Package 'SurvLong'

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)

---

Half Kernel Estimation with 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 using half kernel imputation of missing values with backward lagged covariates.

Usage

halfKernel(
  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

fullKernel, lastValue, nearValue

Examples

data(SurvLongData)

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

---

Last Value Carried Forward Method

Description

A simple approach to evaluate the effects of longitudinal covariates on the occurrence of events when the time-dependent covariates are measured intermittently. Regression parameter are estimated using last value carried forward imputation of missing values.

Usage

lastValue(X, Z, tau, 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.
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

• 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.

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

fullKernel, halfKernel, nearValue

Examples

data(SurvLongData)
 # A truncated dataset to keep example run time brief
 exp <- lastValue(X = X[1:200,], Z = Z, tau = 1.0)

---

Nearest Value Method

Description

A simple approach to evaluate the effects of longitudinal covariates on the occurrence of events when the time-dependent covariates are measured intermittently. Regression parameters are estimated using the nearest value to imputate missing values.

Usage

nearValue(X, Z, tau, 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.
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

• 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.

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

fullKernel, halfKernel, lastValue

Examples

data(SurvLongData)
 # A truncated dataset to keep example run time brief
 exp <- nearValue(X = X[1:100,], Z = Z, tau = 1.0)

---

Generated Sparse Longitudinal Data

Description

For the purposes of the package examples, the dataset was adapted from the numerical simulations of the original manuscript.

Format

X is a data frame with 400 observations on the following 3 variables.

ID

patient identifier, there are 400 patients.

Time

the time to event or censoring

Delta

a numeric vector with 0 denoting censoring and 1 event

Z is a data frame with 3237 observations on the following 3 variables.

ID

patient identifier, there are 400 patients.

obsTime

the covariate observation times.

x1

the covariate generated through a piecewise constant function.

Details

Data was generated for 400 subjects. The total number of covariate observation times was Poisson distributed with intensity rate 8. The covariate observation times are generated from a uniform distribution Unif(0,1) independently. The covariate process is piecewise constant, with values being multivariate normal with mean 0, variance 1 and correlation $\exp(-|i - j|/20)$. The survival time were generated from the Cox model $\lambda(t | Z(r), r \le t) = \lambda_0 \exp(\beta Z(t))$, where $\beta$ = 1.5, and $\lambda_0$ = 1.0. Covariates are dataset Z. Event times and indicators are dataset X.

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.

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