R/PNfrailtyHL.R

In frailtyHL: Frailty Models via Hierarchical Likelihood

PNfrailtyHL <-
function (x, z, y, del, Mi, idx2, t2, di, beta_h0, v_h0, alpha_h0, 
    mord, dord, varfixed = FALSE,varnonneg) 
{
    n <- nrow(x)
    p <- ncol(x)
    nrand <- length(z)
    q <- rep(0, nrand)
    for (i in 1:nrand) q[i] <- dim(z[[i]])[2]
    qcum <- cumsum(c(0, q))
    beta_h <- beta_h0
    v_h <- v_h0
    for (i in 1:nrand) {
        if (alpha_h0[i] < 1e-06) 
            alpha_h0[i] <- 1e-06
    }
    alpha_h <- alpha_h0
    zz <- z[[1]]
    if (nrand > 1) {
        index1 <- nrand
        for (i in 2:index1) zz <- cbind(zz, z[[i]])
    }
    z <- matrix(0, n, qcum[nrand + 1])
    z[1:n, 1:qcum[nrand + 1]] <- zz[1:n, 1:qcum[nrand + 1]]
    muh <- x %*% beta_h0 + z %*% v_h0
    expeta <- exp(muh)
    cla0 <- di/(t(Mi) %*% expeta)
    Wi <- diag(expeta[, 1])
    Ai <- diag(cla0[, 1])
    done <- matrix(1, idx2, 1)
    oq <- matrix(1, qcum[nrand + 1], 1)
    oq1 <- matrix(1, qcum[nrand + 1], 1)
    clam0 <- Mi %*% Ai %*% done
    for (i in 1:nrand) {
        index1 <- qcum[i] + 1
        oq1[index1:qcum[i + 1]] <- alpha_h[i]
    }
    D <- diag(oq1[, 1])
    iD <- solve(D)
    dft1 <- t(x) %*% (del - Wi %*% clam0)
    if (mord == 1) {
        U <- iD
        Bi <- diag(clam0[, 1])
        temp4 <- cla0^2/di
        As <- diag(temp4[, 1])
        mat <- (Wi %*% Bi) - (Wi %*% Mi) %*% As %*% (t(Mi) %*% 
            Wi)
        dinv <- solve(t(z) %*% mat %*% z + U)
        mu0 <- exp(x %*% beta_h0 + z %*% v_h0)
        mu <- exp(x %*% beta_h0 + z %*% v_h0) * clam0
        dcla0be <- -As %*% (t(Mi) %*% Wi)
        dcla0b <- matrix(0, idx2, p)
        dv_db <- matrix(0, qcum[nrand + 1], p)
        xz <- matrix(0, n, p)
        dmu0 <- matrix(0, n, p)
        dw_db1 <- matrix(0, n, p)
        xk <- matrix(0, n, 1)
        ad1 <- matrix(0, p, 1)
        for (k in 1:p) {
            xk[, 1] <- x[, k]
            dv_db[, k] <- -dinv %*% (t(z) %*% mat %*% xk)
            xz[, k] <- xk + z %*% (dv_db[, k])
            dcla0b[, k] <- dcla0be %*% (xz[, k])
            dc <- Mi %*% diag(dcla0b[, k]) %*% done
            dmu0[, k] <- mu0 * (xz[, k])
            dw_db1[, k] <- dc * mu0 + mu * xz[, k]
            temp4 <- (2 * cla0/di) * (dcla0b[, k])
            dw_db2 <- ((diag(dmu0[, k])) %*% Mi %*% As %*% t(Mi) %*% 
                Wi) + (Wi %*% Mi %*% diag(temp4[, 1]) %*% t(Mi) %*% 
                Wi) + (Wi %*% Mi %*% As %*% t(Mi) %*% (diag(dmu0[, 
                k])))
            dw_db <- diag(dw_db1[, k]) - dw_db2
            ad1[k, 1] <- sum(diag(dinv %*% (t(z) %*% dw_db %*% 
                z)))
        }
        dft1 <- dft1 - 0.5 * ad1
    }
    dft2 <- t(z) %*% (del - Wi %*% clam0) - (iD %*% v_h0)
    dft <- rbind(dft1, dft2)
    Bi <- diag(clam0[, 1])
    temp4 <- cla0^2/di
    Adi <- diag(temp4[, 1])
    As <- Adi
    mat <- (Wi %*% Bi) - (Wi %*% Mi) %*% Adi %*% (t(Mi) %*% Wi)
    U <- iD
    H <- rbind(cbind(t(x) %*% mat %*% x, t(x) %*% mat %*% z), 
        cbind(t(z) %*% mat %*% x, t(z) %*% mat %*% z + U))
    H0 <- rbind(cbind(t(x) %*% mat %*% x, t(x) %*% mat %*% z), 
        cbind(t(z) %*% mat %*% x, t(z) %*% mat %*% z))
    Hinv <- solve(H)
    be_h0 <- rbind(beta_h0, v_h0)
    be_h <- be_h0 + (Hinv %*% dft)
    beta_h[1:p, 1] <- be_h[1:p, 1]
    se_beta_h <- matrix(0, p, 1)
    for (i in 1:p) se_beta_h[i, 1] <- sqrt(Hinv[i, i])
    index2 <- qcum[nrand + 1]
    index3 <- p + 1
    index4 <- p + qcum[nrand + 1]
    v_h[1:index2, 1] <- be_h[index3:index4, 1]
    nonneg_adj=0
    if (varnonneg == TRUE) nonneg_adj=2
    for (i in 1:nrand) {
        if (dord == 0) {
            index1 <- p + qcum[i] + 1
            index2 <- p + qcum[i + 1]
            gamma <- sum(diag(Hinv[index1:index2, index1:index2]))/alpha_h[i]
            index1 <- qcum[i] + 1
            index2 <- qcum[i + 1]
            if (varfixed == FALSE) 
                alpha_h[i] <- sum(v_h[index1:index2, 1]^2)/(q[i] - 
                  gamma-nonneg_adj)
        }
        if (dord == 1 | dord == 2) {
            H22 <- solve(t(z) %*% mat %*% z + U)
            ial1 <- 1/alpha_h[i]
            iA <- iD
            C <- matrix(0, qcum[nrand + 1], qcum[nrand + 1])
            index1 <- qcum[i] + 1
            index2 <- qcum[i + 1]
            for (j in index1:index2) C[j, j] <- 1
            iB1 <- iA %*% C %*% iA
            c_vh1 <- iB1 %*% v_h
            dv1 <- H22 %*% c_vh1
            dexpeta1 <- expeta * (z %*% dv1)
            dcla01 <- -(di/((t(Mi) %*% expeta)^2)) * (t(Mi) %*% 
                dexpeta1)
            dWi1 <- diag(dexpeta1[, 1])
            dAi1 <- diag(dcla01[, 1])
            temp4 <- Mi %*% dAi1 %*% done
            dBi1 <- diag(temp4[, 1])
            dvec1 <- 2 * (cla0 * dcla01)
            temp4 <- dvec1/di
            dAs1 <- diag(temp4[, 1])
            dmat1 <- (dWi1 %*% Bi) + (Wi %*% dBi1) - (dWi1 %*% 
                Mi %*% As %*% t(Mi) %*% Wi) - (Wi %*% Mi %*% 
                dAs1 %*% t(Mi) %*% Wi) - (Wi %*% Mi %*% As %*% 
                t(Mi) %*% dWi1)
            dia1 <- -iB1
            Hd1 <- rbind(cbind(t(x) %*% dmat1 %*% x, t(x) %*% 
                dmat1 %*% z), cbind(t(z) %*% dmat1 %*% x, t(z) %*% 
                dmat1 %*% z + dia1))
            gamma1 <- -alpha_h[i] * sum(diag((Hinv %*% Hd1)))
            if (dord == 2) {
                expeta <- exp(x %*% beta_h + z %*% v_h)
                ial1 <- 1/alpha_h[i]
                muu <- exp(x %*% beta_h) * clam0
                zmuu <- t(z) %*% muu
                u_h <- exp(v_h)
                ude1 <- u_h * dv1
                aa1 <- (zmuu * u_h) + ial1
                bb1 <- (zmuu * ude1) - (ial1^2)
                term11 <- ((aa1 * zmuu * ude1) - (2 * zmuu * 
                  u_h * bb1))/(aa1^3)
                term21 <- ((2 * aa1 * zmuu * zmuu * u_h * ude1) - 
                  (3 * ((zmuu * u_h)^2) * bb1))/(aa1^4)
                term1 <- (3 * term11) - (5 * term21)
                SS1 <- diag(term1[, 1])
                gamma21 <- -(alpha_h[i]/12) * sum(diag(SS1))
            }
            if (dord == 1) {
                gamma21 <- 0
            }
            k21 <- q[i] - gamma1 - gamma21 - sum(v_h[index1:index2, 
                1]^2)/(alpha_h[i])
            if (varfixed == FALSE) 
                alpha_h[i] <- sum(v_h[index1:index2, 1]^2)/(q[i] - 
                  gamma1 - gamma21-nonneg_adj)
        }
    }
    res <- list(x, z, y, del, Mi, idx2, t2, di, beta_h0, v_h0, 
        beta_h, v_h, alpha_h0, alpha_h, dft, Hinv, clam0, H, 
        mat, se_beta_h, U, H0)
    return(res)
}