R/fun_mrypt.R

In ClinicalTrialSummary: Summary Measures for Clinical Trials with Survival Outcomes

fun_mrypt <- function(oy, od, oz, best, tau, alpha, repnum, ...) {

    n <- length(oy)

    oyl <- c(0, oy[1:(n - 1)])
    oyr <- c(oy[2:n], tau)

    bt <- exp(-best)
    bt1 <- bt[1]
    bt2 <- bt[2]

    jh <- 1e-08
    K <- n:1

    b <- as.numeric(best) + cbind(c(jh, 0), -c(jh, 0), c(0, jh), -c(0,
        jh))
    gamma1 <- exp(-matrix(b[1, ], nrow = 1) %x% oz)
    gamma2 <- exp(-matrix(b[2, ], nrow = 1) %x% oz)
    Lambda2 <- apply(od * gamma2/K, 2, cumsum)
    P <- exp(-Lambda2)
    PL <- rbind(1, P[1:(n - 1), ])
    R <- apply(PL * od * gamma1/K, 2, cumsum)/P

    denom <- gamma1 + gamma2 * R
    u1 <- -(oz * od) %*% (gamma1/denom) + oz %*% (R/denom)
    u2 <- -(oz * od) %*% (gamma2 * R/denom) + oz %*% (log(denom/gamma1)/gamma2) -
        oz %*% (R/denom)
    qf <- rbind(u1, u2)
    pq <- cbind(qf[, 1] - qf[, 2], qf[, 3] - qf[, 4])/2/jh
    pr <- cbind(R[, 1] - R[, 2], R[, 3] - R[, 4])/2/jh

    inq <- solve(-pq/n)


    r <- R[, 1]
    rl <- c(0, r[1:(n - 1)])
    dr <- r - rl
    po <- P[, 1]
    plo <- PL[, 1]
    g1 <- gamma1[, 1]
    g2 <- gamma2[, 1]
    den <- bt1 + bt2 * r

    lamh2 <- log(1 + bt2/bt1 * r)/bt2
    lamh1 <- log(1 + r)

    fc <- r/(1 + r)
    ft <- 1 - exp(-lamh2)

    ntl <- sum(oy < tau)
    dytau <- c(oy[1:ntl], tau) - c(0, oy[1:ntl])
    dy <- oy - c(0, oy[1:(n - 1)])

    rmc <- as.numeric(t(c(0, fc[1:ntl])) %*% dytau)
    rmr <- as.numeric(t(c(0, ft[1:ntl])) %*% dytau/rmc)

    Bt1 <- r/den
    Bt2 <- lamh2 - Bt1
    Bt <- cbind(Bt1, Bt2)
    Btt <- Bt + pr/den
    Btc <- pr/(1 + r)

    Btt0 <- (1 - ft) * Btt
    Btc0 <- (1 - fc) * Btc
    Btt0l <- rbind(0, Btt0[1:(n - 1), ])
    Btc0l <- rbind(0, Btc0[1:(n - 1), ])

    Ct0 <- (1 - ft)/po/den
    Cc0 <- (1 - fc)/po/(1 + r)

    Ct0l <- c(exp(best[1]), Ct0[1:(n - 1)])
    Cc0l <- c(1, Cc0[1:(n - 1)])

    Ct <- cumsum(dy * Ct0l) - dy * Ct0l
    Cc <- cumsum(dy * Cc0l) - dy * Cc0l

    B1 <- t(dytau) %*% rbind(0, Btt0[1:ntl, ]) - rmr * (t(dytau) %*% rbind(0,
        Btc0[1:ntl, ]))
    B1 <- B1/rmc
    B2 <- t(dytau) %*% c(c(Ct0[1:ntl], Ct0[min(c(n, ntl + 1))]) - rmr *
        c(Cc0[1:ntl], Cc0[min(c(n, ntl + 1))]))
    B2 <- as.numeric(t(dytau) %*% c(c(exp(best[1]), Ct0[1:ntl]) - rmr *
        c(1, Cc0[1:ntl])))

    Cb <- (B2 - Ct + rmr * Cc) * (oy <= tau)/rmc


    inrs1 <- c()
    inrs2 <- c()
    inrw <- c()
    inrsw1 <- c()
    inrsw2 <- c()
    for (ti in 1:n) {
        yk <- (oy >= oy[ti])
        dk <- g1 + r[ti] * g2
        tek <- yk/dk
        inrs1[ti] <- t(oz) %*% (g1 * tek/dk)
        inrs2[ti] <- R[ti] * t(oz) %*% (g2 * tek/dk)
        inrw[ti] <- t(g2) %*% tek
        inrsw1[ti] <- t(oz) %*% (g1 * g2 * tek/dk^2)
        inrsw2[ti] <- R[ti] * t(oz) %*% (g2^2 * tek/dk^2)
    }

    inr1 <- (inrsw1 - inrw * inrs1/K) * dr/po
    inr2 <- (inrsw2 - inrw * inrs2/K) * dr/po

    inr1 <- inr1 + sum(inr1) - cumsum(inr1)
    inr2 <- inr2 + sum(inr2) - cumsum(inr2)

    rmul <- plo/K
    inr1 <- inr1 * rmul
    inr2 <- inr2 * rmul

    di <- g1 + g2 * r

    xi1d <- oz * g1/di - inrs1 * di/K + inr1 * di
    xi2d <- oz * g2 * r/di - inrs2 * di/K + inr2 * di

    xi1d <- xi1d * od
    xi2d <- xi2d * od

    cid <- sqrt(n) * plo/K * di * od

    B1inq <-  as.numeric(B1 %*% inq)
    cids1 <- Cb * cid
    cids2 <- rep(0, length(cids1))

    mb <- ransamf(repnum = repnum, n = n, B1inq = B1inq, xi1d = xi1d, xi2d = xi2d, cids1 = cids1, cids2 = cids2)

    stmb <- sd(mb)
    ca3 <- qnorm(1 - alpha/2)
    uppc <- rmr * exp(ca3 * stmb/rmr/sqrt(n))
    lowc <- rmr * exp(-ca3 * stmb/rmr/sqrt(n))
    zv <- sqrt(n) * log(rmr) * rmr/stmb

    result <- list()
    result$estimate <- rmr
    result$lower <- lowc
    result$upper <- uppc
    result$z <- as.numeric(zv)
    result$pvalue <- 2 * (1 - pnorm(abs(zv)))

    return(result)
}