Bias-Corrected Kernel Estimating Equations by Extrapolation in the Bandwidth

Applies the bandwidth selection and bias correction of skmle_bc() to the kernel estimating-equation estimators of Cao and coauthors: kee_cox() for the proportional hazards model with sparse longitudinal covariates, and kee_async() for regression of an asynchronous longitudinal response. Each function fits its estimator over a grid of bandwidths, chooses a bandwidth by a plug-in estimate of the mean squared error of the coefficients, and extrapolates the coefficients to bandwidth zero. The standard error accounts for the correlation between fits at different bandwidths and for the data-driven choice of bandwidth. See skmle_bc() for details of the method.

Usage

kee_cox_bc(
  formula,
  data,
  id,
  obs_times,
  h_grid = NULL,
  n_h = 12,
  degree = 1,
  n_boot = 2000,
  seed = NULL,
  quiet = FALSE,
  ...
)

kee_async_bc(
  data_y,
  data_x,
  formula,
  id,
  time,
  h_grid = NULL,
  n_h = 12,
  degree = 1,
  n_boot = 2000,
  seed = NULL,
  quiet = FALSE,
  ...
)

Arguments

formula, data, id, obs_times

As in kee_cox().

h_grid

Optional vector of candidate bandwidths. If NULL, n_h log-spaced values are used. kee_cox_bc() uses the default grid of skmle_bc(). kee_async_bc() uses values from \(2\,\mathrm{IQR}\,n^{-0.6}\) to the range of the pooled observation times, where IQR is the interquartile range of those times.

n_h

Number of candidate bandwidths when h_grid is NULL.

degree

Degree in \(h\) of the bias model and of the extrapolation, as in skmle_bc(). The default 1 removes the first-order bias of a one-sided kernel, and of a two-sided kernel when the covariate path is not smooth. When the bias of a two-sided kernel is of order \(h^2\), linear extrapolation leaves a remainder of order \(\hat h^2\), which is small relative to the standard error at the selected bandwidth. 2 removes this remainder but gives a larger variance.

n_boot, seed, quiet

As in skmle_bc().

...

Further arguments passed to kee_cox() or kee_async(), such as one_sided, weight or link.

data_y, data_x, time

As in kee_async().

Value

An object of class c("kee_bc", "bc") with the components described in skmle_bc(); fit is the kee_cox() or kee_async() fit at the selected bandwidth.

See also

skmle_bc(), kee_cox(), kee_async(), kee_async_cv()