Calibration by a Reference Sample • midar

Feature abundances in samples can also be calibrated to corresponding abundances in a specified reference sample. MiDAR supports absolute (re-)calibration and normalization (relative calibration).

Absolute calibration of feature abundances is based on known metabolite concentrations in a reference sample (e.g., NIST SRM1950 plasma). Normalization (relative calibration) is based on calculating the abundance ratios of features in samples and a reference sample.

Below, we will demonstrate both absolute and relative calibration using NIST SRM1950 plasma samples that were measured as part of the same analysis..

Import data and metata,

library(midar)

# Get example data paths
dat_file = system.file("extdata", "S1P_MHQuant.csv", package = "midar")
meta_file = system.file("extdata", "S1P_metadata_tables.xlsx", package = "midar")

# Load data and metadata
mexp <- MidarExperiment()
mexp <- import_data_masshunter(mexp, dat_file, import_metadata = FALSE)
mexp <- import_metadata_analyses(mexp, path = meta_file, sheet = "Analyses")
mexp <- import_metadata_features(mexp, path = meta_file, sheet = "Features")
mexp <- import_metadata_istds(mexp, path = meta_file, sheet = "ISTDs")

Load known analyte concentrations of the reference sample

A table containing the known analyte concentrations for the NIST SRM1950 reference sample is now been added to the MidarExperiment object. Please note that the S1P concentrations provided in this table are intended for illustrative purposes only. The actual absolute S1P concentrations in NIST SRM1950 may differ significantly.

mexp <- import_metadata_qcconcentrations(mexp, path = meta_file, sheet = "QCconcentrations")
#> ✔ Analysis metadata associated with 65 analyses.
#> ✔ Feature metadata associated with 16 features.
#> ✔ Internal Standard metadata associated with 2 ISTDs.
#> ✔ QC concentration metadata associated with 1 annotated samples and 6 annotated analytes

Process the data

The analysis was performed using HILIC chromatography; thus, we need to correct for the isotope interferences from S1P 18:2;O2 M+2 and S1P 18:1;O2 M+2. Subsequently, initial quantification is done using the spiked-in ISTD concentration.

# Isotope correction
mexp <- midar::correct_interferences(mexp)
#> ✔ Interference-correction has been applied to 4 of the 16 features.

# Quantify the data
mexp <- normalize_by_istd(mexp)
#> ✔ 14 features normalized with 2 ISTDs in 65 analyses.
mexp <- quantify_by_istd(mexp)
#> ✔ 14 feature concentrations calculated based on 2 ISTDs and sample amounts of 65 analyses.
#> ℹ Concentrations are given in μmol/L.

Absolute calibration

We perform the absolute re-calibration using the function calibrate_by_reference(). The reference sample is set via reference_sample_id. In cases where multiple analyses of the same reference sample are present in the dataset, either the mean or median is calculated (defined via the summarize_fun).

The calibrated concentration is calculated as:

$c_\text{calibrated}^\text{Analyte} = \frac{c_\text{sample}^\text{Analyte}}{c_\text{ref}^\text{Analyte}} \times c_\text{known}^\text{Analyte}$

mexp_res <- calibrate_by_reference(
    data = mexp,
    variable = "conc",
    reference_sample_id = "SRM1950",
    absolute_calibration = TRUE,
    batch_wise = FALSE,
    summarize_fun = "mean",
    undefined_conc_action = "na"
  )
#> ! One or more feature concentration are not defined in the reference sample SRM1950. `NA` will be returned for these features. To change this, modify `undefined_conc_action` argument.
#> ✔ 6 feature concentrations were re-calibrated using the reference sample SRM1950.
#> ℹ Concentrations are given in umol/L.

The re-calibrated concentrations are stored in the variable conc , overwriting any previously calculated concentrations. The original concentrations, however, are still available via the variable conc_beforecal.

The re-calibrated concentrations can be exported as usual, and they also appear in the MiDAR XLSX report as concentrations.

# Export absolute calibration concentrations
save_dataset_csv(mexp, "calibrated.csv", variable = "conc")
#> ✔ Concentration values for 65 analyses and 7 features have been exported to 'calibrated.csv'.
  
# Export non-calibrated concentrations
save_dataset_csv(mexp_res, "noncalibrated.csv", variable = "conc_beforecal")
#> ✔ Conc_beforecal values for 65 analyses and 16 features have been exported to 'noncalibrated.csv'.

# Create XLSX report with calibrated concentrations as filtered dataset
save_report_xlsx(mexp_res, "report.xlsx", filtered_variable = "conc")
#> Saving report to disk - please wait...
#> ✔ The data processing report has been saved to 'report.xlsx'.

Normalization (relative calibration)

We can perform a simple normalization with a reference sample using the calibrate_by_reference() function, setting absolute_calibration = FALSE. In this approach, in cases where multiple analyses of the same reference sample are present in the dataset, either the mean or median is calculated (defined via the summarize_fun).

mexp_res <- calibrate_by_reference(
    data = mexp,
    variable = "conc",
    reference_sample_id = "SRM1950",
    absolute_calibration = FALSE,
    summarize_fun = "mean"
  )
#> ✔ All features were normalized with reference sample SRM1950 features.
#> ℹ Unit is: sample [conc] / SRM1950 [conc]

The results of the normalization are stored, unlike for the absolute calibration, as ratios, in a new variable, [VARIABLE]_normalized, where [VARIABLE] is the input variable, e.g., conc_normalized or intensity_normalized.

The normalized concentrations can be exported as [VARIABLE]_normalized using save_dataset_csv(). In the MiDAR XLSX report generated by save_report_xlsx(), the unfiltered dataset with normalized concentrations is included by default. To include the normalized concentrations as the filtered dataset, set filtered_variable = “[VARIABLE]_normalized as an argument.

# Export NIST1950-normalized concentrations
save_dataset_csv(mexp_res, "norm.csv", variable = "conc_normalized")
#> ✔ Conc_normalized values for 65 analyses and 16 features have been exported to 'norm.csv'.

# Create XLSX report with normalized concentrations as filtered dataset
save_report_xlsx(mexp_res, "report_norm.xlsx", filtered_variable = "conc_normalized")
#> Saving report to disk - please wait...
#> ✔ The data processing report has been saved to 'report_norm.xlsx'.

Batch-wise calibration

Calibration can also be applied batch-wise, in which case each batch is calibrated separately with the data from the reference sample in the same batch. This is done by setting batch_wise = TRUE and can be used in both absolute and relative calibration.

This approach can be used to correct batches or assays/plates using a reference material shared across the batches.

mexp_res <- calibrate_by_reference(
    data = mexp,
    variable = "conc",
    reference_sample_id = "SRM1950",
    absolute_calibration = TRUE,
    batch_wise = TRUE,
    summarize_fun = "mean",
    undefined_conc_action = "na"
  )
#> ! One or more feature concentration are not defined in the reference sample SRM1950. `NA` will be returned for these features. To change this, modify `undefined_conc_action` argument.
#> ✔ 6 feature concentrations were batch-wise re-calibrated using the reference sample SRM1950.
#> ℹ Concentrations are given in umol/L.

save_dataset_csv(mexp_res, "bathwise_calibrated.csv", variable = "conc_beforecal")
#> ✔ Conc_beforecal values for 65 analyses and 16 features have been exported to 'bathwise_calibrated.csv'.

Concentration ratio and bias

To examine the ratio between measured and expected (known) concentrations in the reference samples, a table with concentration ratios can be generated using the code below.

The ratio is calculated as follows:

$R_\text{ratio}^\text{Analyte} = \frac{c_\text{measured}^\text{Analyte}}{c_\text{expected}^\text{Analyte}}$

mexp_res <- calibrate_by_reference(
    data = mexp,
    variable = "conc",
    reference_sample_id = "SRM1950",
    absolute_calibration = TRUE,
    summarize_fun = "mean",
    undefined_conc_action = "na",
    store_conc_ratio = TRUE
  )
#> ! One or more feature concentration are not defined in the reference sample SRM1950. `NA` will be returned for these features. To change this, modify `undefined_conc_action` argument.
#> ✔ 6 feature concentrations were re-calibrated using the reference sample SRM1950.
#> ℹ Concentrations are given in umol/L.

tbl_ref_bias <- mexp_res$dataset |> 
  filter(sample_id == "SRM1950", is_quantifier) |> 
  group_by(feature_id) |> 
  summarise(bias_mean = mean(feature_conc_ratio))

gt::gt(tbl_ref_bias)

feature_id	bias_mean
S1P d16:1 [M>60]	0.4323975
S1P d17:1 [M>60]	0.3452700
S1P d18:0 [M>60]	0.2917255
S1P d18:1 13C2D2 (ISTD) [M>60]	NA
S1P d18:1 [M>60]	0.3453086
S1P d18:2 [M>60]	0.3554366
S1P d19:1 [M>60]	0.3081062
S1P d20:1 [M>60]	NA

A ratio value of 1 indicates perfect agreement between the measured and expected concentrations.
Values greater than 1 suggest overestimation, while values less than 1 indicate underestimation.
The ratio values can also be visualized or further analyzed to identify outliers or investigate potential issues in the analytical process or calibration.

We can also calculate ratio and bias of QC samples directly without haveing to apply calibrate_by_reference(). For illustration, we calculated the ratio and bias of the QC samples using the re-calibrated data from above, expecting the all corrected feature concentrations in the reference sample to have no bias (0%) and a ratio of 1.

tbl <- get_qc_bias_variability(mexp_res, qc_types = "NIST")
gt::gt(tbl) |> gt::fmt_number(decimals = 3)

feature_id	sample_id	qc_type	n	conc_target	conc_mean	conc_sd	cv_intra
S1P d16:1 [M>60]	SRM1950	NIST	2.000	0.107	0.107	0.016	14.771
S1P d17:1 [M>60]	SRM1950	NIST	2.000	0.028	0.028	0.001	3.550
S1P d18:0 [M>60]	SRM1950	NIST	2.000	0.149	0.149	0.001	0.995
S1P d18:1 [M>60]	SRM1950	NIST	2.000	0.985	0.985	0.000	0.040
S1P d18:2 [M>60]	SRM1950	NIST	2.000	0.290	0.290	0.004	1.460
S1P d19:1 [M>60]	SRM1950	NIST	2.000	0.025	0.025	0.002	9.713

The bias and concentration rations before the re-calibration can be viewed by using the MidarExperient object that had no calibration applied

tbl <- get_qc_bias_variability(mexp, qc_types = "NIST", with_conc_ratio = TRUE)
gt::gt(tbl) |> gt::fmt_number(decimals = 3)

feature_id	sample_id	qc_type	n	conc_target	conc_mean	conc_sd	cv_intra	bias	conc_ratio
S1P d16:1 [M>60]	SRM1950	NIST	2.000	0.107	0.046	0.007	14.771	−56.760	0.432
S1P d17:1 [M>60]	SRM1950	NIST	2.000	0.028	0.010	0.000	3.550	−65.473	0.345
S1P d18:0 [M>60]	SRM1950	NIST	2.000	0.149	0.043	0.000	0.995	−70.827	0.292
S1P d18:1 [M>60]	SRM1950	NIST	2.000	0.985	0.340	0.000	0.040	−65.469	0.345
S1P d18:2 [M>60]	SRM1950	NIST	2.000	0.290	0.103	0.002	1.460	−64.456	0.355
S1P d19:1 [M>60]	SRM1950	NIST	2.000	0.025	0.008	0.001	9.713	−69.189	0.308