qpcR (version 1.2-1)

ratiocalc: Calculation of ratios/propagated errors/confidence intervals/permutation p-values from qPCR runs with/without reference data

Description

For multiple qPCR data from type 'pcrbatch', this function calculates ratios between two samples, 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 (bootstrap) approach similar to the popular REST software and by (first-order) error propagation. Statistical significance for the ratios is calculated by a permutation approach of reallocated vs. non-reallocated data. See 'Details'.

Usage

ratiocalc(data, group = NULL, which.eff = c("sig", "sli", "exp"), 
          type.eff = c("individual", "mean.single", "median.single", 
                       "mean.pair", "median.pair"),
          which.cp = c("cpD2", "cpD1", "cpE", "cpR", "cpT", "Cy0"),
          perm = c("cp", "eff", "both", NULL), 
          pval = c("up", "down"), ...)

Arguments

data

multiple qPCR data generated by pcrbatch.

group

a character vector defining the replicates (if any) as well as target and reference data. See 'Details'

which.eff

efficiency calculated by which method. Defaults to sigmoidal fit. See output of pcrbatch. Alternatively, a fixed numeric value between 1 and 2 that is used for all runs.

type.eff

type of efficiency to be supplied for the error analysis. See 'Details'.

which.cp

type of crossing point to be used for the analysis. See output of efficiency.

perm

the variables subjected to the permutation approach (reallocation). See 'Details'.

pval

the direction of gene-regulation to be confirmed by permutation p-value. See 'Details'.

...

other parameters to be passed to propagate.

Value

• A list with the following components: The complete output from propagate, attached with the data that was transferred to propagate for the error analysis as item data.

Details

The replicates of the 'pcrbatch' data columns are to be defined as a character vector with the following abbreviations: "gs": gene-of-interest in target sample "gc": gene-of-interest in control sample "rs": reference gene in target 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 target sample are defined as c("gs", "gs", "gs"). The error analysis calculates statistics from ALL replicates, so that a further sub-categorization of runs seems superfluous. Examples: No replicates: NULL. 2 runs with 2 replicates each, no reference: c("gs", "gs", "gs", "gs", "gc", "gc", "gc", "gc"). 1 run with two replicates each and reference data: 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 target sample and control. "median.pair": Same as above but median instead of mean. The ratios are calculated according to the following formulas: Without reference PCR: $$\frac{E.gc^{cp.gc}}{E.gs^{cp.gs}}$$ With reference PCR: $$\frac{E.gc^{cp.gc}}{E.gs^{cp.gs}}\cdot\frac{E.rs^{cp.rs}}{E.rc^{cp.rc}}$$ The permutation approach reallocates either crossing points ("cp"), efficiencies ("E") or "both" between target sample and control groups. Ratios are calculated for each reallocation and compared to ratios obtained if samples were permutated but not reallocated. A p-value is calculated from all scenarios in which the reallocation gave a similar/higher ratio than the original data if pval = "up" or similar/lower if pval = "down". The resulting p-value is thus a measure for the frequency of difference in means of the original data and randomly perturbed data. 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

Livak KJ et al. (2001) Analysis of relative gene expression data using real-time quantitative PCR and the 2(-Delta Delta C(T)) method. Methods, 25: 402-428. Tichopad A et al. (2003) Standardized determination of real-time PCR efficiency from a single reaction set-up. Nucleic Acids Res, 31: e122. Liu W & Saint DA (2002) Validation of a quantitative method for real time PCR kinetics. Biochem Biophys Res Commun, 294: 347-53. Pfaffl M et al. (2002) Relative expression software tool (REST) for group-wise comparison and statistical analysis of relative expression results in real-time PCR. Nucl Acids Res, 30: e36.

Examples

## only target sample and control,
## no reference, 4 replicates each
## individual efficiencies for error
## calculation
DAT <- pcrbatch(reps, 2:9, l4)
GROUP <- c("gs", "gs", "gs", "gs", "gc", "gc", "gc", "gc")
res <- ratiocalc(DAT, GROUP, which.eff = "sli", type.eff = "individual",
          which.cp = "cpD2", perm = "cp", pval = "up")

## Typical for using individual efficiencies,
## this inflates the error. 95\% confidence intervals 
## include 1 (no differential regulation) and errors are
## also extremely high (over 100\%).
res$conf.Sim
res$conf.Perm
res$error.Prop/res$eval.Prop

## Gets better using averaged efficiencies 
## over all replicates
res2 <- ratiocalc(DAT, GROUP, which.eff = "sli", type.eff = "mean.single",
          which.cp = "cpD2", perm = "cp", pval = "up")
res2$conf.Sim
res2$conf.Perm
res2$error.Prop/res$eval.Prop

## p-value indicates significant upregulation
## in comparison to randomly reallocated 
## threshold cycles (similar to REST software)
res2$pval.Perm

## using reference data.
## toy example is same data as above
## but replicated as reference such
## that the ratio should be 1.
DAT2 <- pcrbatch(reps, c(2:9, 2:9), l4)
GROUP2 <- c("gs", "gs", "gs", "gs", 
            "gc", "gc", "gc", "gc",
            "rs", "rs", "rs", "rs",
            "rc", "rc", "rc", "rc")
res2 <- ratiocalc(DAT2, GROUP2, which.eff = "sli", type.eff = "mean.single",
          which.cp = "cpD2", perm = "cp", pval = "up")
res2$conf.Sim
res2$conf.Perm
res2$error.Prop/res$eval.Prop
res2$pval.Perm

## same as above, but reference data
## is mirrored such that the ratio 
## is squared.
DAT3 <- pcrbatch(reps, c(2:9, 9:2), 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", perm = "cp", pval = "up")
res3$conf.Sim
res3$conf.Perm
res3$error.Prop/res$eval.Prop
res3$pval.Perm

## compare 'propagate' to REST software
## using the data from the REST 2008
## manual (http://rest.gene-quantification.info/),
## have to create dataframe with values as we do
## not use 'pcrbatch', but external cp's & eff's!
## ties define random reallocation of crossing points
## between control and sample.
## See help for 'propagate'.
EXPR <- expression((2.01^(cp.gc - cp.gs)/1.97^(cp.rc - cp.rs)))
cp.rc <- c(26.74, 26.85, 26.83, 26.68, 27.39, 27.03, 26.78, 27.32, NA, NA)
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, NA, NA)
cp.gs <- c(24.54, 24.95, 24.57, 24.63, 24.66, 24.89, 24.71, 24.9, 24.26, 24.44)
DAT <- cbind(cp.rc, cp.rs, cp.gc, cp.gs)
res <- propagate(EXPR, DAT, do.sim = TRUE, do.perm = TRUE, ties = c(1, 1, 2, 2))
res$conf.Sim
res$conf.Perm
res$eval.Prop
res$error.Prop

## Does error propagation in qPCR quantitation make sense?
## In ratio calculations based on (E1^cp1)/(E2^cp2),
## only 2\% error in each of the variables result in
## over 50\% propagated error!
x <- NULL
y <- NULL
for (i in seq(0, 0.1, by = 0.01)) {
      E1 <- c(1.7, 1.7 * i)
      cp1 <- c(15, 15 * i)
      E2 <- c(1.7, 1.7 * i)
      cp2 <- c(18, 18 * i)
      DF <- cbind(E1, cp1, E2, cp2)
      res <- propagate(expression((E1^cp1)/(E2^cp2)), DF, type = "stat", plot = FALSE)
      x <- c(x, i * 100)
      y <- c(y, (res$error.Prop/res$eval.Prop) * 100)
}
plot(x, y, xlim = c(0, 10), lwd = 2, xlab = "c.v. [%]", ylab = "c.v. (prop) [%]")