Standard Curve: log10(Conc) vs CT
Traditional Standard Curve: CT vs log10(Conc)
Fitted Formula
Model 1: log10(Conc) vs CT (For Concentration Prediction)
Parameter Estimates with 95% CI
Model 2: Traditional Standard Curve (CT vs log10 Conc)
Amplification Efficiency
Replicate Precision (CV Analysis)
Outlier Detection (|Residual| > 2 SD)
LOD / LOQ Estimation
Standard Curve Quality Assessment
Residuals
Normality Check (Q-Q Plot)
p < 0.05: residuals deviate from normality (consider reviewing data)
qPCR Absolute Quantification - User Guide
1. Overview
This app performs qPCR absolute quantification by constructing a standard curve from known-concentration samples, then using that curve to calculate the concentration of unknown samples. The standard curve relates CT (Cycle Threshold) values to the logarithm of known concentrations via linear regression.
2. Data Input Methods
A. Demo Data
Pre-loaded example data: 10-fold serial dilution from 10^8 to 10^3 copies/uL, 3 replicates per point.
B. Upload File
Upload an Excel (.xlsx) or CSV file. The app auto-detects CT and Concentration columns. Multiple CT columns (CT1, CT2, CT3) are auto-stacked into long format.
Concentration CT1 CT2 CT3 1e+08 15.51 15.52 15.50 1e+07 18.91 18.84 18.73 ...
Tip: Click 'Download Standard Curve Template (.xlsx)' for a pre-formatted file.
C. Manual Input
Enter CT values directly. Specify starting concentration and dilution factor, then enter 1-3 CT values per dilution point. Concentrations are calculated automatically.
3. Standard Curve & Algorithms
The app fits two equivalent linear regression models:
Model 1 (for prediction): log10(Conc) = a + b * CT
Model 2 (traditional): CT = c + d * log10(Conc)
where b = 1/d (slope relationship between the two models)
Concentration prediction: Given an unknown sample CT value:
log10(Conc) = a + b * CT
Conc = 10^(a + b * CT)
Conc_final = Conc * Dilution_Factor
95% Prediction Interval: Using residual SE (s), df, and leverage:
PI = y_hat +/- t(0.975, df) * s * sqrt(1 + 1/n + (x - x_bar)^2 / Sxx)
Conc_Lower = 10^(y_hat - PI), Conc_Upper = 10^(y_hat + PI)
Amplification Efficiency:
E = 10^(-1/d) - 1 (d = slope of CT vs log10(Conc))
95% CI via Delta method: dE/dd = 10^(-1/d) * ln(10) / d^2. Acceptable: 90%-110% (d: -3.58 to -3.10). Ideal: E=100% (d=-3.32).
LOD / LOQ Estimation:
LOD (prediction-based) = 10^(y_pred_low - 3 * s)
LOQ = 10^(y_pred_low - 10 * s)
LOD (ICH style) = 10^(3.3 * s / |slope|)
s = residual standard error, y_pred_low = predicted log10(Conc) at lowest concentration point.
Outlier Detection: Points where |residual| > 2 * SD(residuals) are flagged as outliers.
Normality Check: Shapiro-Wilk test on residuals. p > 0.05 indicates normal distribution. Q-Q plot provided.
4. Gene Summary (Replicate Grouping)
When batch upload file contains a gene/identifier column (Gene, Target, ID, Name, Sample, etc.), the app groups identical names and computes:
Mean_CT = mean(CT_1, ..., CT_n)
SD_CT = sd(CT_1, ..., CT_n), CV_CT(%) = SD_CT / Mean_CT * 100
Predicted_log10_Conc = mean(log10(Conc_i))
Geometric_Mean_Conc = 10^mean(log10(Conc_i)) (recommended for qPCR)
Arithmetic_Mean_Conc = mean(Conc_1, ..., Conc_n)
Error bounds (Conc_Lower / Conc_Upper):
N = 1 (single replicate):
Uses standard curve 95% prediction interval: 10^(y_hat +/- t * s * sqrt(...))
N >= 2 (multiple replicates):
Conc_Lower = mean(Conc) - t(0.975, n-1) * SD(Conc) / sqrt(n)
Conc_Upper = mean(Conc) + t(0.975, n-1) * SD(Conc) / sqrt(n)
Gene names can be anonymous - the app only requires identical strings to group replicates.
Batch Upload File Format
Upload an Excel or CSV file with CT values. The app auto-detects the CT column and gene/identifier column.
Gene CT Sample GAPDH 20.51 S1 GAPDH 20.62 S1 GAPDH 20.48 S1 ACTB 22.15 S2 ACTB 22.31 S2 B2M 19.87 S3
Gene/ID column:
Target gene or sample identifier. Auto-detected from columns named Gene, Target, ID, Name, Sample, or any header containing these keywords. Same values are grouped as replicates.
CT:
Numeric CT value from qPCR instrument.
Other columns:
Additional columns (Sample, Well, Notes) are preserved in output.
Tip: Click 'Download Batch Template (.xlsx)' in the sidebar for a pre-formatted file.
5. Quality Control Checklist
| Criterion | Acceptable | Pass Rule |
|---|---|---|
| R-squared | >= 0.98 | Pass if >= 0.98 |
| Efficiency (E) | 90% - 110% | Pass if in range |
| Replicates CV | < 5% | Pass if < 5% |
| Outliers | 0 | Pass if none |
Overall Grade: Excellent (4/4 pass), Acceptable (2-3/4), Poor (0-1/4).
6. Excel Full Report
6 sheets: (1) Parameters & Statistics, (2) Standard Curve Data, (3) Quality Score, (4) Outliers, (5) Gene Summary, (6) Quantification Results.
7. Tips & Troubleshooting
- Use 5-6 dilution points spanning 5-7 orders of magnitude.
- Run 2-3 technical replicates per dilution point.
- If E < 90%, check for PCR inhibitors or primer issues.
- If R-squared < 0.98, check pipetting accuracy and outliers.
- Gene names can be fake/anonymous - only identical strings are needed for grouping.
- If Gene Summary does not appear, ensure your file has a column named Gene, Target, ID, Name, or Sample.