ratiocalc: Calculation of ratios from qPCR runs with/without reference...
In qpcR: Modelling and Analysis of Real-Time PCR Data
Description
Usage
Arguments
Details
Value
Note
Author(s)
References
See Also
Examples
Description
For multiple qPCR data from type 'pcrbatch', this function calculates ratios between two samples (control/treatment) of a gene-of-interest, using normalization against a reference gene, if supplied. The input can be single qPCR data or (more likely) data containing replicates. Errors and confidence intervals for the obtained ratios can be calculated by Monte-Carlo simulation, a permutation approach similar to the popular REST software and by error propagation. Statistical significance for the ratios is calculated by a permutation approach of randomly reallocated vs. non-reallocated data. See 'Details'.
Usage
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Arguments
data
multiple qPCR data generated by pcrbatch.
group
a character vector defining the replicates (if any) of control/treatment samples and reference genes/genes-of-interest. See 'Details'.
which.eff
efficiency calculated by which method. Defaults to sigmoidal fit. See output of pcrbatch. Alternatively, a numeric value for all runs, a vector of external efficiencies with one element per run or directly transferred from ratioPar.
type.eff
type of efficiency pre-processing prior to error analysis. See 'Details'.
which.cp
type of threshold cycles to be used for the analysis. See output of efficiency. Alternatively, a vector of external threshold cycles with one element per run or directly transferred from ratioPar.
...
other parameters to be passed to propagate.
Details
The replicates for the data columns are to be defined as a character vector with the following abbreviations:
"gs": gene-of-interest in treatment sample
"gc": gene-of-interest in control sample
"rs": reference gene in treatment sample
"rc": reference gene in control sample
There is no distinction between the different runs of the same sample, so that three different runs of a gene-of-interest in a treatment sample are defined as c("gs", "gs", "gs"). The error analysis calculates statistics from ALL replicates, so that a further sub-categorization of runs is superfluous. NOTE: If the setup consists of different sample or gene combinations, use ratiobatch!
Examples:
No replicates: NULL.
2 runs with 2 replicates each, no reference gene: c("gs", "gs", "gs", "gs", "gc", "gc", "gc", "gc").
1 run with two replicates each and reference gene: c("gs", "gs", "gc", "gc", "rs", "rs", "rc", "rc").
type.eff defines the pre-processing of the efficiencies before being transferred to propagate. The qPCR community sometimes uses single efficiencies, or averaged over replicates etc., so that different settings were implemented. In detail, these are the following:
"individual": The individual efficiencies from each run are used.
"mean.single": Efficiencies are averaged over all replicates.
"median.single": Same as above but median instead of mean.
"mean.pair": Efficiencies are averaged from all replicates of treatment sample AND control.
"median.pair": Same as above but median instead of mean.
Efficiencies can be taken from the individual curves or averaged from the replicates as described in the documentation to ratiocalc. The different combinations of type.eff, which.eff and which.cp can yield very different results in ratio calculation. We observed a relatively stable setup which minimizes the overall variance using the combination
type.eff = "mean.single" # averaging efficiency across replicates
which.eff = "sli" # taking efficiency from the sliding window method
which.cp = "sig" # using the second derivative maximum of a sigmoidal fit
The ratios are calculated according to the following formulas:
Without reference gene:
\frac{E(gc)^{cp(gc)}}{E(gs)^{cp(gs)}}
With reference gene:
\frac{E(gc)^{cp(gc)}}{E(gs)^{cp(gs)}}/\frac{E(rc)^{cp(rc)}}{E(rs)^{cp(rs)}}
The permutation approach permutates threshold cycles and efficiency replicates within treatment and control samples. The treatment/control samples (and their respective efficiencies) are tied together, which is similar to the popular REST software approach ("pairwise-reallocation test"). Ratios are calculated for each permutation and compared to ratios obtained if samples were randomly reallocated from the treatment to the control group. Three p-values are calculated from all permutations that gave a higher/equal/lower ratio than the original data. The resulting p-values are thus an indication for the significance in any direction AGAINST the null hypothesis that ratios calculated by permutation are just by chance.
If the mechanistic mak2/mak2i/mak3/mak3i/cm3 models are used in pcrbatch, set which.eff = "mak" for ratio calculations from the D0 values of the model:
Without reference gene:
\frac{D_0(gs)}{D_0(gc)}
With reference gene:
\frac{D_0(gs)}{D_0(gc)}/\frac{D_0(rs)}{D_0(rc)}
Confidence values are returned for all three methods (Monte Carlo, permutation, error propagation) as follows:
Monte-Carlo: From the evaluations of the Monte-Carlo simulated data.
Permutation: From the evaluations of the within-group permutated data.
Propagation: From the propagated error, assuming normality.
Value
A list with the following components:
data: the data that was transferred to propagate for the error analysis.
data.Sim, data.Perm, data.Prop, derivs, covMat: The complete output from propagate.
summary: a summary of the results obtained from the Monte Carlo simulation, permutation and error propagation.
Note
The error calculated from qPCR data by propagate often seems quite high. This largely depends on the error of the base (i.e. efficiency) of the exponential function. The error usually decreases when setting use.cov = TRUE in the ... part of the function. It can be debated anyhow, if the variables 'efficiency' and 'threshold cycles' have a covariance structure. As the efficiency is deduced at the second derivative maximum of the sigmoidal curve, variance in the second should show an effect on the first, such that the use of a var-cov matrix might be feasible. It is also commonly encountered that the propagated error is much higher when using reference genes, as the number of partial derivative functions increases.
Author(s)
Andrej-Nikolai Spiess
References
Analysis of relative gene expression data using real-time quantitative PCR and the 2(-Delta Delta C(T)) method.
Livak KJ & Schmittgen TD.
Methods (2001), 25: 402-428.
Standardized determination of real-time PCR efficiency from a single reaction set-up.
Tichopad A, Dilger M, Schwarz G, Pfaffl MW.
Nucleic Acids Res (2003), 31: e122.
Validation of a quantitative method for real time PCR kinetics.
Liu W & Saint DA.
Biochem Biophys Res Commun (2002), 294: 347-53.
Relative expression software tool (REST) for group-wise comparison and statistical analysis of relative expression results in real-time PCR.
Pfaffl MW, Horgan GW, Dempfle L.
Nucl Acids Res (2002), 30: e36.
See Also
The function ratioPar, which is a much better and simpler way if only external threshold cycles/efficiencies should be used.
Examples
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## Only treatment sample and control,
## no reference gene, 4 replicates each.
## Individual efficiencies for error calculation.
DAT1 <- pcrbatch(reps, fluo = 2:9, model = l4)
GROUP1 <- c("gs", "gs", "gs", "gs", "gc", "gc", "gc", "gc")
RES1 <- ratiocalc(DAT1, group = GROUP1, which.eff = "sli",
type.eff = "individual", which.cp = "cpD2")
RES1$summary
## Not run:
## Gets even better using averaged efficiencies
## over all replicates.
## p-value indicates significant upregulation in
## comparison to randomly reallocated
## samples (similar to REST software)
RES2 <- ratiocalc(DAT1, GROUP1, which.eff = "sli",
type.eff = "mean.single", which.cp = "cpD2")
RES2$summary
## Using reference data.
## Toy example is same data as above
## but replicated as reference such
## that the ratio should be 1.
DAT3 <- pcrbatch(reps, fluo = c(2:9, 2:9), model = l4)
GROUP3 <- c("gs", "gs", "gs", "gs",
"gc", "gc", "gc", "gc",
"rs", "rs", "rs", "rs",
"rc", "rc", "rc", "rc")
RES3 <- ratiocalc(DAT3, GROUP3, which.eff = "sli",
type.eff = "mean.single", which.cp = "cpD2")
RES3$summary
## Using one of the mechanistic models
## => ratios are calculated from the replicate
## D0 values, without reference genes.
DAT4 <- pcrbatch(reps, fluo = 2:9,
methods = c("sigfit", "sliwin", "mak3"))
GROUP4 <- c("gs", "gs", "gs", "gs", "gc", "gc", "gc", "gc")
RES4 <- ratiocalc(DAT4, GROUP4, which.eff = "mak")
RES4$summary
## Example without replicates
## => no Monte-Carlo simulations
## and hence no plots.
DAT5 <- pcrbatch(reps, fluo = 2:5, model = l4)
GROUP5 <- c("gs", "gc", "rs", "rc")
RES5 <- ratiocalc(DAT5, GROUP5, which.eff = "sli",
type.eff = "individual", which.cp = "cpD2")
RES5$summary
## Using external efficiencies.
DAT6 <- pcrbatch(reps, fluo = 2:9, model = l5)
GROUP6 <- c("gs", "gs", "gs", "gs", "gc", "gc", "gc", "gc")
EFF6 <- rep(c(1.72, 1.76), c(4, 4))
RES6 <- ratiocalc(DAT6, GROUP6, which.eff = EFF6,
type.eff = "individual", which.cp = "cpD2")
RES6$summary
## Using external efficiencies AND
## external threshold cycles.
DAT7 <- pcrbatch(reps, fluo = 2:9, model = l5)
GROUP7 <- c("gs", "gs", "gs", "gs", "gc", "gc", "gc", "gc")
EFF7 <- rep(c(1.72, 1.76), c(4, 4))
CP7 <- c(15.44, 15.33, 14.84, 15.34, 18.89, 18.71, 18.13, 17.22)
RES7 <- ratiocalc(DAT7, GROUP7, which.eff = EFF7,
type.eff = "individual", which.cp = CP7)
RES7$summary
## Compare 'ratiocalc' to REST software
## using the data from the REST 2008
## manual (http://rest.gene-quantification.info/).
## We supply the threshold cycles/efficiencies from the
## manual as external data to 'dummy' pcrbatch data.
## BETTER: use 'ratioPar' function!
cp.rc <- c(26.74, 26.85, 26.83, 26.68, 27.39, 27.03, 26.78, 27.32)
cp.rs <- c(26.77, 26.47, 27.03, 26.92, 26.97, 26.97, 26.07, 26.3, 26.14, 26.81)
cp.gc <- c(27.57, 27.61, 27.82, 27.12, 27.76, 27.74, 26.91, 27.49)
cp.gs <- c(24.54, 24.95, 24.57, 24.63, 24.66, 24.89, 24.71, 24.9, 24.26, 24.44)
eff.rc <- rep(1.97, 8)
eff.rs <- rep(1.97, 10)
eff.gc <- rep(2.01, 8)
eff.gs <- rep(2.01, 10)
CP8 <- c(cp.rc, cp.rs, cp.gc, cp.gs)
EFF8 <- c(eff.rc, eff.rs, eff.gc, eff.gs)
DAT8 <- pcrbatch(rutledge, 1, 2:37, model = l4)
GROUP8 <- rep(c("rc", "rs", "gc", "gs"), c(8, 10, 8, 10))
RES8 <- ratiocalc(DAT8, GROUP8, which.eff = EFF8, which.cp = CP8)
RES8$summary
## => Confidence interval: 2.983/9.996
## REST 2008 manual, page 10: 2.983/9.996
## End(Not run)
qpcR documentation built on May 2, 2019, 5:17 a.m.
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Description Usage Arguments Details Value Note Author(s) References See Also Examples
Description
For multiple qPCR data from type 'pcrbatch', this function calculates ratios between two samples (control/treatment) of a gene-of-interest, using normalization against a reference gene, if supplied. The input can be single qPCR data or (more likely) data containing replicates. Errors and confidence intervals for the obtained ratios can be calculated by Monte-Carlo simulation, a permutation approach similar to the popular REST software and by error propagation. Statistical significance for the ratios is calculated by a permutation approach of randomly reallocated vs. non-reallocated data. See 'Details'.
Usage
1 2 3 4 5 6 |
Arguments
data |
multiple qPCR data generated by |
group |
a character vector defining the replicates (if any) of control/treatment samples and reference genes/genes-of-interest. See 'Details'. |
which.eff |
efficiency calculated by which method. Defaults to sigmoidal fit. See output of |
type.eff |
type of efficiency pre-processing prior to error analysis. See 'Details'. |
which.cp |
type of threshold cycles to be used for the analysis. See output of |
... |
other parameters to be passed to |
Details
The replicates for the data columns are to be defined as a character vector with the following abbreviations:
"gs": gene-of-interest in treatment sample
"gc": gene-of-interest in control sample
"rs": reference gene in treatment sample
"rc": reference gene in control sample
There is no distinction between the different runs of the same sample, so that three different runs of a gene-of-interest in a treatment sample are defined as c("gs", "gs", "gs"). The error analysis calculates statistics from ALL replicates, so that a further sub-categorization of runs is superfluous. NOTE: If the setup consists of different sample or gene combinations, use ratiobatch!
Examples:
No replicates: NULL.
2 runs with 2 replicates each, no reference gene: c("gs", "gs", "gs", "gs", "gc", "gc", "gc", "gc").
1 run with two replicates each and reference gene: c("gs", "gs", "gc", "gc", "rs", "rs", "rc", "rc").
type.eff defines the pre-processing of the efficiencies before being transferred to propagate. The qPCR community sometimes uses single efficiencies, or averaged over replicates etc., so that different settings were implemented. In detail, these are the following:
"individual": The individual efficiencies from each run are used.
"mean.single": Efficiencies are averaged over all replicates.
"median.single": Same as above but median instead of mean.
"mean.pair": Efficiencies are averaged from all replicates of treatment sample AND control.
"median.pair": Same as above but median instead of mean.
Efficiencies can be taken from the individual curves or averaged from the replicates as described in the documentation to ratiocalc. The different combinations of type.eff, which.eff and which.cp can yield very different results in ratio calculation. We observed a relatively stable setup which minimizes the overall variance using the combination
type.eff = "mean.single" # averaging efficiency across replicates
which.eff = "sli" # taking efficiency from the sliding window method
which.cp = "sig" # using the second derivative maximum of a sigmoidal fit
The ratios are calculated according to the following formulas:
Without reference gene:
\frac{E(gc)^{cp(gc)}}{E(gs)^{cp(gs)}}
With reference gene:
\frac{E(gc)^{cp(gc)}}{E(gs)^{cp(gs)}}/\frac{E(rc)^{cp(rc)}}{E(rs)^{cp(rs)}}
The permutation approach permutates threshold cycles and efficiency replicates within treatment and control samples. The treatment/control samples (and their respective efficiencies) are tied together, which is similar to the popular REST software approach ("pairwise-reallocation test"). Ratios are calculated for each permutation and compared to ratios obtained if samples were randomly reallocated from the treatment to the control group. Three p-values are calculated from all permutations that gave a higher/equal/lower ratio than the original data. The resulting p-values are thus an indication for the significance in any direction AGAINST the null hypothesis that ratios calculated by permutation are just by chance.
If the mechanistic mak2/mak2i/mak3/mak3i/cm3 models are used in pcrbatch, set which.eff = "mak" for ratio calculations from the D0 values of the model:
Without reference gene:
\frac{D_0(gs)}{D_0(gc)}
With reference gene:
\frac{D_0(gs)}{D_0(gc)}/\frac{D_0(rs)}{D_0(rc)}
Confidence values are returned for all three methods (Monte Carlo, permutation, error propagation) as follows:
Monte-Carlo: From the evaluations of the Monte-Carlo simulated data.
Permutation: From the evaluations of the within-group permutated data.
Propagation: From the propagated error, assuming normality.
Value
A list with the following components:
data: the data that was transferred to propagate for the error analysis.
data.Sim, data.Perm, data.Prop, derivs, covMat: The complete output from propagate.
summary: a summary of the results obtained from the Monte Carlo simulation, permutation and error propagation.
Note
The error calculated from qPCR data by propagate often seems quite high. This largely depends on the error of the base (i.e. efficiency) of the exponential function. The error usually decreases when setting use.cov = TRUE in the ... part of the function. It can be debated anyhow, if the variables 'efficiency' and 'threshold cycles' have a covariance structure. As the efficiency is deduced at the second derivative maximum of the sigmoidal curve, variance in the second should show an effect on the first, such that the use of a var-cov matrix might be feasible. It is also commonly encountered that the propagated error is much higher when using reference genes, as the number of partial derivative functions increases.
Author(s)
Andrej-Nikolai Spiess
References
Analysis of relative gene expression data using real-time quantitative PCR and the 2(-Delta Delta C(T)) method.
Livak KJ & Schmittgen TD.
Methods (2001), 25: 402-428.
Standardized determination of real-time PCR efficiency from a single reaction set-up.
Tichopad A, Dilger M, Schwarz G, Pfaffl MW.
Nucleic Acids Res (2003), 31: e122.
Validation of a quantitative method for real time PCR kinetics.
Liu W & Saint DA.
Biochem Biophys Res Commun (2002), 294: 347-53.
Relative expression software tool (REST) for group-wise comparison and statistical analysis of relative expression results in real-time PCR.
Pfaffl MW, Horgan GW, Dempfle L.
Nucl Acids Res (2002), 30: e36.
See Also
The function ratioPar, which is a much better and simpler way if only external threshold cycles/efficiencies should be used.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 | ## Only treatment sample and control,
## no reference gene, 4 replicates each.
## Individual efficiencies for error calculation.
DAT1 <- pcrbatch(reps, fluo = 2:9, model = l4)
GROUP1 <- c("gs", "gs", "gs", "gs", "gc", "gc", "gc", "gc")
RES1 <- ratiocalc(DAT1, group = GROUP1, which.eff = "sli",
type.eff = "individual", which.cp = "cpD2")
RES1$summary
## Not run:
## Gets even better using averaged efficiencies
## over all replicates.
## p-value indicates significant upregulation in
## comparison to randomly reallocated
## samples (similar to REST software)
RES2 <- ratiocalc(DAT1, GROUP1, which.eff = "sli",
type.eff = "mean.single", which.cp = "cpD2")
RES2$summary
## Using reference data.
## Toy example is same data as above
## but replicated as reference such
## that the ratio should be 1.
DAT3 <- pcrbatch(reps, fluo = c(2:9, 2:9), model = l4)
GROUP3 <- c("gs", "gs", "gs", "gs",
"gc", "gc", "gc", "gc",
"rs", "rs", "rs", "rs",
"rc", "rc", "rc", "rc")
RES3 <- ratiocalc(DAT3, GROUP3, which.eff = "sli",
type.eff = "mean.single", which.cp = "cpD2")
RES3$summary
## Using one of the mechanistic models
## => ratios are calculated from the replicate
## D0 values, without reference genes.
DAT4 <- pcrbatch(reps, fluo = 2:9,
methods = c("sigfit", "sliwin", "mak3"))
GROUP4 <- c("gs", "gs", "gs", "gs", "gc", "gc", "gc", "gc")
RES4 <- ratiocalc(DAT4, GROUP4, which.eff = "mak")
RES4$summary
## Example without replicates
## => no Monte-Carlo simulations
## and hence no plots.
DAT5 <- pcrbatch(reps, fluo = 2:5, model = l4)
GROUP5 <- c("gs", "gc", "rs", "rc")
RES5 <- ratiocalc(DAT5, GROUP5, which.eff = "sli",
type.eff = "individual", which.cp = "cpD2")
RES5$summary
## Using external efficiencies.
DAT6 <- pcrbatch(reps, fluo = 2:9, model = l5)
GROUP6 <- c("gs", "gs", "gs", "gs", "gc", "gc", "gc", "gc")
EFF6 <- rep(c(1.72, 1.76), c(4, 4))
RES6 <- ratiocalc(DAT6, GROUP6, which.eff = EFF6,
type.eff = "individual", which.cp = "cpD2")
RES6$summary
## Using external efficiencies AND
## external threshold cycles.
DAT7 <- pcrbatch(reps, fluo = 2:9, model = l5)
GROUP7 <- c("gs", "gs", "gs", "gs", "gc", "gc", "gc", "gc")
EFF7 <- rep(c(1.72, 1.76), c(4, 4))
CP7 <- c(15.44, 15.33, 14.84, 15.34, 18.89, 18.71, 18.13, 17.22)
RES7 <- ratiocalc(DAT7, GROUP7, which.eff = EFF7,
type.eff = "individual", which.cp = CP7)
RES7$summary
## Compare 'ratiocalc' to REST software
## using the data from the REST 2008
## manual (http://rest.gene-quantification.info/).
## We supply the threshold cycles/efficiencies from the
## manual as external data to 'dummy' pcrbatch data.
## BETTER: use 'ratioPar' function!
cp.rc <- c(26.74, 26.85, 26.83, 26.68, 27.39, 27.03, 26.78, 27.32)
cp.rs <- c(26.77, 26.47, 27.03, 26.92, 26.97, 26.97, 26.07, 26.3, 26.14, 26.81)
cp.gc <- c(27.57, 27.61, 27.82, 27.12, 27.76, 27.74, 26.91, 27.49)
cp.gs <- c(24.54, 24.95, 24.57, 24.63, 24.66, 24.89, 24.71, 24.9, 24.26, 24.44)
eff.rc <- rep(1.97, 8)
eff.rs <- rep(1.97, 10)
eff.gc <- rep(2.01, 8)
eff.gs <- rep(2.01, 10)
CP8 <- c(cp.rc, cp.rs, cp.gc, cp.gs)
EFF8 <- c(eff.rc, eff.rs, eff.gc, eff.gs)
DAT8 <- pcrbatch(rutledge, 1, 2:37, model = l4)
GROUP8 <- rep(c("rc", "rs", "gc", "gs"), c(8, 10, 8, 10))
RES8 <- ratiocalc(DAT8, GROUP8, which.eff = EFF8, which.cp = CP8)
RES8$summary
## => Confidence interval: 2.983/9.996
## REST 2008 manual, page 10: 2.983/9.996
## End(Not run)
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