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=linked,
                             MxI=TRUE,
                          varMxI=TRUE, bias=TRUE, alpha=0.05 )
  VC.est( data, linked=TRUE, IxR=linked,
                             MxI=TRUE,
                          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.
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.
print Logical. Should the estimated bias and variance components be printed?

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

A list with four elements; BA.est returns a list with elements Bias, Var.comp, LoA, Rep.coef; VC.est returns (invisibly!) a list with elements Bias, Var.comp, Mu, Ran.eff. These are:

Bias Vector of estimates of alpha_m, the first element is always 0.
Var.comp Two-column matrix of sds and variances of the variance components, nM tau's, one nu if linked, and nM sigma's. Only those in the model specified are included.
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.
Rep.coef 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.
Ran.eff 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, tab.repl, 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 0.5.0 Index]