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surv_stoEM_regression <- function(data, zetat, zetaz, B = 100, theta = 0.5, offset = TRUE){
t = data$t
d = data$d
Z = data$Z
X = data.matrix(data$X)
nx = dim(X)[2]
n = length(t)
if(offset){
# Record coefficients with simulated U
Coefz = Coefz.se = matrix(0, nrow = B, ncol = nx+1)
Coeft1 = Coeft1.se = matrix(0, nrow = B, ncol = nx+1)
partialR2z = c()
partialR2t1 = c()
for (j in 1:B){
Usim = SimulateU_surv(t, d, Z, X, zetat = zetat, zetaz = zetaz, theta = theta, offset = TRUE)
Z.fit = glm(Z ~ X, offset = zetaz * Usim$U, family=binomial(link="probit"))
Coefz[j,] = Z.fit$coefficients
Coefz.se[j,] = summary(Z.fit)$coefficients[,'Std. Error']
# Calculate partial R-sq of z ~ u | x
Z.fit_reduced = glm(Z ~ X, family=binomial(link="probit"))
if (zetaz >= 0)
partialR2z[j] = 1 - exp((Z.fit$deviance-Z.fit_reduced$deviance)/n)
else
partialR2z[j] = - (1 - exp((Z.fit$deviance-Z.fit_reduced$deviance)/n))
t1.fit = coxph(Surv(t, d) ~ X + Z + offset(zetat * Usim$U))
Coeft1[j,] = t1.fit$coefficients
Coeft1.se[j,] = summary(t1.fit)$coefficients[,'se(coef)']
# Calculate partial R-sq of (t, d) ~ u | x, z
t1.fit_reduced = coxph(Surv(t, d) ~ X + Z)
logtest <- -2 * (t1.fit_reduced$loglik[2] - t1.fit$loglik[2])
if (zetat >= 0)
partialR2t1[j] = (1 - exp(-logtest/t1.fit$nevent))
else
partialR2t1[j] = - (1 - exp(-logtest/t1.fit$nevent))
}
colnames(Coefz) = colnames(Coefz.se) = names(Z.fit$coefficients)
colnames(Coeft1) = colnames(Coeft1.se) = names(t1.fit$coefficients)
}
else{
# Record coefficients with simulated U
Coefz = Coefz.se = matrix(0, nrow = B, ncol = nx + 2)
Coeft1 = Coeft1.se = matrix(0, nrow = B, ncol = nx + 2)
partialR2z = c()
partialR2t1 = c()
for (j in 1:B){
Usim = SimulateU_surv(t, d, Z, X, zetat = zetat, zetaz = zetaz, theta = theta, offset = FALSE)
Z.fit = glm(Z ~ X + Usim$U, family=binomial(link="probit"))
Coefz[j,] = Z.fit$coefficients
Coefz.se[j,] = summary(Z.fit)$coefficients[,'Std. Error']
# Calculate partial R-sq of z ~ u | x
Z.fit_reduced = glm(Z ~ X, family=binomial(link="probit"))
if (zetaz >= 0)
partialR2z[j] = 1 - exp((Z.fit$deviance-Z.fit_reduced$deviance)/n)
else
partialR2z[j] = - (1 - exp((Z.fit$deviance-Z.fit_reduced$deviance)/n))
t1.fit = coxph(Surv(t, d) ~ X + Z + Usim$U)
Coeft1[j,] = t1.fit$coefficients
Coeft1.se[j,] = summary(t1.fit)$coefficients[,'se(coef)']
# Calculate partial R-sq of (t, d) ~ u | x, z
t1.fit_reduced = coxph(Surv(t, d) ~ X + Z)
logtest <- -2 * (t1.fit_reduced$loglik[2] - t1.fit$loglik[2])
if (zetat >= 0)
partialR2t1[j] = (1 - exp(-logtest/t1.fit$nevent))
else
partialR2t1[j] = - (1 - exp(-logtest/t1.fit$nevent))
}
colnames(Coefz) = colnames(Coefz.se) = names(Z.fit$coefficients)
colnames(Coeft1) = colnames(Coeft1.se) = names(t1.fit$coefficients)
}
tau1 = mean(Coeft1[,"Z"])
tau1.se = sqrt(mean((Coeft1.se[,"Z"])^2) + (1+1/B) * var(Coeft1[,"Z"]))
pR2z = mean(partialR2z)
pR2t1 = mean(partialR2t1)
return (list(tau1 = tau1, tau1.se = tau1.se, pR2z = pR2z, pR2t1 = pR2t1))
}
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