Linear Regression Absolute Quantification

linear-regression-absolute-quantification

Summary

Fit a weighted linear regression model to calibration-line samples with known concentrations, then use the fitted model to predict absolute concentrations for study samples from their measured compound/internal-standard ratios. This enables absolute quantification of metabolites in untargeted metabolomics workflows.

When to use

Apply this skill when you have a set of calibration samples (spiked compounds) with known concentrations, measured compound and internal-standard peak areas, and you need to convert compound/internal-standard ratios from study samples into absolute concentrations. The calibration samples must span a relevant concentration range that brackets the expected study sample concentrations.

When NOT to use

• Study samples lack corresponding internal-standard measurements or peak areas are zero/missing.
• Calibration line contains fewer than 3 reliable points or spans an insufficient concentration range for the unknowns.
• Study sample ratios fall far outside the range of calibration-line ratios (extrapolation beyond model validity).

Inputs

• SummarizedExperiment object with compound peak areas, internal-standard peak areas, and a concentration column (with values for calibration samples, NA for study samples)
• Tab-delimited text file with calibration sample metadata including concentration values
• Calculated compound/internal-standard ratios for all samples

Outputs

• Predicted absolute concentrations for all study samples
• Fitted linear regression model (coefficients, R² value)
• Concentration plot (scatter plot showing calibration points, fitted line, and predicted sample concentrations)
• Updated SummarizedExperiment object with concentration predictions and R² in assay and rowData slots

How to apply

First, filter the experiment object to retain only calibration samples (those with non-missing concentration values in the concentration column). Calculate the compound/internal-standard ratio for each calibration sample from their measured peak areas. Fit a weighted linear regression model with the ratio as the predictor variable and the known concentration as the response variable using R's lm() or weighted.lm() function (weighting by measurement precision or area values reduces influence of outliers). Apply the fitted model coefficients to all study samples (those with concentration = NA) to generate predicted concentrations from their measured ratios. The workflow should also compute and report the R² value of the calibration line as a quality metric for the fitted model. Ideally, predicted study sample concentrations should fall within or near the range spanned by the calibration line; predictions far outside this range indicate extrapolation and reduced reliability.

Related tools

• mzQuality (R package that implements the complete workflow: reads experiment data into SummarizedExperiment objects, calculates compound/internal-standard ratios, fits weighted linear models to calibration samples, predicts concentrations for study samples, and generates concentration plots) — https://github.com/hankemeierlab/mzQuality
• SummarizedExperiment (Bioconductor container object that stores assays (peak areas, ratios, concentrations), rowData (compound metadata), and colData (sample metadata including concentration labels and type)) — https://bioconductor.org/packages/release/bioc/html/SummarizedExperiment.html
• R lm/weighted.lm (Base R and stats functions used to fit the linear regression model with optional weights)
• mzQualityDashboard (Shiny application frontend that provides interactive visualization and parameter control for the concentration plot and model fitting workflow without requiring R programming) — https://github.com/hankemeierlab/mzQualityDashboard

Examples

exp <- doAnalysis(exp = exp); concentrationPlot(exp)

Evaluation signals

• R² value of the fitted calibration line should be ≥ 0.90 (or user-defined threshold) to indicate a strong linear relationship.
• Residuals of calibration samples should be approximately normally distributed and homoscedastic (constant variance) when plotted against fitted values.
• Predicted concentrations for study samples should fall within or near the concentration range of the calibration line; predictions requiring large extrapolation warrant flagging.
• Concentration plot should show calibration points scattered around the fitted line with study sample predictions projected onto or near the line.
• The fitted model coefficients (slope and intercept) should be positive (or match expected stoichiometry) and remain stable across repeated analyses of the same calibration samples.

Limitations

• Requires calibration samples with accurately known concentrations; mislabeled or contaminated calibration samples will produce invalid models.
• Linear regression assumes a linear relationship between ratio and concentration; non-linear or saturation effects at high concentrations may violate this assumption.
• Predictions outside the calibration concentration range are unreliable and should not be reported without explicit uncertainty intervals.
• The method depends on the stability and accuracy of internal-standard peak area measurements; poor IS performance compromises ratio-based quantification.
• Weighted regression requires careful choice of weights; inappropriate weighting can introduce bias or over-fit noise.

Evidence

• [other] Calibration line filtering and ratio calculation: "Filter the experiment object to retain only calibration samples with known concentrations using the concentration column. Calculate the compound/internal-standard ratio for each calibration sample."
• [other] Linear regression fitting step: "Fit a weighted linear regression model with ratio as predictor and concentration as response using R's lm or weighted-lm function."
• [other] Prediction and visualization: "Apply the fitted model to all study samples (those with concentration = NA) to predict their absolute concentrations from their measured ratios. Generate a concentration plot showing calibration"
• [intro] mzQuality absolute concentration calculation capability: "by supplying calibration line samples and known concentrations for spiked compounds, mzQuality is able to calculate absolute concentrations"
• [intro] Concentration plot interpretation: "The Concentration Plot is a scatter plot with a linear model added, based on the calculated ratio and known concentration. The measurements of the other samples are projected on this line,"
• [readme] doAnalysis workflow includes concentration calculation: "If known concentrations for calibration lines have been supplied, the doAnalysis function will also calculate the concentrations and the corresponding R2 value given the provided calibration lines."