R/leeall_multivariate.R

In SandraCastroPearson/BivRec: Bivariate Alternating Recurrent Event Data Analysis

##------symmetric O function
#o.fun=function(t,s,L) {log(min(max(t,s),L))-log(L)}

##-----estimation functions
##proposed method
MPro.ee1=function(beta1,mdat, amat) {

  n=mdat$n
  xmat=mdat$xmat
  delta1=mdat$delta1
  g1mat=mdat$g1mat
  l1=mdat$l1
  mstar=mdat$mstar
  nparams = length(beta1)
  subsum = rep(0, n)

  tmp.out=NULL
  for (i in 1:n) {
    A=t(t(amat)-amat[i,])
    expA=apply(A,1,function(x)exp(x%*%beta1))
    di <- delta1[i,1:mstar[i]]
    xmati <- xmat[i,1:mstar[i]]
    gmati <- g1mat[i,1:mstar[i]]
    subsum <- r2f.mpro.ee1(n, nparams, di, xmati, gmati, L=l1, expA, subsum, kcount=mstar[i])
    #subsum=sapply(expA,function(x)mean(delta1[i,1:mstar[i]]*sapply(xmat[i,1:mstar[i]],function(t)o.fun(t,x*t,l1))/g1mat[i,1:mstar[i]]))
    tmp.out=rbind(tmp.out,apply(A*subsum,2,sum))
  }
  out=apply(tmp.out,2,sum)/(n^2)

  return(out)
}

MPro.uf1=function(beta1,mdat, amat) {
  tmp.out=MPro.ee1(beta1,mdat, amat)
  out=tmp.out%*%tmp.out
  return(out)
}

MPro.uest1=function(init,mdat, amat) {
  res=optim(init, MPro.uf1, mdat=mdat, amat=amat, control=list(maxit=20000))
  return(list(par=res$par,value=res$value,conv=res$convergence))
}

MPro.ee2=function(beta2,beta1,mdat, amat) {
  n=mdat$n
  xmat=mdat$xmat
  ymat=mdat$ymat
  #zmat=mdat$zmat
  #delta1=mdat$delta1
  delta2=mdat$delta2
  #g1mat=mdat$g1mat
  g2mat=mdat$g2mat
  #l1=mdat$l1
  l2=mdat$l2
  mstar=mdat$mstar
  nparams = length(beta1)
  subsum = rep(0, n)

  tmp.out=NULL
  for (i in 1:n) {
    A=t(t(amat)-amat[i,])
    expA1=apply(A,1,function(x)exp(x%*%beta1))
    expA2=apply(A,1,function(x)exp(x%*%beta2))
    expA=cbind(expA1,expA2)
    di <- delta2[i,1:mstar[i]]
    xmati <- xmat[i,1:mstar[i]]
    ymati <- ymat[i,1:mstar[i]]
    gmati <- g2mat[i,1:mstar[i]]
    subsum <- r2f.mpro.ee2(n, nparams, di, xmati, ymati, gmati, L=l2, expA, subsum, kcount=mstar[i])
    #subsum=apply(expA,1,function(x)mean(delta2[i,1:mstar[i]]*apply(cbind(xmat[i,1:mstar[i]],ymat[i,1:mstar[i]]),1,function(t)o.fun(sum(t),x[1]*t[1]+x[2]*t[2],l2))/g2mat[i,1:mstar[i]]))
    tmp.out=rbind(tmp.out,apply(A*subsum,2,sum))
  }
  out=apply(tmp.out,2,sum)/(n^2)
  return(out)
}

MPro.uf2 <- function(beta2,beta1,mdat, amat) {
  tmp.out <- MPro.ee2(beta2,beta1,mdat, amat)
  out <- tmp.out%*%tmp.out
  return(out)
}

MPro.uest2 <- function(init, beta1, mdat, amat) {
  res <- optim(init, MPro.uf2, beta1=beta1, mdat=mdat, amat=amat, control=list(maxit=20000))
  return(list(par=res$par,value=res$value,conv=res$convergence))
}

##variance estimation
Mvar.est=function(beta1,beta2,mdat, amat) {
  n=mdat$n
  xmat=mdat$xmat
  ymat=mdat$ymat
  mc=mdat$mc
  #zmat=mdat$zmat
  delta1=mdat$delta1
  delta2=mdat$delta2
  g1mat=mdat$g1mat
  g2mat=mdat$g2mat
  l1=mdat$l1
  l2=mdat$l2
  mstar=mdat$mstar

  xi=matrix(0,length(c(beta1,beta2)),length(c(beta1,beta2)))
  gam1=gam21=gam22=rep(0,length(beta1))
  nparams <- length(beta1)

  for (i in 1:n) {
    A=t(t(amat)-amat[i,])
    expA1=apply(A,1,function(x)exp(x%*%beta1))
    expA2=apply(A,1,function(x)exp(x%*%beta2))
    expA=cbind(expA1,expA2)
    d1i <- delta1[i,1:mstar[i]]
    d2i <- delta2[i,1:mstar[i]]
    xmati <- xmat[i,1:mstar[i]]
    ymati <- ymat[i,1:mstar[i]]
    gmati1 <- g1mat[i,1:mstar[i]]
    gmati2 <- g2mat[i,1:mstar[i]]

    subsum <- rep(0,n)

    sub1.xi1 <- r2f.mpro.ee1(n, nparams, di=d1i, xmati, gmati=gmati1, L=l1, expA=expA1, subsum, kcount=mstar[i])
    sub1.xi2 <- r2f.mpro.ee2(n, nparams, di=d2i, xmati, ymati, gmati=gmati2, L=l2, expA, subsum, kcount=mstar[i])

    #sub1.xi1=sapply(expA1,function(x)mean(delta1[i,1:mstar[i]]*sapply(xmat[i,1:mstar[i]],function(t)o.fun(t,x*t,l1))/g1mat[i,1:mstar[i]]))
    #sub1.xi2=apply(expA,1,function(x)mean(delta2[i,1:mstar[i]]*apply(cbind(xmat[i,1:mstar[i]],ymat[i,1:mstar[i]]),1,function(t)o.fun(sum(t),x[1]*t[1]+x[2]*t[2],l2))/g2mat[i,1:mstar[i]]))

    sub2 <- r2f.mpro.var(n, nparams, xmat, ymat, gmatx=g1mat, gmaty=g2mat, l1, l2,
                         expAx=expA1, expAy=expA2, subsumx=subsum, subsumy=subsum, dx=delta1, dy=delta2, mstar, mc)
    sub2.xi1 <- sub2[,1]
    sub2.xi2 <- sub2[,2]

    # sub2.xi1 = sub2.xi2 = rep(0, n)
    # for (j in 1:n) {
    #   sub2.xi1[j]=mean(delta1[j,1:mstar[j]]*sapply(xmat[j,1:mstar[j]],function(t)o.fun(t,t/expA1[j],l1))/g1mat[j,1:mstar[j]])
    #   sub2.xi2[j]=mean(delta2[j,1:mstar[j]]*apply(cbind(xmat[j,1:mstar[j]],ymat[j,1:mstar[j]]),1,function(t)o.fun(sum(t),t[1]/expA1[j]+t[2]/expA2[j],l2))/g2mat[j,1:mstar[j]])
    # }

    tmp.xi1=apply(A*(sub1.xi1-sub2.xi1),2,sum)/(n^(3/2))
    tmp.xi2=apply(A*(sub1.xi2-sub2.xi2),2,sum)/(n^(3/2))

    xi=xi+c(tmp.xi1,tmp.xi2)%o%c(tmp.xi1,tmp.xi2)

    Amat=apply(A,1,function(x) x%o%x)
    tmp.sub.gam1=apply(cbind(xmat[i,1],expA1*xmat[i,1],l1),1,function(x)(x[1]<=x[2])*(max(x[1],x[2])<=x[3]))
    tmp.sub.gam2=apply(cbind(xmat[i,1]+ymat[i,1],expA1*xmat[i,1]+expA2*ymat[i,1],l2),1,function(x)(x[1]<=x[2])*(max(x[1],x[2])<=x[3]))
    sub.gam1=t(Amat)*tmp.sub.gam1*mean(delta1[i,1:mstar[i]]/g1mat[i,1:mstar[i]])
    sub.gam21=t(Amat)*tmp.sub.gam2*apply(expA,1,function(x) mean(delta2[i,1:mstar[i]]*(x[1]*xmat[i,1:mstar[i]])/((x[1]*xmat[i,1:mstar[i]]+x[2]*ymat[i,1:mstar[i]])*g2mat[i,1:mstar[i]])))
    sub.gam22=t(Amat)*tmp.sub.gam2*apply(expA,1,function(x) mean(delta2[i,1:mstar[i]]*(x[2]*ymat[i,1:mstar[i]])/((x[1]*xmat[i,1:mstar[i]]+x[2]*ymat[i,1:mstar[i]])*g2mat[i,1:mstar[i]])))

    gam1=gam1+apply(sub.gam1,2,sum)/(n^2)
    gam21=gam21+apply(sub.gam21,2,sum)/(n^2)
    gam22=gam22+apply(sub.gam22,2,sum)/(n^2)
  }

  gam1=matrix(gam1,length(beta1),length(beta1))
  gam21=matrix(gam21,length(beta2),length(beta2))
  gam22=matrix(gam22,length(beta2),length(beta2))
  gamm=rbind(cbind(gam1,matrix(0,length(beta1),length(beta2))),cbind(gam21,gam22))

  mat=solve(gamm)%*%xi%*%t(solve(gamm))
  se = sqrt(diag(mat)/n)
  return(list(se, mat/n))
}

##################################################################
##################### FUNCTION NOT FOR USER ######################
##################################################################
#' A Function for multivariate fits using semiparametric regression method on a bivrecSurv object
#'
#' @description
#' This function fits the semiparametric model given one  covariate. Called from bivrecReg(). No user interface.
#' @param response Passed from bivrecReg().
#' @param amat Passed from bivrecReg().
#' @param cov_names Passed from bivrecReg().
#' @param SE Passed from bivrecReg()
#' @return A list with estimates, SE and variance-covariance matrix.
#'
#' @importFrom stats na.omit
#' @importFrom stats optim
#' @importFrom stats optimize
#' @importFrom stats qnorm
#' @importFrom stringr str_c
#'
#' @noRd
#' @keywords internal


#multivariable regression analysis
leeall_multivariate <- function(response, amat, cov_names, SE) {

  print(paste("Fitting model with covariates:", stringr::str_c(cov_names, collapse = ", "), sep=" "))
  n_params <- length(cov_names)

  #solve first equation to get beta1 values - related to xij
  mpro1 <- MPro.uest1(init=rep(0, n_params), mdat=response, amat=amat)

  #solve second equation to get beta2 values - related to yij
  mpro2 <- MPro.uest2(init=rep(0, n_params), beta1=mpro1$par, mdat=response, amat = amat)

  if (SE==TRUE) {

    print("Estimating standard errors")
    #estimate covariance matrix and get diagonal then std. errors
    se_est <- Mvar.est(beta1=mpro1$par, beta2=mpro2$par, mdat=response, amat = amat)
    #join all info and calculate CIs, put in nice table
    fit <- data.frame(c(mpro1$par, mpro2$par), se_est[[1]])
    colnames(fit) <- c("Estimate", "SE")
    rownames(fit) <- c(paste("xij", cov_names),
                       paste("yij", cov_names))
    result <- list(fit = as.matrix(fit), vcovmat = se_est[[2]])

  } else {
    #return point estimates only
    fit <- data.frame(c(mpro1$par, mpro2$par))
    colnames(fit) <- c("Estimate")
    rownames(fit) <- c(paste("xij", cov_names), paste("yij", cov_names))
    result <- list(mpro1$par, mpro2$par, fit)
  }
  return(result)
}