Q1 {HQM}

Bandwidth selection score Q1

Description

Calculates a part for the K-fold cross validation score.

Usage

Q1(h_xt_mat, int_X, size_X_grid, n, Yi)

Arguments

h_xt_mat

A matrix of the estimator for the future conditional hazard rate for all values x and t.

int_X

Vector of the position of the observed marker values in the grid for marker values.

size_X_grid

Numeric value indicating the number of grid points for marker values.

n

Number of individuals.

Yi

A matrix made by make_Yi indicating the exposure.

Details

The function implements

Q_1 = \sum_{i = 1}^N \int_0^T \int_s^T Z_i(t)Z_i(s)\hat{h}_{X_i(s)}^2(t-s) dt ds,

where \hat{h} is the hqm estimator, Z the exposure and X the marker.

Value

A value of the score Q1.

See Also

b_selection

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)
Ni  <- make_Ni(br_s, size_s_grid, ss, delta, n)

t = 2

h_xt_mat = t(sapply(br_s[1:99],
            function(si){h_xt_vec(br_X, br_s, size_s_grid, alpha, t, b, Yi, int_X, n)}))

Q = Q1(h_xt_mat, int_X, size_X_grid, n, Yi)