R: Bayesian analysis for a semiparametric random effects...

DPmultmeta {DPpackage} | R Documentation

## Bayesian analysis for a semiparametric random effects multivariate meta-analysis model using a MDP

### Description

This function generates a posterior density sample for a semiparametric random effects multivariate meta-analysis model using a Dirichlet process or a Mixture of Dirichlet process prior for the distribution of the random effects. Support provided by the NIH/NCI R01CA75981 grant.

### Usage

    DPmultmeta(y,asymvar,prior,mcmc,state,status,
               data=sys.frame(sys.parent()))

### Arguments

`y` | a vector or matrix giving the data or effects from which the density estimate is to be computed.
`asymvar` | a vactor or matrix giving the asymptotic covariance matrix for each effect. The dimension of this matrix is the number of records/studies times the the half-stored elements of the study-specific covariance matrix.
`prior` | a list giving the prior information. The list includes the following parameter: `a0` and `b0` giving the hyperparameters for prior distribution of the precision parameter of the Dirichlet process prior, `alpha` giving the value of the precision parameter (it must be specified if `a0` is missing, see details below), `m2` and `s2` giving the mean and the covariance of the normal prior for the mean, `m1`, of the mean of the normal baseline distribution, respectively, `m1` giving the mean of the baseline distribution (it must be specified if `m2` is missing), `nu` and `psiinv` giving the hyperparameters of the inverted Wishart distribution on the covariance matrix `s1` of the normal baseline distribution, and `s1` giving the covariance matrix of the baseline distribution (it must be specified if `nu` is missing).
`mcmc` | a list giving the MCMC parameters. The list must include the following integers: `nburn` giving the number of burn-in scans, `nskip` giving the thinning interval, `nsave` giving the total number of scans to be saved, and `ndisplay` giving the number of saved scans to be displayed on screen (the function reports on the screen when every `ndisplay` iterations have been carried out).
`state` | a list giving the current value of the parameters. This list is used if the current analysis is the continuation of a previous analysis.
`status` | a logical variable indicating whether this run is new (`TRUE`) or the continuation of a previous analysis (`FALSE`). In the latter case the current value of the parameters must be specified in the object `state`.
`data` | data frame.

### Details

This generic function fits a semiparametric random effects multivariate meta-analysis model:

yi ~ N(thetai, Sigmai), i=1,…,n

thetai | G ~ G

G | alpha, G0 ~ DP(alpha G0)

where, G0=N(theta| m1, s1). To complete the model specification, independent hyperpriors are assumed,

alpha | a0, b0 ~ Gamma(a0,b0)

m1 | m2, s2 ~ N(m2,s2)

s1 | nu, psi ~ IW(nu,psi)

Note that the inverted-Wishart prior is parametrized such that if A ~ IWq(nu, psi) then E(A)= psiinv/(nu-q-1).

To let part of the baseline distribution fixed at a particular value, set the corresponding hyperparameters of the prior distributions to NULL in the hyperprior specification of the model.

The computational implementation of the model is based on the marginalization of the `DP` and on the use of MCMC methods for conjugate priors for a collapsed state of MacEachern (1998).

### Value

An object of class `DPmultmeta` representing the random effects model fit. Generic functions such as `print`, `plot`, and `summary`, have methods to show the results of the fit. The results include `m1`, `s1`, `alpha`, and the number of clusters.

The list `state` in the output object contains the current value of the parameters necessary to restart the analysis. If you want to specify different starting values to run multiple chains set `status=TRUE` and create the list state based on this starting values. In this case the list `state` must include the following objects:

`ncluster` | an integer giving the number of clusters.
`alpha` | giving the value of the precision parameter
`muclus` | a matrix of dimension (nobservations+1)*(nvariables) giving the means of the clusters (only the first `ncluster` are considered to start the chain).
`ss` | an interger vector defining to which of the `ncluster` clusters each subject belongs.
`m1` | giving the mean of the normal baseline distributions.
`s1` | giving the covariance matrix of the normal baseline distributions.

### Author(s)

Alejandro Jara <atjara@uc.cl>

Peter Mueller <pmueller@mdanderson.org>

### References

MacEachern, S.N. (1998) Computational Methods for Mixture of Dirichlet Process Models, in Practical Nonparametric and Semiparametric Bayesian Statistics, eds: D. Dey, P. Muller, D. Sinha, New York: Springer-Verlag, pp. 23-44.

### See Also

`DPmeta`

### Examples

    ## Not run:
        ######################################################################
        # Simulated Data:
        #         mu_i ~ 0.5 N(mub1,Sigmab1) + 0.5 N(mub2,Sigmab2)
        #         y_i ~ N(mu_i,Sigma_i)
        #         Sigma_1=...=Sigma_n=Sigma assumed to be known
        ######################################################################
          nvar <- 2
          nrec <- 100
          Sigma <- matrix(c(0.25,0.15,0.15,0.25),nrow=nvar,ncol=nvar)
          mub1 <- rep(-1.5,nvar)
          mub2 <- rep( 0.5,nvar)
          Sigmab1 <- matrix(c(0.25,-0.175,-0.175,0.25),nrow=nvar,ncol=nvar)
          Sigmab2 <- matrix(c(0.25, 0.0875, 0.0875,0.25),nrow=nvar,ncol=nvar)

          ind <- rbinom(nrec,1,0.5)
          z1 <- mub1+matrix(rnorm(nvar*nrec),nrow=nrec,ncol=nvar)
          z2 <- mub2+matrix(rnorm(nvar*nrec),nrow=nrec,ncol=nvar)
          mu <- ind*z1+(1-ind)*z2

          y <- NULL
          for(i in 1:nrec)
          {
              z <- mu[i,]+matrix(rnorm(nvar),nrow=1,ncol=nvar)
              y <- rbind(y,z)

          }
          colnames(y) <- c("y1","y2")

        ######################################################################
        # Asymptotic variance
        ######################################################################
          z <- NULL
          for(i in 1:nvar)
          {
              for(j in i:nvar)
              {
                    z <- c(z,Sigma[i,j])
              }
          }
          asymvar <- matrix(z,nrow=nrec,ncol=nvar*(nvar+1)/2,byrow=TRUE)

        # Prior information

          s2 <-diag(100,nvar)
          m2 <-rep(0,nvar)
          nu <- 4
          psiinv <- diag(1,nvar)

          prior<-list(a0=1,
                      b0=1/5,
                      nu=nu,
                      m2=m2,
                      s2=s2,
                      psiinv=psiinv)

        # Initial state
          state <- NULL

        # MCMC parameters

          nburn <- 500
          nsave <- 1000
          nskip <- 0
          ndisplay <- 100
          mcmc <- list(nburn=nburn,
                       nsave=nsave,
                       nskip=nskip,
                       ndisplay=ndisplay)

        # Fitting the model
          fit1 <- DPmultmeta(y=y,asymvar=asymvar,prior=prior,
                             mcmc=mcmc,state=state,status=TRUE)

    ## End(Not run)

[Package DPpackage version 1.1-7.4 Index]