expectreg.ipc {dirttee}

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 \phi 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)