD" "CO-F-075-01-BA" "CO-F-089-02-DC" "CO-H-SD-004-CG"
#> [77] "CO-H-SK-051-DA" "CO-H-RK-010-VP" "CO-F-180-03-DR" "CO-F-276-01-ME"
#> [81] "CO-F-134-02-GM" "CO-F-402-01-BH" "CO-H-SD-043-BS" "CO-H-SK-039-AA"
#> [85] "CO-F-260-02-GC" "CO-F-075-02-FM" "CO-F-139-01-BP" "CO-H-SD-021-PC"
#> [89] "CO-H-SK-056-MN" "CO-F-027-02-SL" "CO-F-180-04-DC" "CO-F-027-01-SF"
#> [93] "CO-F-156-01-GA" "CO-F-402-02-DV" "CO-H-SK-018-VC" "CO-F-045-01-SN"
plate$analyte_names
#>  [1] "Spike_6P"      "ME"            "HKU1_S"        "OC43_NP"      
#>  [5] "OC43_S"        "HKU1_NP"       "X229E_NP"      "Mumps_NP"     
#>  [9] "RBD_B16171"    "NL63_NP"       "RBD_B16172"    "RBD_wuhan"    
#> [13] "NL63_S"        "X229E_S"       "Spike_B16172"  "Spike_B117"   
#> [17] "Measles_NP"    "Ade5"          "NP"            "Spike_P1"     
#> [21] "Rub"           "Ade40"         "RBD_B117"      "Spike_B1351"  
#> [25] "FluA"          "RBD_B1351"     "RBD_P15"       "S2"           
#> [29] "Spike_omicron" "RBD_omicron"

The summary can also be accessed using the built-in generic method summary.

summary(plate)
#> Summary of the plate with name 'CovidOISExPONTENT':
#> Total number of samples: 96
#> Number of blank samples: 1
#> Number of standard curve samples: 11
#> Number of positive control samples: 0
#> Number of negative control samples: 0
#> Number of test samples: 84
#> Number of analytes: 30

Quality control

The package can plot the dilutions along the MFI values, allowing manual inspection of the standard curve. This method raises a warning in case the MFI values were not adjusted using the blank samples.

plot_standard_curve_analyte(plate, analyte_name = "OC43_S")

plate$blank_adjustment()
#> Plate with 96 samples and 30 analytes
print(plate$blank_adjusted)
#> [1] TRUE
plot_standard_curve_analyte(plate, analyte_name = "OC43_S")

We can also plot the standard curve for different analytes and data types. A list of all available analytes on the plate can be accessed using the command plate$analyte_names.

By default, all the operations are performed on the Median value of the samples; this option can be selected from the data_type parameter of the function.

plot_standard_curve_analyte(plate, analyte_name = "RBD_wuhan", data_type = "Mean")

plot_standard_curve_analyte(plate, analyte_name = "RBD_wuhan", data_type = "Avg Net MFI")

This plot may be used to assess the quality of the standard curve and anticipate some of the potential issues with the data. For instance, if we plotted the standard curve for the analyte, ME we could notice that the Median value of the sample with a dilution of 1/25600 is abnormally large, which may indicate a problem with the data.

plot_standard_curve_analyte(plate, analyte_name = "ME")

plot_standard_curve_analyte(plate, analyte_name = "ME", log_scale = "all")

The plotting function has more options, such as selecting which axis the log scale should be applied or reversing the curve. More detailed information can be found in the function documentation, accessed by executing the command ?plot_standard_curve_analyte.

Another useful method of inspecting the potential errors of the data is plot_mfi_for_analyte. This method plots the MFI values of standard curve samples for a given analyte along the boxplot of the MFI values of the test samples.

It helps identify the outlier samples and check if the test samples are within the range of the standard curve samples.

plot_mfi_for_analyte(plate, analyte_name = "OC43_S")

plot_mfi_for_analyte(plate, analyte_name = "Spike_6P")

It can be seen that for the Spike_6P analyte, the MFI values don’t fall within the range of the standard curve samples, which could be problematic for the model. The values of test dilutions will be extrapolated from the standard curve, which may lead to incorrect results.

Normalization

After inspection, we may create the model for the standard curve of a certain antibody. The model is fitted using the nplr package, which provides a simple interface for fitting n-parameter logistic regression models, but to create a clearer interface for the user, we encapsulated this model into our own class called Model for simplicity. The detailed documentation of the Model class can be found by executing the command ?Model.

The model is then used to predict the dilutions of the samples based on the MFI values.

nplr package fits the model using the formula:

\[ y = B + \frac{T - B}{[1 + 10^{b \cdot (x_{mid} - x)}]^s} \]

Where:

  • \(y\) is the predicted value, MFI in our case,

  • \(x\) is the independent variable, dilution in our case,

  • \(B\) is the bottom plateau - the right horizontal asymptote,

  • \(T\) is the top plateau - the left horizontal asymptote,

  • \(b\) is the slope of the curve at the inflection point,

  • \(x_{mid}\) is x-coordinate at the inflection point,

  • \(s\) is the asymmetric coefficient.

This equation is referred to as the Richards’ equation. More information about the model can be found in the nplr package documentation.

By default, the nplr model transforms the x values using the log10 function.

model <- create_standard_curve_model_analyte(plate, analyte_name = "OC43_S")

model
#> Instance of the Model class fitted for analyte ' OC43_S ': 
#>  - fitted with 5 parameters
#>  - using 11 samples
#>  - using log residuals (mfi):  TRUE 
#>  - using log dilution:  TRUE 
#>  - top asymptote: 28414.96 
#>  - bottom asymptote: 38.60885 
#>  - goodness of fit: 0.9970645 
#>  - weighted goodness of fit: 0.9998947

Since our model object contains all the characteristics and parameters of the fitted regression model. The model can be used to predict the dilutions of the samples based on the MFI values. The output above shows the most important parameters of the fitted model.

The predicted values may be used to plot the standard curve, which can be compared to the sample values.

plot_standard_curve_analyte_with_model(plate, model, log_scale = c("all"))

plot_standard_curve_analyte_with_model(plate, model, log_scale = c("all"), plot_asymptote = FALSE)

Apart from the plotting, the package can predict the values of all the samples on the plate.

mfi_values <- plate$data$Median$OC43_S
head(mfi_values)
#> [1]   43.0 4193.0 1982.0 1308.0  681.0  365.5
predicted_dilutions <- predict(model, mfi_values)

head(predicted_dilutions)
#>      MFI dilution.025     dilution dilution.975
#> 1   43.0 4.962680e-08 2.375259e-06 1.171298e-05
#> 2 4193.0 1.716079e-02 2.068201e-02 2.526140e-02
#> 3 1982.0 7.086349e-03 8.326658e-03 9.802462e-03
#> 4 1308.0 4.489496e-03 5.240371e-03 6.128349e-03
#> 5  681.0 2.178984e-03 2.556577e-03 3.002350e-03
#> 6  365.5 1.038248e-03 1.242669e-03 1.483215e-03

The dataframe contains original MFI values and the predicted dilutions based on the model. Since the dilution values are obtained by reversing the logistic model formula, the predictions also include the confidence intervals for the dilutions. The interval is represented as its upper and bottom bounds, which are stored in columns dilution.025 and dilution.975, respectively.