BA.est {MethComp}R Documentation

Bias and variance components for a Bland-Altman plot.

Description

A variance component model is fitted to method comparison data with replicate measurements in each method by item stratum. The purpose is to simplify the construction of a correct Bland-Altman-plot when replicate measurements are available, and to give the REML-estimates of the relevant variance components.

Usage

  BA.est( data, linked=TRUE, IxR=has.repl(data),
                             MxI=has.repl(data),
                          varMxI=TRUE, bias=TRUE, alpha=0.05,
                Transform = NULL,
                trans.tol = 1e-6 )
  ## S3 method for class 'BA.est':
  bias( obj, ref=1, ... )
  VC.est( data,
           IxR = has.repl(data), linked = IxR,
           MxI = has.repl(data), matrix = MxI,
        varMxI = TRUE, bias = TRUE, print = FALSE )
  

Arguments

data A data frame representing method comparison data with replicate measurements, i.e. with columns meth, item, repl and y.
linked Logical. Are the replicated linked within item across methods?
IxR Logical. Should in item by repl interaction be included in the model. This is needed when the replicates are linked within item across methods, so it is just another name for the linked argument.
MxI Logical. Should the method by item interaction (matrix effect) be included in the model.
matrix Logical. Alias for MxI.
varMxI Logical. Should the method by item interaction have a variance that varies between methods. Ignored if only two methods are compared.
bias Logical. Should a systematic bias between methods be estimated? If FALSE no bias between methods are assumed, i.e. alpha_m=0, m=1,...,M.
alpha Numerical. Significance level. By default the value 2 is used when computing prediction intervals, otherwise the 1-alpha/2 t-quantile is used. The number of d.f. is taken as the number of units minus the number of items minus the number of methods minus 1.
Transform Transformation of data (y) before analysis. See check.trans.
trans.tol The tolerance used to check whether the supplied transformation and its inverse combine to the identity.
obj A BA.est object from which to extract the biases between methods.
ref Numeric or character. The reference method for the biases: the method with bias 0.
print Logical. Should the estimated bias and variance components be printed?
... Further argumenst passed on. Curently ignored.

Details

The model fitted is:

y=alpha_m + mu_i + c_mi + a_ir + e_ir, var(c_mi)=tau_m^2, var(a_ir)=omega^2, var(e_mir)=sigma_m^2

We can only fit separate variances for the tau's if more than two methods are compared (i.e. nM > 2), hence varMxI is ignored when nM==2.

The function VC.est is the workhorse; BA.est just calls it. VC.est figures out which model to fit by lme, and returns the estimates. VC.est is also used as part of the fitting algorithm in AltReg, where each iteration step requires fit of this model.

Value

BA.est returns an object of class c("MethComp","BA.est"), a list with four elements Conv, VarComp, LoA, RepCoef; VC.est returns (invisibly!) a list with elements Bias, VarComp, Mu, RanEff. These list components are:

Conv 3-dimensional array with dimensions "To", "From" and unnamed. The first two doemsions have the methods compared as levels, that last one c("alpha","beta","sd"). It represnets the mean conversions between methods and the prediciton standard deviation. Where "To" and "From" take the same value the value of the "sd" component is sqrt(2) times the residual variation for the method.
VarComp A matrix of variance components (on the SD scale) with methods as rows and variance components "IxR", "MxI" and "res" as columns.
LoA Four-column matrix with mean difference, lower and upper limit of agreement and prediction SD. Each row in the matrix represents a pair of methods.
RepCoef Two-column matrix of repeatability SDs and repeatability coefficients. The SDs are the standard deviation of the difference between two measurements by the same method on the item inder identical circumstances; the repeatability coefficient the numerical extent of the prediction interval for this difference.
Mu Estimates of the item-specific parameters.
RanEff Estimates of the randome effects form thr model (BLUPS). This is a (possibly empty) list with possible elements named MxI and IxR according to whether these random effects are in the model.

Author(s)

Bendix Carstensen

References

Carstensen, Simpson & Gurrin: Statistical models for assessing agreement in method comparison studies with replicate measurements, The International Journal of Biostatistics: Vol. 4 : Iss. 1, Article 16. http://www.bepress.com/ijb/vol4/iss1/16.

See Also

BA.plot, perm.repl

Examples

data( ox )
BA.est( ox )
BA.est( ox, linked=FALSE )
data( sbp )
BA.est( sbp )
BA.est( sbp, linked=FALSE )
# Check what you get from VC.est
str( VC.est( sbp ) )

[Package MethComp version 0.6.0 Index]