Pairwise comparisons of relative expression values (Delta Ct or Delta Delta Ct) using a fitted model
Source:R/Means_DDCt.r
Means_DDCt.RdPerforms relative expression (fold change) analysis based on the
\(\Delta C_T\) or \(\Delta \Delta C_T\) methods using a fitted model object produced by
ANOVA_DCt(), ANOVA_DDCt() or REPEATED_DDCt().
Arguments
- model
A fitted model object (typically an
lmerorlmobject) created byANOVA_DCt(),ANOVA_DDCt()orREPEATED_DDCt().- specs
A character string or character vector specifying the predictors or combinations of predictors over which relative expression values are desired. This argument follows the specification syntax used by
emmeans::emmeans()(e.g.,"Factor","Factor1 | Factor2").- p.adj
Character string specifying the method for adjusting p-values. See
p.adjustfor available options.
Value
A data frame containing estimated relative expression values, confidence intervals, p-values, and significance levels derived from the fitted model.
Details
The Means_DDCt function performs pairwise comparisons of relative expression values fo all combinations using
estimated marginal means derived from a fitted model.
For ANOVA models, relative expression values can be obtained for main effects,
interactions, and sliced (simple) effects.
For ANCOVA models returned by the rtpcr package, only simple
effects are supported.
Internally, this function relies on the emmeans package to compute marginal means and contrasts, which are then back-transformed to fold change values using the \(\Delta \Delta C_T\) framework.
Examples
# Obtain a fitted model from ANOVA_DDCt
res <- ANOVA_DDCt(
data_3factor,
numOfFactors = 3,
numberOfrefGenes = 1,
mainFactor.column = 1,
block = NULL)
#> NOTE: Results may be misleading due to involvement in interactions
#> ANOVA table
#> Analysis of Variance Table
#>
#> Response: wDCt
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Type 1 24.834 24.8336 84.8207 2.392e-09 ***
#> Conc 2 45.454 22.7269 77.6252 3.319e-11 ***
#> SA 1 0.032 0.0324 0.1107 0.7422776
#> Type:Conc 2 10.641 5.3203 18.1718 1.567e-05 ***
#> Type:SA 1 6.317 6.3168 21.5756 0.0001024 ***
#> Conc:SA 2 3.030 1.5150 5.1747 0.0135366 *
#> Type:Conc:SA 2 3.694 1.8470 6.3086 0.0062852 **
#> Residuals 24 7.027 0.2928
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> ANCOVA table
#> Analysis of Variance Table
#>
#> Response: wDCt
#> Df Sum Sq Mean Sq F value Pr(>F)
#> SA 1 0.032 0.0324 0.0327 0.8577
#> Conc 2 45.454 22.7269 22.9429 7.682e-07 ***
#> Type 1 24.834 24.8336 25.0696 2.105e-05 ***
#> Residuals 31 30.708 0.9906
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Expression table
#> contrast RE log2FC pvalue sig LCL UCL se Lower.se.RE
#> 1 R 1.0000 0.0000 1 0.0000 0.0000 0.3939 0.7611
#> 2 S vs R 3.1626 1.6611 0 *** 2.4433 4.0936 0.3064 2.5575
#> Upper.se.RE Lower.se.log2FC Upper.se.log2FC
#> 1 1.3139 0.0000 0.0000
#> 2 3.9109 1.3433 2.0542
#> *** The R level was used as calibrator.
#>
#> Relative Expression
#> gene contrast RE log2FC pvalue sig LCL UCL se Lower.se.RE
#> 1 E_PO R 1.0000 0.0000 1 0.0000 0.0000 0.3939 0.7611
#> 2 E_PO S vs R 3.1626 1.6611 0 *** 2.4433 4.0936 0.3064 2.5575
#> Upper.se.RE Lower.se.log2FC Upper.se.log2FC
#> 1 1.3139 0.0000 0.0000
#> 2 3.9109 1.3433 2.0542
# Relative expression values for Type main effect
Means_DDCt(res$perGene$E_PO$lm_ANOVA, specs = "Type")
#> contrast RE SE df LCL UCL p.value sig
#> S vs R 3.1626 0.1803631 24 2.443349 4.093578 <0.0001 ***
#>
#> Results are averaged over the levels of: Conc, SA
#> Confidence level used: 0.95
# Relative expression values for Concentration main effect
Means_DDCt(res$perGene$E_PO$lm_ANOVA, 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(res$perGene$E_PO$lm_ANOVA, specs = "Conc | Type")
#> Type = R:
#> contrast RE SE df LCL UCL p.value sig
#> L vs H 0.103187 0.3123981 24 0.0659984 0.161331 <0.0001 ***
#> M vs H 0.339151 0.3123981 24 0.2169210 0.530255 <0.0001 ***
#> M vs L 3.286761 0.3123981 24 2.1022126 5.138776 <0.0001 ***
#>
#> Type = S:
#> contrast RE SE df LCL UCL p.value sig
#> L vs H 0.281265 0.3123981 24 0.1798969 0.439751 <0.0001 ***
#> M vs H 0.146266 0.3123981 24 0.0935518 0.228684 <0.0001 ***
#> M vs L 0.520030 0.3123981 24 0.3326112 0.813055 0.0059 **
#>
#> Results are averaged over the levels of: SA
#> Confidence level used: 0.95
# Relative expression values for Concentration sliced by Type and SA
Means_DDCt(res$perGene$E_PO$lm_ANOVA, specs = "Conc | Type * SA")
#> Type = R, SA = A1:
#> contrast RE SE df LCL UCL p.value sig
#> L vs H 0.288505 0.4417977 24 0.1533437 0.542800 0.0005 ***
#> M vs H 0.634342 0.4417977 24 0.3371606 1.193467 0.1502
#> M vs L 2.198724 0.4417977 24 1.1686485 4.136734 0.0167 *
#>
#> Type = S, SA = A1:
#> contrast RE SE df LCL UCL p.value sig
#> L vs H 0.267943 0.4417977 24 0.1424151 0.504115 0.0002 ***
#> M vs H 0.139661 0.4417977 24 0.0742315 0.262761 <0.0001 ***
#> M vs L 0.521233 0.4417977 24 0.2770416 0.980660 0.0438 *
#>
#> Type = R, SA = A2:
#> contrast RE SE df LCL UCL p.value sig
#> L vs H 0.036906 0.4417977 24 0.0196160 0.069436 <0.0001 ***
#> M vs H 0.181327 0.4417977 24 0.0963776 0.341153 <0.0001 ***
#> M vs L 4.913213 0.4417977 24 2.6114319 9.243840 <0.0001 ***
#>
#> Type = S, SA = A2:
#> contrast RE SE df LCL UCL p.value sig
#> L vs H 0.295248 0.4417977 24 0.1569280 0.555487 0.0005 ***
#> M vs H 0.153184 0.4417977 24 0.0814189 0.288203 <0.0001 ***
#> M vs L 0.518830 0.4417977 24 0.2757643 0.976139 0.0425 *
#>
#> Confidence level used: 0.95
data <- read.csv(system.file("extdata", "data_3factor.csv", package = "rtpcr"))
res <- ANOVA_DCt(
data,
numOfFactors = 3,
numberOfrefGenes = 1,
block = NULL)
#> NULL
#>
#> Relative expression (DCt method)
#> Type Conc SA RE log2FC LCL UCL se Lower.se.RE Upper.se.RE
#> 1 S H A2 5.1934 2.3767 8.1197 3.3217 0.1309 4.7428 5.6867
#> 2 S H A1 2.9690 1.5700 4.6420 1.8990 0.0551 2.8578 3.0846
#> 3 R H A2 1.7371 0.7967 2.7159 1.1110 0.0837 1.6391 1.8409
#> 4 S L A2 1.5333 0.6167 2.3973 0.9807 0.0865 1.4441 1.6280
#> 5 R H A1 0.9885 -0.0167 1.5455 0.6323 0.0841 0.9325 1.0479
#> 6 S L A1 0.7955 -0.3300 1.2438 0.5088 0.2128 0.6864 0.9220
#> 7 S M A2 0.7955 -0.3300 1.2438 0.5088 0.2571 0.6657 0.9507
#> 8 R M A1 0.6271 -0.6733 0.9804 0.4011 0.4388 0.4626 0.8500
#> 9 S M A1 0.4147 -1.2700 0.6483 0.2652 0.2540 0.3477 0.4945
#> 10 R M A2 0.3150 -1.6667 0.4925 0.2015 0.2890 0.2578 0.3848
#> 11 R L A1 0.2852 -1.8100 0.4459 0.1824 0.0208 0.2811 0.2893
#> 12 R L A2 0.0641 -3.9633 0.1002 0.0410 0.8228 0.0362 0.1134
#> Lower.se.log2FC Upper.se.log2FC sig
#> 1 2.1705 2.6025 a
#> 2 1.5112 1.6311 ab
#> 3 0.7517 0.8443 bc
#> 4 0.5808 0.6548 c
#> 5 -0.0177 -0.0157 cd
#> 6 -0.3825 -0.2847 d
#> 7 -0.3944 -0.2761 d
#> 8 -0.9127 -0.4968 de
#> 9 -1.5145 -1.0650 ef
#> 10 -2.0363 -1.3641 f
#> 11 -1.8363 -1.7841 f
#> 12 -7.0103 -2.2407 g
#>
#> Combined Expression Table (all genes)
#> gene Type Conc SA RE log2FC LCL UCL se Lower.se.RE
#> 1 PO S H A2 5.1934 2.3767 8.1197 3.3217 0.1309 4.7428
#> 2 PO S H A1 2.9690 1.5700 4.6420 1.8990 0.0551 2.8578
#> 3 PO R H A2 1.7371 0.7967 2.7159 1.1110 0.0837 1.6391
#> 4 PO S L A2 1.5333 0.6167 2.3973 0.9807 0.0865 1.4441
#> 5 PO R H A1 0.9885 -0.0167 1.5455 0.6323 0.0841 0.9325
#> 6 PO S L A1 0.7955 -0.3300 1.2438 0.5088 0.2128 0.6864
#> 7 PO S M A2 0.7955 -0.3300 1.2438 0.5088 0.2571 0.6657
#> 8 PO R M A1 0.6271 -0.6733 0.9804 0.4011 0.4388 0.4626
#> 9 PO S M A1 0.4147 -1.2700 0.6483 0.2652 0.2540 0.3477
#> 10 PO R M A2 0.3150 -1.6667 0.4925 0.2015 0.2890 0.2578
#> 11 PO R L A1 0.2852 -1.8100 0.4459 0.1824 0.0208 0.2811
#> 12 PO R L A2 0.0641 -3.9633 0.1002 0.0410 0.8228 0.0362
#> Upper.se.RE Lower.se.log2FC Upper.se.log2FC sig
#> 1 5.6867 2.1705 2.6025 a
#> 2 3.0846 1.5112 1.6311 ab
#> 3 1.8409 0.7517 0.8443 bc
#> 4 1.6280 0.5808 0.6548 c
#> 5 1.0479 -0.0177 -0.0157 cd
#> 6 0.9220 -0.3825 -0.2847 d
#> 7 0.9507 -0.3944 -0.2761 d
#> 8 0.8500 -0.9127 -0.4968 de
#> 9 0.4945 -1.5145 -1.0650 ef
#> 10 0.3848 -2.0363 -1.3641 f
#> 11 0.2893 -1.8363 -1.7841 f
#> 12 0.1134 -7.0103 -2.2407 g
# lm <- res$perGene$PO$lm_factorial
# Means_DDCt(lm, specs = "Type * Conc * SA", p.adj = "none")