lmw                   package:plw                   R Documentation

_L_o_c_a_l_l_y _M_o_d_e_r_a_t_e_d _W_e_i_g_h_t_e_d-_t.

_D_e_s_c_r_i_p_t_i_o_n:

     Computes Locally Moderated Weighted t-test for microarray data.

_U_s_a_g_e:

     lmw(x,design=rep(1,ncol(x)),contrast=matrix(1), meanX=NULL,
         maxIter = 200, epsilon = 1e-06, verbose = TRUE,
         nknots = 10, nOut = 2000, nIn = 4000, knots = NULL,
         checkRegulation = TRUE)

_A_r_g_u_m_e_n_t_s:

       x: Data, log2 expression indexes.

  design: design matrix

contrast: contrast matrix

   meanX: Covariate used to model scale parameter, default=NULL (see
          details)

 maxIter: maximum number of iterations

 epsilon: convergence criteria

 verbose: print computation info or not

  nknots: Number of knots of spline for v

    nOut: Parameter for calculating knots, see getKnots

     nIn: Parameter for calculating knots, see getKnots

   knots: Knots, if not NULL it overrides nknots, nOut and nIn

checkRegulation: If TRUE, data is checked for a correct specified
          contrast (see details)

_D_e_t_a_i_l_s:

     This function computes the Locally Moderated Weighted-t statistic
     (LMW) described in Astrand (2007b), thus calculating locally
     moderated weighted t-statistic, p-value and log2(FC) for each row
     of the data matrix x.

     Each gene g (row of x) is modeled as:

                     y_g|c_g ~ N(mu_g,c_g*Sigma)


                       c ~ InvGamma(m/2,m*v/2)

     where v is function of the mean intensity: v(mean(mu_g)), N
     denotes a multivariate normal distribution,  Sigma is a covariance
     matrix and  InvGamma(a,b) is the inverse-gamma distribution with
     density function

                f(x)=b^a exp{-b/x} x^{-a-1} /Gamma(a)


     Given the design matrix D, mu_g equals D*gamma_g,  and given the
     contrast matrix C the hypothesis C*gamma_g=0 is tested. C should
     be a one row matrix of same length as the column vector gamma_g.

     See examples on how to specify the design and contrast matrices.

     A cubic spline is used to parameterize the smooth function v(x) 

                        v(x)=exp{H(x)^T beta}

     where  H:R->R^(2p-1)  is a set B-spline basis functions for a
     given set of p interior spline-knots, see chapter 5 of Hastie et
     al. (2001).

     For details about the model see Kristiansson et al. (2005),
     Astrand et al. (2007a,2007b).

     As specified above, v is modeled as a function of mean intensity:
     v(mean(mu_g)). If the parameter meanX is not NULL, meanX is used
     instead of the mean intensity when modeling v. Thus, if meanX is
     not NULL, meanX must be a vector of length equal to the number of
     rows of the data matrix x.

     The parameter estimation procedure is based on the assumption that
     the specified contrast is close to zero for most genes, or at
     least that the median contrast over all genes is close to zero. A
     check is run on data to validate this assumptions. If the checking
     fails, with the error message "warning: most genes appears to be
     regulated..." and if YOU ARE SURE that the design and contrast is
     correct, use checkRegulation=FALSE.

_V_a_l_u_e:

   Sigma: Estimated covariance matrix for y=P' x

       m: Estimated shape parameter for inverse-gamma prior for gene
          variances

       v: Estimated scale parameter curve for inverse-gamma prior for
          gene variances

converged: T if the EM algorithms converged

    iter: Number of iterations

   modS2: Moderated estimator of gene-specific variances

histLogS2: Histogram of log(s2) where s2 is the ordinary variance
          estimator

fittedDensityLogS2: The fitted density for log(s2)

   logs2: Variance estimators, logged with base 2.

       t: Moderated t-statistic

coefficients: Estimated contrast

 p.value: P-value from the moderated t-statistic

     dfT: Degrees of freedom of the moderated t-statistic

 weights: Weights for estimating the contrast

       P: Transformation matrix

    beta: Estimated parameter vector beta of spline for v(x) 

   knots: The knots used in spline for v(x)

_A_u_t_h_o_r(_s):

     Magnus Astrand

_R_e_f_e_r_e_n_c_e_s:

     Hastie, T., Tibshirani, R., and Friedman, J. (2001). The Elements
     of Statistical Learning, volume 1. Springer, first edition.

     Kristiansson, E., Sjogren, A., Rudemo, M., Nerman, O. (2005).
     Weighted Analysis of Paired Microarray Experiments. Statistical
     Applications in Genetics and Molecular Biology 4(1)

     Astrand, M. et al. (2007a). Improved covariance matrix estimators
     for weighted analysis of microarray data. Journal of Computational
     Biology, Accepted.strand

     Astrand, M. et al. (2007b). Empirical Bayes models for
     multiple-probe type arrays at the probe level. Bioinformatics,
     Submitted 1 October 2007.

_S_e_e _A_l_s_o:

     estimateSigmaMVbeta, plw

_E_x_a_m_p_l_e_s:

     # ------------------------------------------
     # Example analyzing the 6 arrays in the 
     # AffySpikeU95Subset data set

     # Loading the data
     data(AffySpikeU95Subset)

     # Defining design and contrast matrix
     group<-factor(rep(1:2,each=3))
     design<-model.matrix(~group-1)
     contrast<-matrix(c(1,-1),1,2)

     # Computing RMA expression index
     data.rma<-exprs(rma(AffySpikeU95Subset))

     # Analyzing
     model1<-lmw(data.rma,design=design,contrast=contrast,epsilon=0.01)

     ## Look at fitted vs observed density for log(s2)
     varHistPlot(model1)

     ## Look at fitted curve for scale parameter
     scaleParameterPlot(model1)

