expectreg.ipc: Expectile regression for right-censored data

In dirttee: Distributional Regression for Time to Event Data

Expectile regression for right-censored data

Description

This function extends expectile regression with inverse probability of censoring (IPC) weights to right-censored data.

Usage

expectreg.ipc(
  formula,
  data = NULL,
  smooth = c("schall", "ocv", "aic", "bic", "cvgrid", "lcurve", "fixed"),
  lambda = 1,
  expectiles = NA,
  LAWSmaxCores = 1,
  IPC_weights = c("IPCRR", "IPCKM"),
  KMweights = NULL,
  ci = FALSE,
  hat1 = FALSE
)

Arguments

formula	A formula object, with the response on the left of the ‘~’ operator, and the terms on the right. The response must be a Surv object as returned by the Surv function. Only right censored data are allowed. Splines can be specified through the function rb.
data	Optional data frame containing the variables used in the model, if the data is not explicitly given in the formula.
smooth	The smoothing method that shall be used. There are different smoothing algorithms that should prevent overfitting. The 'schall' algorithm balances variance of errors and contrasts. Ordinary cross- validation 'ocv' minimizes a score-function using nlminb or with a grid search by 'cvgrid' or the function uses a fixed penalty. The numerical minimizatioin is also possible with AIC or BIC as score. The L-curve is an experimental grid search by Frasso and Eilers.
lambda	The fixed penalty can be adjusted. Also serves as starting value for the smoothing algorithms.
expectiles	In default setting, the expectiles (0.01,0.02,0.05,0.1,0.2,0.5,0.8,0.9,0.95,0.98,0.99) are calculated. You may specify your own set of expectiles in a vector.
LAWSmaxCores	How many cores should maximally be used by parallelization. Currently only implemented for Unix-like OS.
IPC_weights	Denotes the kind of IPC weights to use. IPCRR weights differ from IPCKM weights by modifying the weights for the last observation if it is censored.
KMweights	Custom IPC weights can be supplied here. This argument is used by modreg.
ci	If TRUE, calculates the covariance matrix
hat1	If TRUE, the hat matrix for the last asymetry level is calculated. This argument is mainly used by modreg.

Details

Fits least asymmetrically weighted squares (LAWS) for each expectile. This function is intended for right-censored data. For uncensored data, expectreg.ls should be used instead. This function modifies expectreg.ls by adding IPC weights. See Seipp et al. (2021) for details on the IPC weights. P-splines can be used with rb. The Schall algorithm is used for choosing the penalty.

Value

A list with the following elements.

lambda	The final smoothing parameters for all expectiles and for all effects in a list.
intercepts	The intercept for each expectile.
coefficients	A matrix of all the coefficients, for each base element a row and for each expectile a column.
values	The fitted values for each observation and all expectiles, separately in a list for each effect in the model, sorted in order of ascending covariate values.
response	Vector of the response variable.
covariates	List with the values of the covariates.
formula	The formula object that was given to the function.
asymmetries	Vector of fitted expectile asymmetries as given by argument expectiles.
effects	List of characters giving the types of covariates.
helper	List of additional parameters like neighbourhood structure for spatial effects or φ for kriging.
design	Complete design matrix.
bases	Bases components of each covariate.
fitted	Fitted values.
covmat	Covariance matrix.
diag.hatma	Diagonal of the hat matrix. Used for model selection criteria.
data	Original data.
smooth_orig	Unchanged original type of smoothing.
KMweights	Vector with IPC weights used in fitting.
aic	Area under the AIC, approximated with a Riemannian sum.
hat	The hat matrix for the last asymmetry level. This is used by modreg.

References

Seipp, A, Uslar, V, Weyhe, D, Timmer, A, Otto-Sobotka, F. Weighted expectile regression for right-censored data. Statistics in Medicine. 2021; 40(25): 5501- 5520. https://doi.org/10.1002/sim.9137

Examples

data(colcancer)

# linear effect
expreg <- expectreg.ipc(Surv(logfollowup, death) ~ sex + age, data = colcancer, 
                        expectiles = c(0.05, 0.2, 0.5, 0.8, 0.95))
coef(expreg)


# with p-splines, smoothing parameter selection with schall algorithm
expreg2 <- expectreg.ipc(Surv(logfollowup, death) ~ sex + rb(age), data = colcancer)
# smoothing parameter selection with AIC
expreg3 <- expectreg.ipc(Surv(logfollowup, death) ~ sex + rb(age), data = colcancer, smooth = "aic")
# manually selected smoothing parameter
expreg4 <- expectreg.ipc(Surv(logfollowup, death) ~ sex + rb(age), data = colcancer, 
                         smooth = "fixed", lambda = 2)

plot(expreg2)
plot(expreg3)
plot(expreg4)

dirttee documentation built on Sept. 14, 2022, 5:06 p.m.