asynchTD {AsynchLong}

Regression Analysis for Time-Dependent Coefficients

Description

Estimation of regression models for sparse asynchronous longitudinal observations with time-dependent coefficients.

Usage

asynchTD(data.x, data.y, times, kType = "epan", lType = "identity", 
                bw=NULL, nCores = 1, verbose = TRUE, ...)

Arguments

data.x

A data.frame of covariates. 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. All times will automatically be rescaled to [0,1].

data.y

A data.frame of response measurements. The structure of the data.frame must be {patient ID, time of measurement, measurement}. 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. All times will automatically be rescaled to [0,1].

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.

lType

An object of class character indicating the type of link function to use for the regression model. Must be one of {"identity","log","logistic"}.

bw

If provided, bw is an object of class numeric containing a single bandwidth at which parameter estimates are to be obtained. If NULL, an “optimal" bandwidth will be determined for each time point 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 pooled sample of measurement times for the covariate and response, and n is the number of patients. For each time point, the optimal bandwidth(s) is taken to be that which minimizes the mean squared error. See original reference for details of the selection procedure.

times

A vector object of class numeric. The time points at which the coefficients are to be estimated.

nCores

A numeric object. For auto-tune method, the number of cores to employ for calculation. If nCores > 1, the bandwidth search space will be distributed across the cores using parallel's parLapply.

verbose

An object of class logical. TRUE results in screen prints.

...

Ignored.

Details

For lType = "log" and lType = "logistic", parameter estimates are obtained by minimizing the estimating equation using optim() with method="Nelder-Mead"; all other arguments take their default values.

For lType = "identity", parameter estimates are obtained using solve().

Upon completion, a single plot is generating showing the time-dependence of each coefficient.

Value

A list is returned. Each element of the list is a matrix, where the ith row corresponds to the ith time point of input argument “times" and the columns correspond to the model parameters.

The returned values are estimated using either the provided bandwidth or the “optimal" bandwidth as determined using the adaptive selection procedure.

betaHat

The estimated model coefficients.

stdErr

The standard errors for each coefficient.

zValue

The estimated z-values for each coefficient.

pValue

The p-values for each coefficient.

If the bandwidth is determined automatically, two additional list elements are returned:

optBW

The estimated optimal bandwidth for each coefficient.

minMSE

The mean squared error at the optimal bandwidth for each coefficient.

Author(s)

Hongyuan Cao, Donglin Zeng, Jason P. Fine, and Shannon T. Holloway

References

Cao, H., Zeng, D., and Fine, J. P. (2014) Regression Analysis of sparse asynchronous longitudinal data. Journal of the Royal Statistical Society: Series B, 77, 755-776.

Examples

  data(asynchDataTD)

  res <- asynchTD(data.x = TD.x, 
                  data.y = TD.y,
                  times = c(0.25, 0.50, 0.75),
                  bw = 0.05,
                  kType = "epan", 
                  lType = "identity")