expectreg.ipc {dirttee} R Documentation

## 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)



[Package dirttee version 1.0.1 Index]