Nothing
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### Reference:
### Tang X, Wahed AS: Cumulative hazard ratio estimation for treatment regimes in
### sequentially randomized clinical trials. Statistics in Biosciences, [Epub ahead of print]
###################################################
###################################################
### code chunk number 1: chunklibraries
###################################################
#Libraries required
require(survival)
###################################################
### code chunk number 2: chunkCHR
###################################################
updateBeta <- function(beta, # Current coefficient(s) for covariate(s)
V, # Covariate(s)
U, # Observed survival time
delta, # Censoring indicator
w11, # Weights for A1B1
w12, # Weights for A1B2
w21, # Weights for A2B1
w22 # Weights for A2B2
) {
#Total number of subjects
n <- length(U)
#If only 1 covariate
if(NCOL(V)==1) {
#Change V from matrix to numeric
V <- as.numeric(V)
#Calcualte exp(beta*V)
e <- exp(beta*V)
#Define ui and derivative of U: dui
ui <- 0
dui <- 0
for(i in 1:length(U)) {
ind <- as.numeric(U >= U[i])
#Calculate s0j
s00 <- sum(ind * w11 * e) / n
s01 <- sum(ind * w12 * e) / n
s02 <- sum(ind * w21 * e) / n
s03 <- sum(ind * w22 * e) / n
#Calculate s1j
s10 <- sum(ind * w11 * e * V) / n
s11 <- sum(ind * w12 * e * V) / n
s12 <- sum(ind * w21 * e * V) / n
s13 <- sum(ind * w22 * e * V) / n
#Calculate s2j
s20 <- sum(ind * w11 * e * V * V) / n
s21 <- sum(ind * w12 * e * V * V) / n
s22 <- sum(ind * w21 * e * V * V) / n
s23 <- sum(ind * w22 * e * V * V) / n
#Calculate v1?_bar
if(s00 != 0) v10_bar <- s10/s00 else v10_bar <- 0
if(s01 != 0) v11_bar <- s11/s01 else v11_bar <- 0
if(s02 != 0) v12_bar <- s12/s02 else v12_bar <- 0
if(s03 != 0) v13_bar <- s13/s03 else v13_bar <- 0
#calculate v2?_bar
if(s00 != 0) v20_bar <- s20/s00 else v20_bar <- 0
if(s01 != 0) v21_bar <- s21/s01 else v21_bar <- 0
if(s02 != 0) v22_bar <- s22/s02 else v22_bar <- 0
if(s03 != 0) v23_bar <- s23/s03 else v23_bar <- 0
#Calculate each ui
ui <- ui + delta[i]*w11[i]*(V[i] - v10_bar) +
delta[i]*w12[i]*(V[i] - v11_bar) +
delta[i]*w21[i]*(V[i] - v12_bar) +
delta[i]*w22[i]*(V[i] - v13_bar)
#Calculate each dui
dui <- dui + delta[i]*w11[i]*(v10_bar^2 - v20_bar) +
delta[i]*w12[i]*(v11_bar^2 - v21_bar) +
delta[i]*w21[i]*(v12_bar^2 - v22_bar) +
delta[i]*w22[i]*(v13_bar^2 - v23_bar)
}
}
#If more than 1 covariates
if(NCOL(V)>1) {
#Calcualte exp(beta*V)
e <- as.numeric(exp(matrix(beta, nrow=1, ncol=NCOL(V)) %*% t(V)))
#Define ui and derivative of U: dui
ui <- matrix(0, nrow=NCOL(V), ncol=1)
dui <- matrix(0, nrow=NCOL(V), ncol=NCOL(V))
for(i in 1:length(U)) {
ind <- as.numeric(U >= U[i])
#Calculate s0j
s00 <- sum(ind * w11 * e) / n
s01 <- sum(ind * w12 * e) / n
s02 <- sum(ind * w21 * e) / n
s03 <- sum(ind * w22 * e) / n
#Calculate s1j
s10 <- t(matrix(ind*w11*e,nrow=1, ncol=n) %*% V / n)
s11 <- t(matrix(ind*w12*e,nrow=1, ncol=n) %*% V / n)
s12 <- t(matrix(ind*w21*e,nrow=1, ncol=n) %*% V / n)
s13 <- t(matrix(ind*w22*e,nrow=1, ncol=n) %*% V / n)
#Calculate s2j
s20 <- t(V) %*% diag(as.numeric(ind*w11*e)) %*% V / n
s21 <- t(V) %*% diag(as.numeric(ind*w12*e)) %*% V / n
s22 <- t(V) %*% diag(as.numeric(ind*w21*e)) %*% V / n
s23 <- t(V) %*% diag(as.numeric(ind*w22*e)) %*% V / n
#Calculate z1?_bar
if(s00 != 0) v10_bar <- s10/s00 else v10_bar <- matrix(0, nrow=NCOL(V), ncol=1)
if(s01 != 0) v11_bar <- s11/s01 else v11_bar <- matrix(0, nrow=NCOL(V), ncol=1)
if(s02 != 0) v12_bar <- s12/s02 else v12_bar <- matrix(0, nrow=NCOL(V), ncol=1)
if(s03 != 0) v13_bar <- s13/s03 else v13_bar <- matrix(0, nrow=NCOL(V), ncol=1)
#calculate z2?_bar
if(s00 != 0) v20_bar <- s20/s00 else v20_bar <- matrix(0, nrow=NCOL(V), ncol=NCOL(V))
if(s01 != 0) v21_bar <- s21/s01 else v21_bar <- matrix(0, nrow=NCOL(V), ncol=NCOL(V))
if(s02 != 0) v22_bar <- s22/s02 else v22_bar <- matrix(0, nrow=NCOL(V), ncol=NCOL(V))
if(s03 != 0) v23_bar <- s23/s03 else v23_bar <- matrix(0, nrow=NCOL(V), ncol=NCOL(V))
#Calculate each ui
ui <- ui + delta[i]*w11[i]*(matrix(V[i,], nrow=NCOL(V), ncol=1) - v10_bar) +
delta[i]*w12[i]*(matrix(V[i,], nrow=NCOL(V), ncol=1) - v11_bar) +
delta[i]*w21[i]*(matrix(V[i,], nrow=NCOL(V), ncol=1) - v12_bar) +
delta[i]*w22[i]*(matrix(V[i,], nrow=NCOL(V), ncol=1) - v13_bar)
#Calculate each dui
dui <- dui + delta[i]*w11[i]*(v10_bar %*% t(v10_bar) - v20_bar) +
delta[i]*w12[i]*(v11_bar %*% t(v11_bar) - v21_bar) +
delta[i]*w21[i]*(v12_bar %*% t(v12_bar) - v22_bar) +
delta[i]*w22[i]*(v13_bar %*% t(v13_bar) - v23_bar)
}
}
#Update beta
beta_up <- beta - solve(dui) %*% ui
return(beta_up)
}
CHRestimate <- function(data, # A complete data frame representing the data for two-stage randomization designs
# data = data frame {X, R, Z, U, delta, V}
# V represents covariates
# There could be one covariate, or more than one covariates
# The function does not allow the absence of covariates
covar=names(data)[!names(data) %in% c("X", "R", "Z", "U", "delta")] # Covariate list
) {
#Retrieve data
n <- nrow(data)
X <- data$X # X=0 for A1, X=1 for A2
R <- data$R
Z <- data$Z # Z=0 for B1, Z=1 for B2
U <- data$U
delta <- data$delta
#Chek for errors
if (is.null(X)) stop("R can not be empty")
if (is.null(R)) stop("R can not be empty")
if (is.null(Z)) stop("Z can not be empty")
if (is.null(U)) stop("V can not be empty")
if (is.null(delta)) stop("delta can not be empty")
#Times to be assessed
t <- unique(U[which(delta==1)])
#Order times
t <- t[order(t)]
#Number at risk
n.risk <- apply(as.array(t), 1, function(x) sum(as.numeric(U >= x)))
#Number event
n.event <- apply(as.array(t), 1, function(x) length(which(U==x & delta==1)))
#Estimate probability of being assigned to A2
pi.x <- sum(X)/n
#Estimate probability of being assigned to B2 (allowing probability to vary across A1 and A2)
pi.z1 <- sum((1-X)*R*Z) / sum((1-X)*R)
pi.z2 <- sum(X*R*Z) / sum(X*R)
#Calculate weight for A1B1, A1B2, A2B1, and A2B2
w11 <- (1-X)*(1-R)/(1-pi.x) + (1-X)*R*(1-Z)/((1-pi.x)*(1-pi.z1))
w12 <- (1-X)*(1-R)/(1-pi.x) + (1-X)*R*Z/((1-pi.x)*pi.z1)
w21 <- X*(1-R)/pi.x + X*R*(1-Z)/(pi.x*(1-pi.z1))
w22 <- X*(1-R)/pi.x + X*R*Z/(pi.x*pi.z1)
#################################################
#################################################
#If no covariates: ERROR
#################################################
#################################################
if(length(covar)==0) { stop("Covariate(s) can not be empty") } else {
if(FALSE %in% (covar %in% names(data))) { stop("Covariate(s) can not be found in the data")
} else { V <- as.matrix(data[, names(data) %in% covar]) }
}
#Define results
est <- lest <- NULL
#################################################
#################################################
#If only 1 covariates
#################################################
#################################################
if(NCOL(V)==1) {
#Obtain the inital beta estimates
beta <- as.numeric(coxph(Surv(U, delta)~., data=data[, names(data) %in% c("U", "delta", covar)])$coef)
#Solve for beta using Newton-Raphson method
cat("Calling for updateBeta() function to solve for coefficients... \n")
for (p in 1:1000) {
#Run updateBeta function
ebeta <- updateBeta(beta, V, U, delta, w11, w12, w21, w22)
#Calculate difference between updated ebeta and beta
index <- max(abs(ebeta-beta))
if (index <= 10^(-6)) break else { beta <- ebeta; p <- p + 1 }
}
cat("Calculating cumulative hazard ratios and variance/covariance... \n")
#Change V from matrix to numeric
V <- as.numeric(V)
#Calcualte exp(beta*V)
e <- exp(ebeta*V)
for(j in 1:length(t)) {
#Define s0 and v1_bar
s00 <- s01 <- s02 <- s03 <- rep(0, n)
v10_bar <- v11_bar <- v12_bar <- v13_bar <- rep(0, n)
#Define lambda and omega
lambda11 <- lambda12 <- lambda21 <- lambda22 <- 0
omega <- 0
#Define h
h11 <- h12 <- h21 <- h22 <- 0
for(i in 1:n) {
ind <- as.numeric(U >= U[i])
#Calculate s0j
s00[i] <- sum(ind * w11 * e) / n
s01[i] <- sum(ind * w12 * e) / n
s02[i] <- sum(ind * w21 * e) / n
s03[i] <- sum(ind * w22 * e) / n
#Calculate s1j
s10 <- sum(ind * w11 * e * V) / n
s11 <- sum(ind * w12 * e * V) / n
s12 <- sum(ind * w21 * e * V) / n
s13 <- sum(ind * w22 * e * V) / n
#Calculate s2j
s20 <- sum(ind * w11 * e * V * V) / n
s21 <- sum(ind * w12 * e * V * V) / n
s22 <- sum(ind * w21 * e * V * V) / n
s23 <- sum(ind * w22 * e * V * V) / n
#Calculate z1?_bar
if(s00[i] != 0) v10_bar[i] <- s10/s00[i] else v10_bar[i] <- 0
if(s01[i] != 0) v11_bar[i] <- s11/s01[i] else v11_bar[i] <- 0
if(s02[i] != 0) v12_bar[i] <- s12/s02[i] else v12_bar[i] <- 0
if(s03[i] != 0) v13_bar[i] <- s13/s03[i] else v13_bar[i] <- 0
#calculate z2?_bar
if(s00[i] != 0) v20_bar <- s20/s00[i] else v20_bar <- 0
if(s01[i] != 0) v21_bar <- s21/s01[i] else v21_bar <- 0
if(s02[i] != 0) v22_bar <- s22/s02[i] else v22_bar <- 0
if(s03[i] != 0) v23_bar <- s23/s03[i] else v23_bar <- 0
#Calculate each cumulative baseline hazards
if(s00[i] != 0) lambda11 <- lambda11 + delta[i] * w11[i] * as.numeric(U[i] <= t[j]) / (n*s00[i])
if(s01[i] != 0) lambda12 <- lambda12 + delta[i] * w12[i] * as.numeric(U[i] <= t[j]) / (n*s01[i])
if(s02[i] != 0) lambda21 <- lambda21 + delta[i] * w21[i] * as.numeric(U[i] <= t[j]) / (n*s02[i])
if(s03[i] != 0) lambda22 <- lambda22 + delta[i] * w22[i] * as.numeric(U[i] <= t[j]) / (n*s03[i])
#Calculate each h
if(s00[i] != 0) h11 <- h11 - delta[i]*w11[i]*as.numeric(U[i] <= t[j])*v10_bar[i] / (n*s00[i])
if(s01[i] != 0) h12 <- h12 - delta[i]*w12[i]*as.numeric(U[i] <= t[j])*v11_bar[i] / (n*s01[i])
if(s02[i] != 0) h21 <- h21 - delta[i]*w21[i]*as.numeric(U[i] <= t[j])*v12_bar[i] / (n*s02[i])
if(s03[i] != 0) h22 <- h22 - delta[i]*w22[i]*as.numeric(U[i] <= t[j])*v13_bar[i] / (n*s03[i])
#Calculate each tao = s2/s0 - v1^2
tao11i <- v20_bar - v10_bar[i] * v10_bar[i]
tao12i <- v21_bar - v11_bar[i] * v11_bar[i]
tao21i <- v22_bar - v12_bar[i] * v12_bar[i]
tao22i <- v23_bar - v13_bar[i] * v13_bar[i]
#Calculate each omega
omega <- omega + (delta[i]*w11[i]*tao11i + delta[i]*w12[i]*tao12i + delta[i]*w21[i]*tao21i + delta[i]*w22[i]*tao22i) / n
}
#Calculate cumulative hazards ratio
CHR1211 <- lambda12 / lambda11; LogCHR1211 <- log(CHR1211)
CHR2111 <- lambda21 / lambda11; LogCHR2111 <- log(CHR2111)
CHR2211 <- lambda22 / lambda11; LogCHR2211 <- log(CHR2211)
CHR2112 <- lambda21 / lambda12; LogCHR2112 <- log(CHR2112)
CHR2212 <- lambda22 / lambda12; LogCHR2212 <- log(CHR2212)
CHR2221 <- lambda22 / lambda21; LogCHR2221 <- log(CHR2221)
# Define xi
xi1211 <- xi2111 <- xi2211 <- xi2112 <- xi2212 <- xi2221 <- rep(0, n)
for(k in 1:n) {
#Defind I(Uk >= U)
uind <- as.numeric(U[k] >= U)
#Calculate each latter part of psi
psi11i <- w11[k]*uind*e[k]*delta*w11*(V[k]-v10_bar) / (n*s00); psi11i[is.na(psi11i)] <- 0
psi12i <- w12[k]*uind*e[k]*delta*w12*(V[k]-v11_bar) / (n*s01); psi12i[is.na(psi12i)] <- 0
psi21i <- w21[k]*uind*e[k]*delta*w21*(V[k]-v12_bar) / (n*s02); psi21i[is.na(psi21i)] <- 0
psi22i <- w22[k]*uind*e[k]*delta*w22*(V[k]-v13_bar) / (n*s03); psi22i[is.na(psi22i)] <- 0
#Calculate psi
psi <- delta[k]*w11[k]*(V[k] - v10_bar[k]) +
delta[k]*w12[k]*(V[k] - v11_bar[k]) +
delta[k]*w21[k]*(V[k] - v12_bar[k]) +
delta[k]*w22[k]*(V[k] - v13_bar[k]) -
sum(psi11i) - sum(psi12i) - sum(psi21i) - sum(psi22i)
#Calculate each latter part of phi integral
intl11i <- w11[k]*uind*e[k]*delta*w11*as.numeric(U<=t[j]) / (n*s00*s00); intl11i[is.na(intl11i)] <- 0
intl12i <- w12[k]*uind*e[k]*delta*w12*as.numeric(U<=t[j]) / (n*s01*s01); intl12i[is.na(intl12i)] <- 0
intl21i <- w21[k]*uind*e[k]*delta*w21*as.numeric(U<=t[j]) / (n*s02*s02); intl21i[is.na(intl21i)] <- 0
intl22i <- w22[k]*uind*e[k]*delta*w22*as.numeric(U<=t[j]) / (n*s03*s03); intl22i[is.na(intl22i)] <- 0
#Calculate each phi_L
if(s00[k] != 0) phiL11i <- delta[k]*w11[k]*as.numeric(U[k]<=t[j])/s00[k] - sum(intl11i) else phiL11i <- 0
if(s01[k] != 0) phiL12i <- delta[k]*w12[k]*as.numeric(U[k]<=t[j])/s01[k] - sum(intl12i) else phiL12i <- 0
if(s02[k] != 0) phiL21i <- delta[k]*w21[k]*as.numeric(U[k]<=t[j])/s02[k] - sum(intl21i) else phiL21i <- 0
if(s03[k] != 0) phiL22i <- delta[k]*w22[k]*as.numeric(U[k]<=t[j])/s03[k] - sum(intl22i) else phiL22i <- 0
#Calculate each phi
phi11 <- h11 * psi / omega + phiL11i
phi12 <- h12 * psi / omega + phiL12i
phi21 <- h21 * psi / omega + phiL21i
phi22 <- h22 * psi / omega + phiL22i
#Calculate individual xi
xi1211[k] <- phi12 / lambda11 - lambda12 * phi11 / (lambda11)^2
xi2111[k] <- phi21 / lambda11 - lambda21 * phi11 / (lambda11)^2
xi2211[k] <- phi22 / lambda11 - lambda22 * phi11 / (lambda11)^2
xi2112[k] <- phi21 / lambda12 - lambda21 * phi12 / (lambda12)^2
xi2212[k] <- phi22 / lambda12 - lambda22 * phi12 / (lambda12)^2
xi2221[k] <- phi22 / lambda21 - lambda22 * phi21 / (lambda21)^2
}
#Save the results
temp <- c(CHR1211, CHR2111, CHR2211, CHR2112, CHR2212, CHR2221,
sqrt(mean(xi1211*xi1211)/n), sqrt(mean(xi2111*xi2111)/n),
sqrt(mean(xi2211*xi2211)/n), sqrt(mean(xi2112*xi2112)/n),
sqrt(mean(xi2212*xi2212)/n), sqrt(mean(xi2221*xi2221)/n),
mean(xi1211*xi2111)/n, mean(xi1211*xi2211)/n, mean(xi1211*xi2112)/n,
mean(xi1211*xi2212)/n, mean(xi1211*xi2221)/n, mean(xi2111*xi2211)/n,
mean(xi2111*xi2112)/n, mean(xi2111*xi2212)/n, mean(xi2111*xi2221)/n,
mean(xi2211*xi2112)/n, mean(xi2211*xi2212)/n, mean(xi2211*xi2221)/n,
mean(xi2112*xi2212)/n, mean(xi2112*xi2221)/n, mean(xi2212*xi2221)/n)
#Change 0 and NaN to NA
temp[which(temp==0 | is.na(temp)==TRUE | temp==Inf | temp==-Inf)] <- NA
est <- rbind(est, temp)
rownames(est) <- NULL
ltemp <- c(LogCHR1211, LogCHR2111, LogCHR2211, LogCHR2112, LogCHR2212, LogCHR2221,
sqrt(mean(xi1211*xi1211)/(n*CHR1211*CHR1211)), sqrt(mean(xi2111*xi2111)/(n*CHR2111*CHR2111)),
sqrt(mean(xi2211*xi2211)/(n*CHR2211*CHR2211)), sqrt(mean(xi2112*xi2112)/(n*CHR2112*CHR2112)),
sqrt(mean(xi2212*xi2212)/(n*CHR2212*CHR2212)), sqrt(mean(xi2221*xi2221)/(n*CHR2221*CHR2221)),
mean(xi1211*xi2111)/(n*CHR1211*CHR2111), mean(xi1211*xi2211)/(n*CHR1211*CHR2211), mean(xi1211*xi2112)/(n*CHR1211*CHR2112),
mean(xi1211*xi2212)/(n*CHR1211*CHR2212), mean(xi1211*xi2221)/(n*CHR1211*CHR2221), mean(xi2111*xi2211)/(n*CHR2111*CHR2211),
mean(xi2111*xi2112)/(n*CHR2111*CHR2112), mean(xi2111*xi2212)/(n*CHR2111*CHR2212), mean(xi2111*xi2221)/(n*CHR2111*CHR2221),
mean(xi2211*xi2112)/(n*CHR2211*CHR2112), mean(xi2211*xi2212)/(n*CHR2211*CHR2212), mean(xi2211*xi2221)/(n*CHR2211*CHR2221),
mean(xi2112*xi2212)/(n*CHR2112*CHR2212), mean(xi2112*xi2221)/(n*CHR2112*CHR2221), mean(xi2212*xi2221)/(n*CHR2212*CHR2221))
ltemp[which(ltemp==0 | is.na(ltemp)==TRUE | ltemp==Inf | ltemp==-Inf)] <- NA
lest <- rbind(lest, ltemp)
rownames(lest) <- NULL
}
}
#################################################
#################################################
#If more than 1 covariates
#################################################
#################################################
if(NCOL(V)>1) {
#Obtain the inital beta estimates
beta <- as.numeric(coxph(Surv(U, delta)~., data=data[, names(data) %in% c("U", "delta", covar)])$coef)
#Solve for beta using Newton-Raphson method
cat("Calling for updateBeta() function to solve for coefficient(s)...\n")
for (p in 1:1000) {
#Run updateBeta function
ebeta <- updateBeta(beta, V, U, delta, w11, w12, w21, w22)
#Calculate difference between updated ebeta and beta
index <- max(abs(ebeta-beta))
if (index <= 10^(-6)) break else { beta <- ebeta; p <- p + 1 }
}
cat("Calculating cumulative hazard ratio and variance/covariance...\n")
#Calcualte exp(beta*V)
e <- as.numeric(exp(matrix(ebeta, nrow=1, ncol=NCOL(V)) %*% t(V)))
for(j in 1:length(t)) {
#Define s0 and v1_bar
s00 <- s01 <- s02 <- s03 <- rep(0, n)
v10_bar <- v11_bar <- v12_bar <- v13_bar <- matrix(0, nrow=NCOL(V), ncol=n)
#Define lambda and omega
lambda11 <- lambda12 <- lambda21 <- lambda22 <- 0
omega <- matrix(0, nrow=NCOL(V), ncol=NCOL(V))
#Define h
h11 <- h12 <- h21 <- h22 <- matrix(0, nrow=NCOL(V), ncol=1)
for(i in 1:n) {
ind <- as.numeric(U >= U[i])
#Calculate s0j
s00[i] <- sum(ind * w11 * e) / n
s01[i] <- sum(ind * w12 * e) / n
s02[i] <- sum(ind * w21 * e) / n
s03[i] <- sum(ind * w22 * e) / n
#Calculate s1j
s10 <- t(matrix(ind*w11*e,nrow=1, ncol=n) %*% V / n)
s11 <- t(matrix(ind*w12*e,nrow=1, ncol=n) %*% V / n)
s12 <- t(matrix(ind*w21*e,nrow=1, ncol=n) %*% V / n)
s13 <- t(matrix(ind*w22*e,nrow=1, ncol=n) %*% V / n)
#Calculate s2j
s20 <- t(V) %*% diag(as.numeric(ind*w11*e)) %*% V / n
s21 <- t(V) %*% diag(as.numeric(ind*w12*e)) %*% V / n
s22 <- t(V) %*% diag(as.numeric(ind*w21*e)) %*% V / n
s23 <- t(V) %*% diag(as.numeric(ind*w22*e)) %*% V / n
#Calculate z1?_bar
if(s00[i] != 0) v10_bar[,i] <- s10/s00[i] else v10_bar[,i] <- matrix(0, nrow=NCOL(V), ncol=1)
if(s01[i] != 0) v11_bar[,i] <- s11/s01[i] else v11_bar[,i] <- matrix(0, nrow=NCOL(V), ncol=1)
if(s02[i] != 0) v12_bar[,i] <- s12/s02[i] else v12_bar[,i] <- matrix(0, nrow=NCOL(V), ncol=1)
if(s03[i] != 0) v13_bar[,i] <- s13/s03[i] else v13_bar[,i] <- matrix(0, nrow=NCOL(V), ncol=1)
#calculate z2?_bar
if(s00[i] != 0) v20_bar <- s20/s00[i] else v20_bar <- matrix(0, nrow=NCOL(V), ncol=NCOL(V))
if(s01[i] != 0) v21_bar <- s21/s01[i] else v21_bar <- matrix(0, nrow=NCOL(V), ncol=NCOL(V))
if(s02[i] != 0) v22_bar <- s22/s02[i] else v22_bar <- matrix(0, nrow=NCOL(V), ncol=NCOL(V))
if(s03[i] != 0) v23_bar <- s23/s03[i] else v23_bar <- matrix(0, nrow=NCOL(V), ncol=NCOL(V))
#Calculate each cumulative baseline hazards
if(s00[i] != 0) lambda11 <- lambda11 + delta[i] * w11[i] * as.numeric(U[i] <= t[j]) / (n*s00[i])
if(s01[i] != 0) lambda12 <- lambda12 + delta[i] * w12[i] * as.numeric(U[i] <= t[j]) / (n*s01[i])
if(s02[i] != 0) lambda21 <- lambda21 + delta[i] * w21[i] * as.numeric(U[i] <= t[j]) / (n*s02[i])
if(s03[i] != 0) lambda22 <- lambda22 + delta[i] * w22[i] * as.numeric(U[i] <= t[j]) / (n*s03[i])
#Calculate each h
if(s00[i] != 0) h11 <- h11 - delta[i]*w11[i]*as.numeric(U[i] <= t[j])*v10_bar[,i] / (n*s00[i])
if(s01[i] != 0) h12 <- h12 - delta[i]*w12[i]*as.numeric(U[i] <= t[j])*v11_bar[,i] / (n*s01[i])
if(s02[i] != 0) h21 <- h21 - delta[i]*w21[i]*as.numeric(U[i] <= t[j])*v12_bar[,i] / (n*s02[i])
if(s03[i] != 0) h22 <- h22 - delta[i]*w22[i]*as.numeric(U[i] <= t[j])*v13_bar[,i] / (n*s03[i])
#Calculate each tao = s2/s0 - v1^2
tao11i <- v20_bar - v10_bar[,i] %*% t(v10_bar[,i])
tao12i <- v21_bar - v11_bar[,i] %*% t(v11_bar[,i])
tao21i <- v22_bar - v12_bar[,i] %*% t(v12_bar[,i])
tao22i <- v23_bar - v13_bar[,i] %*% t(v13_bar[,i])
#Calculate each omega
omega <- omega + (delta[i]*w11[i]*tao11i + delta[i]*w12[i]*tao12i + delta[i]*w21[i]*tao21i + delta[i]*w22[i]*tao22i) / n
}
#Calculate cumulative hazards ratio
CHR1211 <- lambda12 / lambda11; LogCHR1211 <- log(CHR1211)
CHR2111 <- lambda21 / lambda11; LogCHR2111 <- log(CHR2111)
CHR2211 <- lambda22 / lambda11; LogCHR2211 <- log(CHR2211)
CHR2112 <- lambda21 / lambda12; LogCHR2112 <- log(CHR2112)
CHR2212 <- lambda22 / lambda12; LogCHR2212 <- log(CHR2212)
CHR2221 <- lambda22 / lambda21; LogCHR2221 <- log(CHR2221)
# Define xi
xi1211 <- xi2111 <- xi2211 <- xi2112 <- xi2212 <- xi2221 <- rep(0, n)
for(k in 1:n) {
#Defind I(Uk >= U)
uind <- as.numeric(U[k] >= U)
#Calculate each latter part of psi
psi11i <- w11[k]*uind*e[k]*delta*w11*(V[k,]-v10_bar) / (n*s00); psi11i[is.na(psi11i)] <- 0
psi12i <- w12[k]*uind*e[k]*delta*w12*(V[k,]-v11_bar) / (n*s01); psi12i[is.na(psi12i)] <- 0
psi21i <- w21[k]*uind*e[k]*delta*w21*(V[k,]-v12_bar) / (n*s02); psi21i[is.na(psi21i)] <- 0
psi22i <- w22[k]*uind*e[k]*delta*w22*(V[k,]-v13_bar) / (n*s03); psi22i[is.na(psi22i)] <- 0
#Calculate psi
psi <- delta[k]*w11[k]*(matrix(V[k,], nrow=NCOL(V), ncol=1) - v10_bar[,k]) +
delta[k]*w12[k]*(matrix(V[k,], nrow=NCOL(V), ncol=1) - v11_bar[,k]) +
delta[k]*w21[k]*(matrix(V[k,], nrow=NCOL(V), ncol=1) - v12_bar[,k]) +
delta[k]*w22[k]*(matrix(V[k,], nrow=NCOL(V), ncol=1) - v13_bar[,k]) -
sum(psi11i) - sum(psi12i) - sum(psi21i) - sum(psi22i)
#Calculate each latter part of phi integral
intl11i <- w11[k]*uind*e[k]*delta*w11*as.numeric(U<=t[j]) / (n*s00*s00); intl11i[is.na(intl11i)] <- 0
intl12i <- w12[k]*uind*e[k]*delta*w12*as.numeric(U<=t[j]) / (n*s01*s01); intl12i[is.na(intl12i)] <- 0
intl21i <- w21[k]*uind*e[k]*delta*w21*as.numeric(U<=t[j]) / (n*s02*s02); intl21i[is.na(intl21i)] <- 0
intl22i <- w22[k]*uind*e[k]*delta*w22*as.numeric(U<=t[j]) / (n*s03*s03); intl22i[is.na(intl22i)] <- 0
#Calculate each phi_L
if(s00[k] != 0) phiL11i <- delta[k]*w11[k]*as.numeric(U[k]<=t[j])/s00[k] - sum(intl11i) else phiL11i <- 0
if(s01[k] != 0) phiL12i <- delta[k]*w12[k]*as.numeric(U[k]<=t[j])/s01[k] - sum(intl12i) else phiL12i <- 0
if(s02[k] != 0) phiL21i <- delta[k]*w21[k]*as.numeric(U[k]<=t[j])/s02[k] - sum(intl21i) else phiL21i <- 0
if(s03[k] != 0) phiL22i <- delta[k]*w22[k]*as.numeric(U[k]<=t[j])/s03[k] - sum(intl22i) else phiL22i <- 0
#Calculate each phi
phi11 <- t(h11) %*% solve(omega) %*% psi + phiL11i
phi12 <- t(h12) %*% solve(omega) %*% psi + phiL12i
phi21 <- t(h21) %*% solve(omega) %*% psi + phiL21i
phi22 <- t(h22) %*% solve(omega) %*% psi + phiL22i
#Calculate individual xi
xi1211[k] <- phi12 / lambda11 - lambda12 * phi11 / (lambda11)^2
xi2111[k] <- phi21 / lambda11 - lambda21 * phi11 / (lambda11)^2
xi2211[k] <- phi22 / lambda11 - lambda22 * phi11 / (lambda11)^2
xi2112[k] <- phi21 / lambda12 - lambda21 * phi12 / (lambda12)^2
xi2212[k] <- phi22 / lambda12 - lambda22 * phi12 / (lambda12)^2
xi2221[k] <- phi22 / lambda21 - lambda22 * phi21 / (lambda21)^2
}
#Save the results
#Save the results
temp <- c(CHR1211, CHR2111, CHR2211, CHR2112, CHR2212, CHR2221,
sqrt(mean(xi1211*xi1211)/n), sqrt(mean(xi2111*xi2111)/n),
sqrt(mean(xi2211*xi2211)/n), sqrt(mean(xi2112*xi2112)/n),
sqrt(mean(xi2212*xi2212)/n), sqrt(mean(xi2221*xi2221)/n),
mean(xi1211*xi2111)/n, mean(xi1211*xi2211)/n, mean(xi1211*xi2112)/n,
mean(xi1211*xi2212)/n, mean(xi1211*xi2221)/n, mean(xi2111*xi2211)/n,
mean(xi2111*xi2112)/n, mean(xi2111*xi2212)/n, mean(xi2111*xi2221)/n,
mean(xi2211*xi2112)/n, mean(xi2211*xi2212)/n, mean(xi2211*xi2221)/n,
mean(xi2112*xi2212)/n, mean(xi2112*xi2221)/n, mean(xi2212*xi2221)/n)
#Change 0 and NaN to NA
temp[which(temp==0 | is.na(temp)==TRUE | temp==Inf | temp==-Inf)] <- NA
est <- rbind(est, temp)
rownames(est) <- NULL
ltemp <- c(LogCHR1211, LogCHR2111, LogCHR2211, LogCHR2112, LogCHR2212, LogCHR2221,
sqrt(mean(xi1211*xi1211)/(n*CHR1211*CHR1211)), sqrt(mean(xi2111*xi2111)/(n*CHR2111*CHR2111)),
sqrt(mean(xi2211*xi2211)/(n*CHR2211*CHR2211)), sqrt(mean(xi2112*xi2112)/(n*CHR2112*CHR2112)),
sqrt(mean(xi2212*xi2212)/(n*CHR2212*CHR2212)), sqrt(mean(xi2221*xi2221)/(n*CHR2221*CHR2221)),
mean(xi1211*xi2111)/(n*CHR1211*CHR2111), mean(xi1211*xi2211)/(n*CHR1211*CHR2211), mean(xi1211*xi2112)/(n*CHR1211*CHR2112),
mean(xi1211*xi2212)/(n*CHR1211*CHR2212), mean(xi1211*xi2221)/(n*CHR1211*CHR2221), mean(xi2111*xi2211)/(n*CHR2111*CHR2211),
mean(xi2111*xi2112)/(n*CHR2111*CHR2112), mean(xi2111*xi2212)/(n*CHR2111*CHR2212), mean(xi2111*xi2221)/(n*CHR2111*CHR2221),
mean(xi2211*xi2112)/(n*CHR2211*CHR2112), mean(xi2211*xi2212)/(n*CHR2211*CHR2212), mean(xi2211*xi2221)/(n*CHR2211*CHR2221),
mean(xi2112*xi2212)/(n*CHR2112*CHR2212), mean(xi2112*xi2221)/(n*CHR2112*CHR2221), mean(xi2212*xi2221)/(n*CHR2212*CHR2221))
ltemp[which(ltemp==0 | is.na(ltemp)==TRUE | ltemp==Inf | ltemp==-Inf)] <- NA
lest <- rbind(lest, ltemp)
rownames(lest) <- NULL
}
}
#Return class
results <- list(Call=match.call(),
coefficients=ebeta,
comparison=c("A1B2 vs. A1B1", "A2B1 vs. A1B1", "A2B2 vs. A1B1",
"A2B1 vs. A1B2", "A2B2 vs. A1B2", "A2B2 vs. A2B1"),
time75P=as.numeric(round(quantile(data$U, probs=0.75),2)),
time=t, n.risk=n.risk, n.event=n.event,
CHR1211=est[,1], CHR2111=est[,2], CHR2211=est[,3],
CHR2112=est[,4], CHR2212=est[,5], CHR2221=est[,6],
SE1211=est[,7], SE2111=est[,8], SE2211=est[,9],
SE2112=est[,10], SE2212=est[,11], SE2221=est[,12],
COV1211_2111=est[,13], COV1211_2211=est[,14], COV1211_2112=est[,15],
COV1211_2212=est[,16], COV1211_2221=est[,17], COV2111_2211=est[,18],
COV2111_2112=est[,19], COV2111_2212=est[,20], COV2111_2221=est[,21],
COV2211_2112=est[,22], COV2211_2212=est[,23], COV2211_2221=est[,24],
COV2112_2212=est[,25], COV2112_2221=est[,26], COV2212_2221=est[,27],
CHR1211.LOG=lest[,1], CHR2111.LOG=lest[,2], CHR2211.LOG=lest[,3],
CHR2112.LOG=lest[,4], CHR2212.LOG=lest[,5], CHR2221.LOG=lest[,6],
SE1211.LOG=lest[,7], SE2111.LOG=lest[,8], SE2211.LOG=lest[,9],
SE2112.LOG=lest[,10], SE2212.LOG=lest[,11], SE2221.LOG=lest[,12],
COV1211_2111.LOG=lest[,13], COV1211_2211.LOG=lest[,14], COV1211_2112.LOG=lest[,15],
COV1211_2212.LOG=lest[,16], COV1211_2221.LOG=lest[,17], COV2111_2211.LOG=lest[,18],
COV2111_2112.LOG=lest[,19], COV2111_2212.LOG=lest[,20], COV2111_2221.LOG=lest[,21],
COV2211_2112.LOG=lest[,22], COV2211_2212.LOG=lest[,23], COV2211_2221.LOG=lest[,24],
COV2112_2212.LOG=lest[,25], COV2112_2221.LOG=lest[,26], COV2212_2221.LOG=lest[,27])
class(results) <- "CHR"
return(results)
}
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