Functions

The rtpcr package gets efficiency (E) the Ct values of genes and performs different analyses using the following functions.

Function	Description
`ANOVA_DCt`	$\Delta Ct$ ANOVA analysis
`ANOVA_DDCt`	$\Delta\Delta Ct$ ANOVA analysis
`ANCOVA_DDCt`	$\Delta\Delta Ct$ ANCOVA analysis
`REPEATED_DDCt`	$\Delta\Delta Ct$ ANOVA analysis for repeated-measures data
`TTEST_DDCt`	$\Delta\Delta Ct$ method t-test analysis
`WILCOX_DDCt`	$\Delta\Delta Ct$ method wilcox.test analysis
`plotFactor`	Bar plot of gene expression for one-, two- or three-factor experiments
`Means_DDCt`	Pairwise comparison of RE values for any user-specified effect
`efficiency`	Amplification efficiency statistics and standard curves
`meanTech`	Calculate mean of technical replicates
`multiplot`	Combine multiple ggplot objects into a single layout
`compute_wDCt`	Cleaning data and weighted delta Ct (wDCt) calculation
`long_to_wide`	Converts a 4-column qPCR long data format to wide format

Quick start

Installing and loading

The rtpcr package can be installed by running the following code in R:

from CRAN:

# Installing from CRAN
install.packages("rtpcr")

# Loading the package
library(rtpcr)

Or from from GitHub (developing version):

devtools::install_github("mirzaghaderi/rtpcr", build_vignettes = TRUE)

Input data structure

For relative expression analysis (using TTEST_DDCt, ANOVA_DCt, ANOVA_DDCt and REPEATED_DDCt functions), the amplification efficiency (E) and Ct or Cq values (the mean of technical replicates) is used for the input table. If the E values are not available you should use ‘2’ instead representing the complete primer amplification efficiency. The required column structure of the input data is:

Experimental condition columns (and one block if available NOTE 1)
Replicates information (biological replicates or subjects; see NOTE 2, and NOTE 3)
Target genes efficiency and Ct values (a pair column for each gene).
Reference genes efficiency and Ct values (a pair column for each gene) NOTE 4.

The package supports one or more target or reference gene(s), supplied as efficiency–Ct column pairs. Reference gene columns must always appear last. A sample input data is presented below.

NOTE 1

When a qPCR experiment is done in multiple qPCR plates, variation resulting from the plates may interfere with the actual amount of gene expression. One solution is to conduct each plate as a randomized block so that at least one replicate of each treatment and control is present on a plate. Block effect is usually considered as random and its interaction with any main effect is not considered.

NOTE 2

For TTEST_DDCt, ANOVA_DCt, and ANOVA_DDCt, each row is from a separate and unique biological replicate. For example, a dataframe with 12 rows has come from an experiment with 12 individuals. The REPEATED_DDCt function is intended for experiments with repeated observations (e.g. time-course data). For REPEATED_DDCt, the Replicate column contains identifiers for each individual (id or subject). For example, all rows with a 1 at Rep column correspond to a single individual, all rows with a 2 correspond to another individual, and so on, which have been sampled at specific time points.

NOTE 3

Your data table may also include a column of technical replicates (so there would be both biological replicates and technical replicate columns in the data). In this case, the meanTech function should be applied first to calculate the mean of the technical replicates. The resulting table is then used as the input for expression analysis. To use the meanTech function correctly, the technical replicate column must appear immediately after the biological replicate column (see Mean of technical replicates for an example).

NOTE 4

Complete amplification efficiency (E) in the rtpcr package is denoted by 2. This means that 2 indicates 100%, and 1.85 and 1.70 indicate 0.85% and 0.70% amplification efficiencies.

Handling missing data

The rtpcr package does not replace a Ct value with a predetermined value (such as a predefined value of 40, mean Ct values of other replicates, or any imputed value). However missing data can be denoted by NA in the input data frame. Values such as ‘0’ and ‘undetermined’ (for any E and Ct) are automatically converted to NA before passing to the downstream analysis. For target genes, NA for E or Ct measurements cause returning NA for the corresponding ΔCt for that replicate which is passed along to downstream statistical analyses. If there are more than one reference genes, NA in the place of the E or the Ct value of any reference gene cause skipping that reference gene and remaining genes are averaged in that replicate. If more sophisticated handling of missing Ct values is desired, qPCR imputation tools can be used in advance of analysis with rtpcr.

Data Analysis

Amplification Efficiency

The efficiency function calculates the amplification efficiency (E), slope, and R² statistics for genes, and performs pairwise comparisons of slopes. It takes a data frame in which the first column contains the dilution ratios, followed by the Ct value columns for each gene.

# Applying the efficiency function
data <- read.csv(system.file("extdata", "data_efficiency1.csv", package = "rtpcr"))
data
dilutions   Gene1   Gene2   Gene3
1.00    25.58   24.25   22.61
1.00    25.54   24.13   22.68
1.00    25.50   24.04   22.63
0.50    26.71   25.56   23.67
0.50    26.73   25.43   23.65
0.50    26.87   26.01   23.70
0.20    28.17   27.37   25.11
0.20    28.07   26.94   25.12
0.20    28.11   27.14   25.11
0.10    29.20   28.05   26.17
0.10    29.49   28.89   26.15
0.10    29.07   28.32   26.15
0.05    30.17   29.50   27.12
0.05    30.14   29.93   27.14
0.05    30.12   29.71   27.16
0.02    31.35   30.69   28.52
0.02    31.35   30.54   28.57
0.02    31.35   30.04   28.53
0.01    32.55   31.12   29.49
0.01    32.45   31.29   29.48
0.01    32.28   31.15   29.26

# Analysis
efficiency(data)

$Efficiency
   Gene     Slope        R2        E
1 Gene1 -3.388094 0.9965504 1.973110
2 Gene2 -3.528125 0.9713914 1.920599
3 Gene3 -3.414551 0.9990278 1.962747

$Slope_compare
$contrasts
 contrast          estimate    SE df t.ratio p.value
 C2H2.26 - C2H2.01   0.1400 0.121 57   1.157  0.4837
 C2H2.26 - GAPDH     0.0265 0.121 57   0.219  0.9740
 C2H2.01 - GAPDH    -0.1136 0.121 57  -0.938  0.6186

Relative expression

Relative expression analysis can be done using $\Delta\Delta Ct$ or $\Delta Ct$ methods through different functions (i.e. TTEST_DDCt, WILCOX_DDCt, ANOVA_DDCt(), REPEATED_DDCt, and ANOVA_DCt()). Below are some examples of expression analysis using $\Delta\Delta Ct$ method.

# An example of a properly arranged dataset from a repeated-measures experiment.
data <- read.csv(system.file("extdata", "data_repeated_measure_1.csv", package = "rtpcr"))
data

time    id  E_Target    Ct_target   E_Ref      Ct_Ref
   1     1      2       18.92   2   32.77
   1     2      2       15.82   2   32.45
   1     3      2       19.84   2   31.62
   2     1      2       19.46   2   33.03
   2     2      2       17.56   2   33.24
   2     3      2       19.74   2   32.08
   3     1      2       15.73   2   32.95
   3     2      2       17.21   2   33.64
   3     3      2       18.09   2   33.40

# Repeated measure analysis
res <- REPEATED_DDCt(
  data,
  numOfFactors = 1,
  numberOfrefGenes = 1,
  mainFactor.column = 1,
  block = NULL)


# Anova analysis
ANOVA_DDCt(
  data,
  mainFactor.column = 1,
  numOfFactors = 1,
  numberOfrefGenes = 1,
  block = NULL)


# Paired t.test (equivalent to repeated measure analysis, but not always the same results, due to different calculation methods!)
TTEST_DDCt(
  data[1:6,], 
  numberOfrefGenes = 1, 
  paired = T)


# Anova analysis
data <- read.csv(system.file("extdata", "data_2factorBlock3ref.csv", package = "rtpcr"))
res <- ANOVA_DDCt(
  x = data,
  mainFactor.column = 1,
  numOfFactors = 2,
  numberOfrefGenes = 1,
  block = "block",
  analyseAllTarget = TRUE)

Output

Data output

All the functions for relative expression analysis (including TTEST_DDCt, WILCOX_DDCt, ANOVA_DDCt(), REPEATED_DDCt, and ANOVA_DCt()) return the relative expression table which include fold change and corresponding statistics. The output of ANOVA_DDCt(), ANCOVA_DDCt(), REPEATED_DDCt, and ANOVA_DCt() also include lm models, residuals, raw data and ANOVA table for each gene. These outputs for each gene can be obtained as follow:

Per_gene Output	Code
expression table	`res$relativeExpression`
ANOVA table	`res$perGene$gene_name$ANOVA_table`
ANOVA lm	`res$perGene$gene_name$lm`
ANOVA lm formula	`res$perGene$gene_name$lm_formula`
Residuals	`resid(res$perGene$gene_name$lm)`

# Relative expression table for the specified column in the input data:
df <- res$relativeExpression
df
Relative Expression
gene   contrast       RE  log2FC pvalue sig    LCL     UCL     se Lower.se.RE Upper.se.RE Lower.se.log2FC Upper.se.log2FC
PO            R   1.0000  0.0000 1.0000     0.0000  0.0000 0.5506      0.6828      1.4647          0.0000          0.0000
PO       S vs R  11.6130  3.5377 0.0001 *** 4.4233 30.4888 0.2286      9.9115     13.6066          3.0193          4.1450
GAPDH         R   1.0000  0.0000 1.0000     0.0000  0.0000 0.4815      0.7162      1.3962          0.0000          0.0000
GAPDH    S vs R   6.6852  2.7410 0.0001 *** 3.0687 14.5641 0.3820      5.1301      8.7118          2.1034          3.5719
ref2          R   1.0000  0.0000 1.0000     0.0000  0.0000 0.6928      0.6186      1.6164          0.0000          0.0000
ref2     S vs R   0.9372 -0.0936 0.9005     0.3145  2.7929 0.2414      0.7927      1.1079         -0.1107         -0.0792

Plot output

A single function of plotFactor is used to produce barplots for one- to three-factor expression tables.

Plot output: example 1

data <- read.csv(system.file("extdata", "data_3factor.csv", package = "rtpcr"))
#Perform analysis first
res <- ANOVA_DCt(
  data,
  numOfFactors = 3,
  numberOfrefGenes = 1,
  block = NULL)
  
df <- res$relativeExpression
df
# Generate three-factor bar plot
plotFactor(
  df,
  x_col = "SA",       
  y_col = "log2FC",       
  group_col = "Type",   
  facet_col = "Conc",    
  Lower.se_col = "Lower.se.log2FC",
  Upper.se_col = "Upper.se.log2FC",
  letters_col = "sig",
  letters_d = 0.3,
  col_width = 0.7, 
  dodge_width = 0.7,
  fill_colors = c("palegreen3", "skyblue"),
  color = "black",
  base_size = 14, 
  alpha = 1,
  legend_position = c(0.1, 0.2))

How to edit ouptput plots?

the rtpcr plotFactor function creates ggplot objects for one to three factor tables. The plot can further be edited by adding new layers:

Task	Example Code
Change y-axis label	`p + ylab("Relative expression ($\Delta\Delta Ct$ method)")`
Add a horizontal reference line	`p + geom_hline(yintercept = 0, linetype = "dashed")`
Change y-axis limits	`p + scale_y_continuous(expand = expansion(mult = c(0, 0.1)))`
Relabel x-axis	`p + scale_x_discrete(labels = c("A" = "Control", "B" = "Treatment"))`
Change fill colors	`p + scale_fill_brewer(palette = "Set2")`

Plot output: example 2

data <- read.csv(system.file("extdata", "data_2factorBlock.csv", package = "rtpcr"))
res <- ANOVA_DCt(data, 
      numOfFactors = 2,
      block = "block",
      numberOfrefGenes = 1)

df <- res$relativeExpression

plotFactor(
  data = df,
  x_col = "factor2",
  y_col = "RE",
  group_col = "factor1",
  Lower.se_col = "Lower.se.RE",
  Upper.se_col = "Upper.se.RE",
  letters_col = "sig",
  letters_d = 0.2,
  fill_colors = c("aquamarine4", "gold2"),
  color = "black",
  alpha = 1,
  col_width = 0.7,
  dodge_width = 0.7,
  base_size = 16, 
  legend_position = c(0.8, 0.8))

Plot output: example 3

# Heffer et al., 2020, PlosOne
library(dplyr)
df <- read.csv(system.file("extdata", "data_Heffer2020PlosOne.csv", package = "rtpcr"))

res <- ANOVA_DDCt(
  df,
  numOfFactors = 1,
  mainFactor.column = 1,
  numberOfrefGenes = 1,
  block = NULL)

data <- res$relativeExpression

# Selecting only the first words in 'contrast' column to be used as the x-axis labels.
data$contrast <- sub(" .*", "", data$contrast)

plotFactor(
  data = data,
  x_col = "contrast",
  y_col = "RE",
  group_col = "contrast",
  facet_col = "gene",
  Lower.se_col = "Lower.se.RE",
  Upper.se_col = "Upper.se.RE",
  letters_col = "sig",
  letters_d = 0.2,
  alpha = 1,
  fill_colors = palette.colors(4, recycle = TRUE),
  color = "black",
  col_width = 0.5,
  dodge_width = 0.5,
  base_size = 16, 
  legend_position = "none")

Post-hoc analysis

Although all the expression analysis functions perform statistical comparisons for the levels of the analysed factor, further Post-hoc analysis is still possible. The Means_DDCt function performs post-hoc comparisons using a fitted model object produced by ANOVA_DCt, ANOVA_DDCt, ANCOVA_DDCt or REPEATED_DDCt. It applies pairwise statistical comparisons of relative expression (RE) values for user-specified effects via the specs argument. Supported effects include simple effects, interactions, and slicing, provided the underlying model is an ANOVA. For ANCOVA models returned by this package, the Means_DDCt output is limited to simple effects only.

res <- ANOVA_DDCt(
  data_3factor,
  numOfFactors = 3,
  numberOfrefGenes = 1,
  mainFactor.column = 1,
  block = NULL)

model <- res$perGene$E_PO$lm
# Relative expression values for Concentration main effect
Means_DDCt(model, specs = "Conc")

 contrast        RE        SE df       LCL       UCL p.value sig
 L vs H   0.1703610 0.2208988 24 0.1242014 0.2336757 <0.0001 ***
 M vs H   0.2227247 0.2208988 24 0.1623772 0.3055004 <0.0001 ***
 M vs L   1.3073692 0.2208988 24 0.9531359 1.7932535  0.0928 .  

Results are averaged over the levels of: Type, SA 
Confidence level used: 0.95 

# Relative expression values for Concentration sliced by Type
Means_DDCt(model, specs = "Conc | Type")

Type = R:
 contrast       RE        SE df       LCL      UCL p.value sig
 L vs H   0.103187 0.3123981 24 0.0659984 0.161331 <0.0001 ***
 M vs H   0.339151 0.3123981 24 0.2169210 0.530255 <0.0001 ***
 M vs L   3.286761 0.3123981 24 2.1022126 5.138776 <0.0001 ***

Type = S:
 contrast       RE        SE df       LCL      UCL p.value sig
 L vs H   0.281265 0.3123981 24 0.1798969 0.439751 <0.0001 ***
 M vs H   0.146266 0.3123981 24 0.0935518 0.228684 <0.0001 ***
 M vs L   0.520030 0.3123981 24 0.3326112 0.813055  0.0059 ** 

Results are averaged over the levels of: SA 
Confidence level used: 0.95 

# Relative expression values for Concentration sliced by Type and SA
Means_DDCt(model, specs = "Conc | Type * SA")

Checking normality of residuals

If the residuals from a t.test or an lm or and lmer object are not normally distributed, the significance results might be violated. In such cases, non-parametric tests can be used. For example, the Mann–Whitney test - also known as the Wilcoxon rank-sum test, (implemented via WILCOX_DDCt() in the rtpcr package), is an alternative to t.test, and kruskal.test() is an alternative to one-way analysis of variance. These tests assess differences between population medians using independent samples. However, the t.test function (also the TTEST_DDCt function described above) includes the var.equal argument. When set to FALSE, performs t.test under the unequal variances hypothesis. Residuals (from ANOVA_DCt, ANOVA_DDCt, and REPEATED_DDCt functions) objects can be extracted from lmand plotted as follow:

data <- read.csv(system.file("extdata", "data_repeated_measure_1.csv", package = "rtpcr"))
res3 <- REPEATED_DDCt(
  data,
  numOfFactors = 1,
  numberOfrefGenes = 1,
  mainFactor.column = 1,
  block = NULL
)
residuals <- resid(res3$perGene$Target$lm)
shapiro.test(residuals) 
par(mfrow = c(1,2))
plot(residuals)
qqnorm(residuals)
qqline(residuals, col = "red")

Mean of technical replicates

Calculating the mean of technical replicates and generating an output table suitable for subsequent ANOVA analysis can be accomplished using the meanTech function. The input dataset must follow the column structure illustrated in the example data below. Columns used for grouping should be explicitly specified via the groups argument of the meanTech function.

# Example input data frame with technical replicates
data1 <- read.csv(system.file("extdata", "data_withTechRep.csv", package = "rtpcr"))

# Calculate mean of technical replicates using first four columns as groups
meanTech(data1,
         groups = 1:2,
         numOfFactors = 1,
         block = NULL)

Contact

Email: gh.mirzaghaderi at uok.ac.ir

Citation

citation("rtpcr")

To cite the package ‘rtpcr’ in publications, please use:

  Ghader Mirzaghaderi (2025). rtpcr: a package for statistical analysis and graphical
  presentation of qPCR data in R. PeerJ 13:e20185. https://doi.org/10.7717/peerj.20185

A BibTeX entry for LaTeX users is

  @Article{,
    title = {rtpcr: A package for statistical analysis and graphical presentation of qPCR data in R},
    author = {Ghader Mirzaghaderi},
    journal = {PeerJ},
    volume = {13},
    pages = {e20185},
    year = {2025},
    doi = {10.7717/peerj.20185},
  }

Getting help

If you encounter a clear bug, please file a minimal reproducible example on github

References

Livak, Kenneth J, and Thomas D Schmittgen. 2001. Analysis of Relative Gene Expression Data Using Real-Time Quantitative PCR and the Double Delta CT Method. Methods 25 (4). doi.org/10.1006/meth.2001.1262.

Ganger, MT, Dietz GD, Ewing SJ. 2017. A common base method for analysis of qPCR data and the application of simple blocking in qPCR experiments. BMC bioinformatics 18, 1-11. doi.org/10.1186/s12859-017-1949-5.

Mirzaghaderi G. 2025. rtpcr: a package for statistical analysis and graphical presentation of qPCR data in R. PeerJ 13, e20185. doi.org/10.7717/peerj.20185.

Pfaffl MW, Horgan GW, Dempfle L. 2002. Relative expression software tool (REST©) for group-wise comparison and statistical analysis of relative expression results in real-time PCR. Nucleic acids research 30, e36-e36. doi.org/10.1093/nar/30.9.e36.

Taylor SC, Nadeau K, Abbasi M, Lachance C, Nguyen M, Fenrich, J. 2019. The ultimate qPCR experiment: producing publication quality, reproducible data the first time. Trends in Biotechnology, 37(7), 761-774. doi.org/10.1016/j.tibtech.2018.12.002.

Yuan, JS, Ann Reed, Feng Chen, and Neal Stewart. 2006. Statistical Analysis of Real-Time PCR Data. BMC Bioinformatics 7 (85). doi.org/10.1186/1471-2105-7-85.

Manual

Overview