MCmcmc {MethComp}

Fit a model for method comparison studies using WinBUGS

Description

A model linking each of a number of methods of measurement linearly to the "true" value is set up in BUGS and run via the function bugs from the R2WinBUGS package.

Usage

MCmcmc(
  data,
  bias = "linear",
  IxR = has.repl(data),
  linked = IxR,
  MxI = TRUE,
  matrix = MxI,
  varMxI = nlevels(factor(data$meth)) > 2,
  n.chains = 4,
  n.iter = 2000,
  n.burnin = n.iter/2,
  n.thin = ceiling((n.iter - n.burnin)/1000),
  bugs.directory = getOption("bugs.directory"),
  debug = FALSE,
  bugs.code.file = "model.txt",
  clearWD = TRUE,
  code.only = FALSE,
  ini.mult = 2,
  list.ini = TRUE,
  org = FALSE,
  program = "JAGS",
  Transform = NULL,
  trans.tol = 1e-06,
  ...
)

Arguments

data

Data frame with variables meth, item, repl and y, possibly a Meth object. y represents a measurement on an item (typically patient or sample) by method meth, in replicate repl.

bias

Character. Indicating how the bias between methods should be modelled. Possible values are "none", "constant", "linear" and "proportional". Only the first three letters are significant. Case insensitive.

IxR

Logical. Are the replicates linked across methods, i.e. should a random item by repl be included in the model.

linked

Logical, alias for IxR.

MxI

Logical, should a meth by item effect be included in the model?

matrix

Logical, alias for MxI.

varMxI

Logical, should the method by item effect have method-specific variances. Ignored if only two methods are compared.

n.chains

How many chains should be run by WinBUGS — passed on to bugs.

n.iter

How many total iterations — passed on to bugs.

n.burnin

How many of these should be burn-in — passed on to bugs.

n.thin

How many should be sampled — passed on to bugs.

bugs.directory

Where is WinBUGS (>=1.4) installed — passed on to bugs. The default is to use a parameter from options(). If you use this routinely, this is most conveniently set in your .Rprofile file.

debug

Should WinBUGS remain open after running — passed on to bugs.

bugs.code.file

Where should the bugs code go?

clearWD

Should the working directory be cleared for junk files after the running of WinBUGS — passed on to bugs.

code.only

Should MCmcmc just create a bugs code file and a set of inits? See the list.ini argument.

ini.mult

Numeric. What factor should be used to randomly perturb the initial values for the variance components, see below in details.

list.ini

List of lists of starting values for the chains, or logical indicating whether starting values should be generated. If TRUE (the default), the function VC.est will be used to generate initial values for the chains. list.ini is a list of length n.chains. Each element of which is a list with the following vectors as elements:

mu

- length I

alpha

- length M

beta

- length M

sigma.mi

- length M - if M is 2 then length 1

sigma.ir

- length 1

sigma.mi

- length M

sigma.res

- length M

If code.only==TRUE, list.ini indicates whether a list of initial values is returned (invisibly) or not. If code.only==FALSE, list.ini==FALSE is ignored.

org

Logical. Should the posterior of the original model parameters be returned too? If TRUE, the MCmcmc object will have an attribute, original, with the posterior of the parameters in the model actually simulated.

program

Which program should be used for the MCMC simulation. Possible values are "BRugs", "ob", "winbugs", "wb" (WinBUGS), "jags" (JAGS). Case insensitive. Defaults to "JAGS" since: 1) JAGS is available on all platforms and 2) JAGS seems to be faster than BRugs on (some) windows machines.

Transform

Transformation of data (y) before analysis. See choose.trans.

trans.tol

The tolerance used to check whether the supplied transformation and its inverse combine to the identity.

...

Additional arguments passed on to bugs.

Details

The model set up for an observation y_{mir} is:

y_{mir} = \alpha_m + \beta_m(\mu_i+b_{ir} + c_{mi}) +

e_{mir}

where b_{ir} is a random item by repl interaction (included if "ir" is in random) and c_{mi} is a random meth by item interaction (included if "mi" is in random). The \mu_i's are parameters in the model but are not monitored — only the \alphas, \betas and the variances of b_{ir}, c_{mi} and e_{mir} are monitored and returned. The estimated parameters are only determined up to a linear transformation of the \mus, but the linear functions linking methods are invariant. The identifiable conversion parameters are:

\alpha_{m\cdot k}=\alpha_m - \alpha_k \beta_m/\beta_k, \quad

\beta_{m\cdot k}=\beta_m/\beta_k

The posteriors of these are derived and included in the posterior, which also will contain the posterior of the variance components (the SDs, that is). Furthermore, the posterior of the point where the conversion lines intersects the identity as well as the prediction SDs between any pairs of methods are included.

The function summary.MCmcmc method gives estimates of the conversion parameters that are consistent. Clearly,

\mathrm{median}(\beta_{1\cdot 2})=

1/\mathrm{median}(\beta_{2\cdot 1})

because the inverse is a monotone transformation, but there is no guarantee that

\mathrm{median}(\alpha_{1\cdot 2})= \mathrm{median}(-\alpha_{2\cdot 1}/

\beta_{2\cdot 1})

and hence no guarantee that the parameters derived as posterior medians produce conversion lines that are the same in both directions. Therefore, summary.MCmcmc computes the estimate for \alpha_{2\cdot 1} as

(\mathrm{median}(\alpha_{1\cdot 2})-\mathrm{median}(\alpha_{2\cdot 1})

/\mathrm{median}(\beta_{2\cdot 1}))/2

and the estimate of \alpha_{1\cdot 2} correspondingly. The resulting parameter estimates defines the same lines.

Value

If code.only==FALSE, an object of class MCmcmc which is a mcmc.list object of the relevant parameters, i.e. the posteriors of the conversion parameters and the variance components transformed to the scales of each of the methods.

Furthermore, the object have the following attributes:

random

Character vector indicating which random effects ("ir","mi") were included in the model.

methods

Character vector with the method names.

data

The data frame used in the analysis. This is used in plot.MCmcmc when plotting points.

mcmc.par

A list giving the number of chains etc. used to generate the object.

original

If org=TRUE, an mcmc.list object with the posterior of the original model parameters, i.e. the variance components and the unidentifiable mean parameters.

Transform

The transformation used to the measurements before the analysis.

If code.only==TRUE, a list containing the initial values is generated.

Author(s)

Bendix Carstensen, Steno Diabetes Center, http://BendixCarstensen.com, Lyle Gurrin, University of Melbourne, http://www.epi.unimelb.edu.au/about/staff/gurrin-lyle.

References

B Carstensen: Comparing and predicting between several methods of measurement, Biostatistics, 5, pp 399-413, 2004

See Also

BA.plot, plot.MCmcmc, print.MCmcmc, check.MCmcmc

Examples

data( ox )
str( ox )
ox <- Meth( ox )
# Writes the BUGS program to your console
MCmcmc( ox, MI=TRUE, IR=TRUE, code.only=TRUE, bugs.code.file="" )

### What is written here is not necessarily correct on your machine.
# ox.MC <- MCmcmc( ox, MI=TRUE, IR=TRUE, n.iter=100, program="JAGS" )
# ox.MC <- MCmcmc( ox, MI=TRUE, IR=TRUE, n.iter=100 )
#  data( ox.MC )
#   str( ox.MC )
# print( ox.MC )