DPpackage (version 1.1-7.4)

DPmultmeta: 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.

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.

Details

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

$$y_i \sim N(\mu_i , \Sigma_i), i=1,\ldots,n$$ $$\theta_i | G \sim G$$ $$G | \alpha, G_0 \sim DP(\alpha G_0)$$

where, \(G_0=N(\theta| m_1, s_1)\). To complete the model specification, independent hyperpriors are assumed, $$\alpha | a_0, b_0 \sim Gamma(a_0,b_0)$$ $$m_1 | m_2, s_2 \sim N(mu_2,s_2)$$ $$s_1 | \nu, \psi \sim IW(\nu,\psi)$$

Note that the inverted-Wishart prior is parametrized such that if \(A \sim IW_q(\nu, \psi)\) then \(E(A)= \psi^{-1}/(\nu-q-1)\).

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).

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)<!-- %*%chol(Sigmab1)         -->
      z2 <- mub2+matrix(rnorm(nvar*nrec),nrow=nrec,ncol=nvar)<!-- %*%chol(Sigmab2)        -->
      mu <- ind*z1+(1-ind)*z2
      
      y <- NULL
      for(i in 1:nrec)
      {
          z <- mu[i,]+matrix(rnorm(nvar),nrow=1,ncol=nvar)<!-- %*%chol(Sigma)         -->
          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)

# }