h_xt_vec {HQM}

Hqm estimator on the marker grid

Description

Computes the hqm estimator on the marker grid.

Usage

h_xt_vec(br_X, br_s, size_s_grid, alpha, t, b, Yi, int_X, n)

Arguments

br_X

Marker value grid points that will be used in the evaluatiuon.

br_s

Time value grid points that will be used in the evaluatiuon.

size_s_grid

Size of the time grid.

alpha

Marker-hazard obtained from get_alpha.

t

Numeric value of the time the function should be evaluated.

b

Bandwidth.

Yi

A matrix made by make_Yi indicating the exposure.

int_X

Position of the linear interpolated marker values on the marker grid.

n

Number of individuals.

Details

The function implements the future conditional hazard estimator

\hat{h}_x(t) = \frac{\sum_{i=1}^n \int_0^T\hat{\alpha}_i(X_i(t+s))Z_i(t+s)Z_i(s)K_{b}(x-X_i(s))\mathrm {d}s}{\sum_{i=1}^n\int_0^TZ_i(t+s)Z_i(s)K_{b}(x-X_i(s))\mathrm {d}s},

for every x on the marker grid where X is the marker, Z is the exposure and \alpha(z) is the marker-only hazard, see get_alpha for more details.

Value

A vector of \hat{h}_{x}(t) for all values x on the marker grid.

Examples

pbc2_id = to_id(pbc2)
size_s_grid <- size_X_grid <- 100
n = max(as.numeric(pbc2$id))
s = pbc2$year
X = pbc2$serBilir
XX = pbc2_id$serBilir
ss <- pbc2_id$years
delta <- pbc2_id$status2
br_s = seq(0, max(s), max(s)/( size_s_grid-1))
br_X = seq(min(X), max(X), (max(X)-min(X))/( size_X_grid-1))

X_lin = lin_interpolate(br_s, pbc2_id$id, pbc2$id, X, s)

int_X <- findInterval(X_lin, br_X)
int_s = rep(1:length(br_s), n)

N <- make_N(pbc2, pbc2_id, br_X, br_s, ss, XX, delta)
Y <- make_Y(pbc2, pbc2_id, X_lin, br_X, br_s,
            size_s_grid, size_X_grid, int_s, int_X, event_time = 'years', n)

b = 1.7
alpha<-get_alpha(N, Y, b, br_X, K=Epan )

Yi <- make_Yi(pbc2, pbc2_id, X_lin, br_X, br_s,
              size_s_grid, size_X_grid, int_s, int_X, event_time = 'years', n)

t = 2

h_xt_vec(br_X, br_s, size_s_grid, alpha, t, b, Yi, int_X, n)