ratiocalc: Calculation of ratios from qPCR runs with/without reference genes

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

ratiocalc(data, group = NULL, 
          which.eff = c("sig", "sli", "exp", "mak", "cm3", "ext"), 
          type.eff = c("individual", "mean.single", "median.single", 
                       "mean.pair", "median.pair"),
          which.cp = c("cpD2", "cpD1", "cpE", "cpR", "cpT", "Cy0", "ext"),
          ...)

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.

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.

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.

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.

Examples

Run this code

# NOT RUN {
## 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
# }

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