fullKernel: Full Kernel Estimation with Forward and Backward Lagged...

In SurvLong: Analysis of Proportional Hazards Model with Sparse Longitudinal Covariates

Full Kernel Estimation with Forward and Backward Lagged Covariates

Description

A kernel weighting scheme to evaluate the effects of longitudinal covariates on the occurrence of events when the time-dependent covariates are measured intermittently. Regression parameter estimation uses full kernel imputation of missing values with both forward and backward lagged covariates.

Usage

fullKernel(
  X,
  Z,
  tau,
  kType = c("epan", "uniform", "gauss"),
  bw = NULL,
  tol = 0.001,
  maxiter = 100L,
  verbose = TRUE
)

Arguments

X	An object of class data.frame. The structure of the data.frame must be {patient ID, event time, event indicator}. Patient IDs must be of class integer or be able to be coerced to class integer without loss of information. Missing values must be indicated as NA. The event indicator is 1 if the event occurred; 0 if censored.
Z	An object of class data.frame. The structure of the data.frame must be {patient ID, time of measurement, measurement(s)}. Patient IDs must be of class integer or be able to be coerced to class integer without loss of information. Missing values must be indicated as NA.
tau	An object of class numeric. The desired time point.
kType	An object of class character indicating the type of smoothing kernel to use in the estimating equation. Must be one of {"epan", "uniform", "gauss"}, where "epan" is the Epanechnikov kernel and "gauss" is the Gaussian kernel.
bw	NULL or a numeric vector. If provided, the bandwidths for which parameter estimates are to be obtained. If NULL, an optimal bandwidth will be determined using an adaptive selection procedure. The range of the bandwidth search space is taken to be 2*(Q3 - Q1)*n^{-0.7} to 2*(Q3 - Q1)*n^{-0.3}, where Q3 is the 0.75 quantile and Q1 is the 0.25 quantile of the measurement times for the covariate and n is the effective number of patients, taken as the total number of patients that experienced an event.
tol	An object of class numeric. The minimum change in the regression parameters deemed to indicate convergence of the Newton-Raphson method.
maxiter	An object of class integer. The maximum number of iterations used to estimate regression parameters.
verbose	An object of class logical. TRUE results in progress screen prints.

Value

A list is returned. If bandwidths are provided, each element is a matrix, where the ith row corresponds to the ith bandwidth of input argument bw, and the columns correspond to the model parameters. If the bandwidth is determined internally, each element of the list is a named vector calculated at the optimal bandwidth.

• betaHat The estimated model coefficients.

• stdErr The standard error for each coefficient.

• zValue The estimated z-value for each coefficient.

• pValue The p-value for each coefficient.

If the bandwidth is determined internally, three additional list elements are returned:

• optBW The estimated optimal bandwidth.

• minMSE The mean squared error at the optimal bandwidth.

• MSE The vector of MSE for each bandwidth.

References

Cao H., Churpek M. M., Zeng D., Fine J. P. (2015). Analysis of the proportional hazards model with sparse longitudinal covariates. Journal of the American Statistical Association, 110, 1187-1196.

See Also

halfKernel, lastValue, nearValue

Examples

 data(SurvLongData)

 exp <- fullKernel(X = X, Z = Z, tau = 1.0, bw = 0.015)

SurvLong documentation built on Oct. 1, 2023, 1:06 a.m.