surv_func_joint {SimSurvNMarker}

Evaluates the Conditional Survival Function Given the Random Effects

Description

Evaluates the conditional survival function given the random effects, \vec U. The conditional hazard function is

h(t \mid \vec u) = \exp(\vec\omega^\top\vec b(t) + \delta + \vec\alpha^\top\vec o + \vec 1^\top(diag(\vec \alpha) \otimes \vec g(t)^\top)vec(B) + \vec 1^\top(diag(\vec \alpha) \otimes \vec m(t)^\top)\vec u).

Usage

surv_func_joint(
  ti,
  B,
  U,
  omega,
  delta,
  alpha,
  b_func,
  m_func,
  gl_dat = get_gl_rule(30L),
  g_func,
  offset
)

Arguments

ti

numeric vector with time points.

B

coefficient matrix for time-varying fixed effects. Use NULL if there is no effect.

U

random effects matrix for time-varying random effects. Use NULL if there is no effects.

omega

numeric vector with coefficients for the baseline hazard.

delta

offset on the log hazard scale. Use NULL if there is no effect.

alpha

numeric vector with association parameters.

b_func

basis function for the baseline hazard like poly.

m_func

basis function for U like poly.

gl_dat

Gauss–Legendre quadrature data. See get_gl_rule.

g_func

basis function for B like poly.

offset

numeric vector with non-time-varying fixed effects.

See Also

sim_marker, draw_U, eval_surv_base_fun

Examples

#####
# example with polynomial basis functions
b_func <- function(x){
  x <- x - 1
  cbind(x^3, x^2, x)
}
g_func <- function(x){
  x <- x - 1
  cbind(x^3, x^2, x)
}
m_func <- function(x){
  x <- x - 1
  cbind(x^2, x, 1)
}

# parameters
omega <- c(1.4, -1.2, -2.1)
Psi <- structure(c(0.18, 0.05, -0.05, 0.1, -0.02, 0.06, 0.05, 0.34, -0.25,
                   -0.06, -0.03, 0.29, -0.05, -0.25, 0.24, 0.04, 0.04,
                   -0.12, 0.1, -0.06, 0.04, 0.34, 0, -0.04, -0.02, -0.03,
                   0.04, 0, 0.1, -0.08, 0.06, 0.29, -0.12, -0.04, -0.08,
                   0.51), .Dim = c(6L, 6L))
B <- structure(c(-0.57, 0.17, -0.48, 0.58, 1, 0.86), .Dim = 3:2)
alpha <- c(.5, .9)

# simulate and draw survival curve
gl_dat <- get_gl_rule(30L)
set.seed(1)
U <- draw_U(chol(Psi), NCOL(B))
tis <- seq(0, 2, length.out = 100)
Survs <- surv_func_joint(ti = tis, B = B, U = U, omega = omega,
                         delta = NULL, alpha = alpha, b_func = b_func,
                         m_func = m_func, gl_dat = gl_dat, g_func = g_func,
                         offset = NULL)
par_old <- par(mar = c(5, 5, 1, 1))
plot(tis, Survs, xlab = "Time", ylab = "Survival", type = "l",
     ylim = c(0, 1), bty = "l", xaxs = "i", yaxs = "i")
par(par_old)