numOSL (version 1.2)

calED: Fitting a dose response curve and calculating an equivalent dose

Description

Fitting a dose response curve and calculating an equivalent dose, the error of the equivalent dose is assessed after Duller GAT (2007a).

Usage

calED(Curvedata, Ltx, 
      model = c("line","exp","line+exp"), origin = FALSE,
      nstart = 100, upb = 1, ErrorMethod = c("mc", "sp"),
      nsim = 1000, plot = TRUE, samplename = NULL)

Arguments

Curvedata

data.frame(required): three columns, i.e. regenerative doses (redose1, redose2, etc), standardized signals (Lx1/Tx1, Lx2/Tx2, etc), errors of standardized signals

Ltx

vector(required): two values (the standardized natural signal and its standard error), then an equivalent dose is estimated with interpolation

model

character(with default): a fitting model ("line", "exp" or "line+exp"), default model="line". See details

origin

logical(optional): force the fitting to pass the origin (x=0,y=0) or not

nstart

numeric(with default): the maximum number of attempts that used for initializing parameters of curve fitting

upb

numeric(with default): the upper limit on b value, initial b value is generated uniformly from the space (0,upb), see details

ErrorMethod

character(with default): method ("sp" or "mc") used for assessing the standard error of equivalent dose. Default ErrorMethod="mc", see details

nsim

numeric(with default): the allowed maximum number of simulations for application of a Monte Carlo method to assess the standard error of an equivalent dose

plot

logical(with default): draw the fitted dose response curve or not

samplename

character(with default): the name of the sample

Value

• Return an invisible list that contains following elements:
• mcED
  an equivalent doses obtained by Monte Carlo simulation, available only if ErrorMethod="mc", or else it will be NULL
• LMpars
  the characteristic parameters and standard errors for the dose response curve estimated with the Levenberg-Marquardt method
• residual
  the sum of square of residuals
• fit.value
  observations and fitted values
• ED
  estimated equivalent dose (and standard error)

Details

This function can be used for both dose response curve fitting and equivalent dose calculating, three fitting methods are available: 1) "line": a linear model, y=a*x+b or y=a*x if origin=TRUE; 2) "exp": an exponential model, y=a*(1-exp(-b*x))+c or y=a*(1-exp(-b*x)) if origin=TRUE; 3) "line+exp": an exponential plus linear model, y=a*(1-exp(-b*x))+c*x+d or y=a*(1-exp(-b*x))+c*x if origin=TRUE. Standard error of equivalent dose can be accessed using two method (Duller GAT, 2007a): a) "sp": a simple transformation of s(Lx/Tx) to s(ED); b) "mc": a Monte Carlo method Curve fitting is performed using the Levenberg-Marquardt algorithm (minpack: original FORTRAN 77 version by Jorge More, Burton Garbow, Kenneth Hillstrom. FORTRAN 90 version by John Burkardt). Interpolation is performed using a combination of golden section search and successive parabolic interpolation (the same as function optimize in package "stats"). As for the fitting of a linear model, initial parameters is not a problem, but if the model that to be fitted is either an exponential or an exponential plus linear model, then a series of b values are initialized randomly from a uniform distribution in the space (0,upb), then other parameters (a or a, c or a, c, d) can be estimated with a Linear Algebra method. User is advised to keep the default setting "plot" to be TRUE if possible in order to see whether the fitted dose response curve is correct.

References

Duller, G.A.T., 2007a. Assessing the error on equivalent dose estimates derived from single aliquot regenerative dose measurements. Ancient TL 25(1), pp. 15-24.

Duller, G., 2007b. Analyst. pp. 27-28.

See Also

sgcED; optimize

Examples

# load package "numOSL"
  library(numOSL)
  # Calculating equivalent doses using data from Duller (2007a)
  data(Curvedata)
  Res<-matrix(nrow=4,ncol=3)
  par(mfrow=c(2,2))
  for (i in 1:4)  {
    model<-ifelse(any(i==c(1,2)),"exp","line")    
    Simple<-calED(Curvedata[[i]][[1]],Curvedata[[i]][[2]],
                  model=model,ErrorMethod="sp",plot=FALSE)
    MonteCarlo<-calED(Curvedata[[i]][[1]],Curvedata[[i]][[2]],
                      model=model,ErrorMethod="mc",plot=TRUE)
    Res[i,1:2]<-Simple$ED
    Res[i,3]<-MonteCarlo$ED[2]
  } # end for
  colnames(Res)<-c("ED","Simp.Error","MC.Error")
  rownames(Res)<-c("Exponential","Exponential","linear","linear")
  print(Res)
  par(mfrow=c(1,1))