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Delta Ct ANOVA analysis with optional model specification

Source: R/ANOVA_DCt.R
ANOVA_DCt.Rd

Performs Delta Ct (dCt) analysis of the data from a factorial experiment with support for both fixed- and mixed-effect models. Per-gene statistical analysis and grouping is also performed.

Usage

ANOVA_DCt(
  x,
  numOfFactors,
  numberOfrefGenes,
  block = NULL,
  alpha = 0.05,
  p.adj = "none",
  analyseAllTarget = TRUE,
  model = NULL,
  modelBased_se = TRUE,
  set_missing_target_Ct_to_40 = FALSE
)

Arguments

x

The input data frame containing experimental design columns, target gene E/Ct column pairs, and reference gene E/Ct column pairs. Reference gene columns must be located at the end of the data frame. See "Input data structure" in vignettes for details about data structure.

numOfFactors

Integer. Number of experimental factor columns (excluding rep and optional block).

numberOfrefGenes

Integer. Number of reference genes. Each reference gene must be represented by two columns (E and Ct).

block

Character. Block column name or NULL. 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: This parameter is ignored if model is provided.

alpha

Statistical level for comparisons (default: 0.05).

p.adj

Method for p-value adjustment. See p.adjust.

analyseAllTarget

Logical or character. If TRUE (default), all detected target genes are analysed. Alternatively, a character vector specifying the names (names of their Efficiency columns) of target genes to be analysed.

model

Optional model formula. If provided, this overrides the automatic formula (CRD or RCBD based on block and numOfFactors). The formula uses wDCt as the response variable. For mixed models, random effects can be defined using lmer syntax (e.g., "wDCt ~ Treatment + (1|Block)"). When using model, the block and numOfFactors arguments are ignored for model specification, but still used for data structure identification.

modelBased_se

Logical. If TRUE (default), standard errors are calculated from model-based residuals. If FALSE, standard errors are calculated directly from the observed wDCt values within each treatment group according to the selected se.type. For single factor data, both methods are the same. It is recommended to use modelBased_se = TRUE (default).

set_missing_target_Ct_to_40

If TRUE, missing target gene Ct values become 40; if FALSE (default), they become NA.

Value

An object containing expression tables, lm/lmer models, ANOVA tables, residuals, and raw data for each gene:

relativeExpression

dCt expression table for all treatment combinations along with per-gene statistical grouping

perGene

Nested list containing detailed results for each target gene:

  • ANOVA_table: Full factorial ANOVA table

  • lm: lm/lmer model for factorial design

  • Final_data: Processed data with wDCt values

  • resid(object$perGene$gene_name$lm): Residuals

Details

The function performs ANOVA analysis on weighted delta Ct (wDCt) values and returns variance components along with an expression table containing:

  • gene: Name of target genes

  • Factor columns: Experimental design factors

  • dCt: Mean weighted delta Ct for each treatment combination

  • RE: Relative expression = fold change = 2^-dCt

  • log2FC: log2 of RE

  • LCL: 95% lower confidence level

  • UCL: 95% upper confidence level

  • se: Standard error

  • Lower.se.RE: Lower limit error bar for RE

  • Upper.se.RE: Upper limit error bar for RE

  • Lower.se.log2FC: Lower limit error bar for log2FC

  • Upper.se.log2FC: Upper limit error bar for log2FC

  • sig: Per-gene significance grouping letters

Examples

# Default usage with fixed effects
result <- ANOVA_DCt(data_2factorBlock3ref, numOfFactors = 2, numberOfrefGenes = 3, 
                    block = "block")
#> 
#> Relative Expression
#> 
#>    gene Type Concentration      dCt      RE   log2FC     LCL     UCL      se
#> 1    PO    R            L1  2.62828 0.16174 -2.62828 0.11704 0.22351 0.03803
#> 2    PO    S            L1  3.12306 0.11478 -3.12306 0.08306 0.15862 0.19479
#> 3    PO    R            L2  1.65834 0.31680 -1.65834 0.22089 0.46897 0.29573
#> 4    PO    S            L2  2.20079 0.21752 -2.20079 0.14694 0.31197 0.05659
#> 5    PO    R            L3  0.08550 0.94246 -0.08550 0.68199 1.30241 0.27565
#> 6    PO    S            L3  1.28189 0.41126 -1.28189 0.29760 0.56833 0.28106
#> 7   NLM    R            L1 -1.32600 2.50707  1.32600 1.92666 3.26233 0.15235
#> 8   NLM    S            L1  3.50923 0.08782 -3.50923 0.06749 0.11428 0.12116
#> 9   NLM    R            L2  1.00339 0.49883 -1.00339 0.38334 0.64910 0.09175
#> 10  NLM    S            L2  2.91119 0.13294 -2.91119 0.10216 0.17298 0.09931
#> 11  NLM    R            L3 -0.41248 1.33097  0.41248 0.97812 1.80481 0.40782
#> 12  NLM    S            L3 -0.29364 1.22573  0.29364 0.94196 1.59498 0.17875
#>    Lower.se.RE Upper.se.RE Lower.se.log2FC Upper.se.log2FC sig
#> 1      0.15753     0.16606        -2.66631        -2.59026  de
#> 2      0.10028     0.13137        -3.31785        -2.92826   e
#> 3      0.25809     0.38888        -1.95407        -1.36261  bc
#> 4      0.20915     0.22622        -2.25738        -2.14421  cd
#> 5      0.77854     1.14089        -0.36115         0.19016   a
#> 6      0.33846     0.49971        -1.56295        -1.00083   b
#> 7      2.25583     2.78629         1.17366         1.47835   a
#> 8      0.08075     0.09552        -3.63039        -3.38807   e
#> 9      0.46809     0.53158        -1.09514        -0.91165   c
#> 10     0.12409     0.14241        -3.01049        -2.81188   d
#> 11     1.00323     1.76577         0.00466         0.82030   b
#> 12     1.08289     1.38741         0.11488         0.47239   b
#> 
#> Note: Using default model for statistical analysis: wDCt ~ block + Type * Concentration 

# Mixed model with random block effect
result <- ANOVA_DCt(data_2factorBlock3ref, numOfFactors = 2, numberOfrefGenes = 3,
                          block = "block")
#> 
#> Relative Expression
#> 
#>    gene Type Concentration      dCt      RE   log2FC     LCL     UCL      se
#> 1    PO    R            L1  2.62828 0.16174 -2.62828 0.11704 0.22351 0.03803
#> 2    PO    S            L1  3.12306 0.11478 -3.12306 0.08306 0.15862 0.19479
#> 3    PO    R            L2  1.65834 0.31680 -1.65834 0.22089 0.46897 0.29573
#> 4    PO    S            L2  2.20079 0.21752 -2.20079 0.14694 0.31197 0.05659
#> 5    PO    R            L3  0.08550 0.94246 -0.08550 0.68199 1.30241 0.27565
#> 6    PO    S            L3  1.28189 0.41126 -1.28189 0.29760 0.56833 0.28106
#> 7   NLM    R            L1 -1.32600 2.50707  1.32600 1.92666 3.26233 0.15235
#> 8   NLM    S            L1  3.50923 0.08782 -3.50923 0.06749 0.11428 0.12116
#> 9   NLM    R            L2  1.00339 0.49883 -1.00339 0.38334 0.64910 0.09175
#> 10  NLM    S            L2  2.91119 0.13294 -2.91119 0.10216 0.17298 0.09931
#> 11  NLM    R            L3 -0.41248 1.33097  0.41248 0.97812 1.80481 0.40782
#> 12  NLM    S            L3 -0.29364 1.22573  0.29364 0.94196 1.59498 0.17875
#>    Lower.se.RE Upper.se.RE Lower.se.log2FC Upper.se.log2FC sig
#> 1      0.15753     0.16606        -2.66631        -2.59026  de
#> 2      0.10028     0.13137        -3.31785        -2.92826   e
#> 3      0.25809     0.38888        -1.95407        -1.36261  bc
#> 4      0.20915     0.22622        -2.25738        -2.14421  cd
#> 5      0.77854     1.14089        -0.36115         0.19016   a
#> 6      0.33846     0.49971        -1.56295        -1.00083   b
#> 7      2.25583     2.78629         1.17366         1.47835   a
#> 8      0.08075     0.09552        -3.63039        -3.38807   e
#> 9      0.46809     0.53158        -1.09514        -0.91165   c
#> 10     0.12409     0.14241        -3.01049        -2.81188   d
#> 11     1.00323     1.76577         0.00466         0.82030   b
#> 12     1.08289     1.38741         0.11488         0.47239   b
#> 
#> Note: Using default model for statistical analysis: wDCt ~ block + Type * Concentration 

# Custom mixed model formula with nested random effects
result_custom <- ANOVA_DCt(data_repeated_measure_2, numOfFactors = 2, numberOfrefGenes = 1,
                            block = NULL,
                            model = wDCt ~ treatment * time + (1 | id))
#> Using user defined formula.
#> 
#> Relative Expression
#> 
#>     gene treatment time       dCt       RE   log2FC       LCL       UCL      se
#> 1 Target untreated   t1 -13.34333 10393.06 13.34333  2420.745  44620.87 0.35860
#> 2 Target   treated   t1 -14.08667 17398.40 14.08667  4052.422  74697.09 0.67044
#> 3 Target untreated   t2 -14.22333 19127.14 14.22333  4455.080  82119.16 0.37483
#> 4 Target   treated   t2 -13.86333 14903.19 13.86333  3471.240  63984.34 0.29080
#> 5 Target untreated   t3 -13.80333 14296.09 13.80333  3329.836  61377.88 0.27656
#> 6 Target   treated   t3 -16.32000 81810.59 16.32000 19055.267 351240.05 0.58482
#>   Lower.se.RE Upper.se.RE Lower.se.log2FC Upper.se.log2FC sig
#> 1    8105.743    13325.83        12.98473        13.70194   b
#> 2   10931.679    27690.55        13.41623        14.75711   b
#> 3   14750.765    24801.93        13.84850        14.59816  ab
#> 4   12182.565    18231.38        13.57253        14.15414   b
#> 5   11802.211    17316.95        13.52677        14.07990  ab
#> 6   54545.868   122703.57        15.73518        16.90482   a