MCmcmc: Fit a model for method comparison studies using WinBUGS
In MethComp: Analysis of Method Comparison studies

Description Usage Arguments Details Value Author(s) References See Also Examples

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 functions jags.model and coda.samples from the rjags package.

  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.code.file = "model.txt",
       clearWD = TRUE,
     code.only = FALSE,
      ini.mult = 2,
      list.ini = TRUE,
           org = FALSE,
     Transform = NULL,
     trans.tol = 1e-6 )
## S3 method for class 'MCmcmc'
summary( object, alpha=0.05, ...)
## S3 method for class 'MCmcmc'
print( x, digits=3, alpha=0.05, ... )
## S3 method for class 'MCmcmc'
subset( x, subset=NULL, allow.repl=FALSE, chains=NULL, ... )
## S3 method for class 'MCmcmc'
mcmc( x, ... )

`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`.
`clearWD`	Should the working directory be cleared for junk files after the running of WinBUGS — passed on to `bugs`.
`bugs.code.file`	Where should the bugs code go?
`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.
`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.
`object`	An `MCmcmc` object
`alpha`	1 minus the the confidence level
`...`	Arguments passed on to other methods
`x`	An `MCmcmc` object
`digits`	Number of digits after the decimal point when printing.
`subset`	Numerical, character or list giving the variables to keep. If numerical, the variables in the `MCmcmc` object with these numbers are selected. If character, each element of the character vector is "grep"ed against the variable names, and the matches are selected to the subset. If a list each element is used in turn, numerical and character elements can be mixed.
`allow.repl`	Should duplicate columns be allowed in the result?
`chains`	Numerical vector giving the number of the chains to keep.

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" %in% random) and c_mi is a random meth by item interaction (included if "mi" %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|k=alpha_m-alpha_k beta_m/beta_k, beta_m|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,

median(beta.1.2)=1/median(beta.2.1)

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

median(alpha.1.2)=median(-alpha.2.1/beta.2.1)

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.2.1 as

(median(alpha.1.2)-median(alpha.2.1)/ median(beta.2.1))/2

and the estimate of alpha.1.2 correspondingly. The resulting parameter estimates defines the same lines.

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, and the generated BUGS code is printed to the console.

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

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

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

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

## Run JAGS
# ox.MC <- MCmcmc( ox, MxI=TRUE, IxR=TRUE, n.iter=100 )
#  data( ox.MC )
#   str( ox.MC )
# print( ox.MC )