Package 'dirttee'

Title: Distributional Regression for Time to Event Data
Description: Semiparametric distributional regression methods (expectile, quantile and mode regression) for time-to-event variables with right-censoring; uses inverse probability of censoring weights or accelerated failure time models with auxiliary likelihoods. Expectile regression using inverse probability of censoring weights has been introduced in Seipp et al. (2021) ``Weighted Expectile Regression for Right-Censored Data'' <doi:10.1002/sim.9137>, mode regression for time-to-event variables has been introduced in Seipp et al. (2022) ``Flexible Semiparametric Mode Regression for Time-to-Event Data'' <doi:10.1177/09622802221122406>.
Authors: Alexander Seipp [aut, cre], Fabian Otto-Sobotka [aut]
Maintainer: Alexander Seipp <[email protected]>
License: GPL (>= 2)
Version: 1.0.2
Built: 2024-11-16 06:34:03 UTC
Source: CRAN

Help Index

DIstributional Regression for Times To EvEnt

Description

This package includes regession methods for right-censored response variables. It allows for the estimation of distributional regression methods with semiparametric predictors, including, for example, nonlinear, spatial or random effects. The distribution of the response can be estimated with expectiles, quantiles and mode regression. Censored observations can be included with accelerated failure time models or inverse probability of censoring weights.

Author(s)

Alexander Seipp, Fabian Otto-Sobotka
Carl von Ossietzky University Oldenburg
https://uol.de/eub

Maintainer: Alexander Seipp <[email protected]>

Special thanks for their help go to Lisa Eilers and Florian Berger!

Partially funded by the German Research Foundation (DFG) grant SO1313/1-1, project 'Distributional Regression for Time-to-Event Data'.

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. doi: 10.1002/sim.9137

Seipp A, Uslar V, Weyhe D, Timmer A, Otto-Sobotka F. Flexible Semiparametric Mode Regression for Time-to-Event Data. Statistical Methods in Medical Research. 2022;31(12):2352-2367. doi: 10.1177/09622802221122406

Examples

data(colcancer)
c100 <- colcancer[1:100,]

#mode regression
reg <- modreg(Surv(logfollowup, death) ~ sex + LNE, data = c100)

#expectile regression
fit_exp <- expectreg.aft(Surv(logfollowup, death) ~ LNE, data = c100,smooth="f")
fit_expipc <- expectreg.ipc(Surv(logfollowup, death) ~ sex + LNE, data = c100)

#quantile regression
qu1 <- qureg.aft(Surv(logfollowup, death) ~ sex + LNE, data=c100, smooth="fixed")

The asymmetric normal distribution.

Description

Density, distribution function, quantile function and random generation for the asymmetric normal distribution with the parameters mu, sigma and tau.

Usage

dasynorm(x, mu = 0, sigma = 1, tau = 0.5)
pasynorm(q, mu = 0, sigma = 1, tau = 0.5)
qasynorm(p, mu = 0, sigma = 1, tau = 0.5)
rasynorm(n, mu = 0, sigma = 1, tau = 0.5)

Arguments

q

vector of quantiles.
mu

location parameter and mode of the distribution.
sigma

comparable to the standard deviation. Must be positive.
tau

asymmetry parameter.
x

vector of locations.
p

vector of probabilities.
n

number of observations. If length(n)>1length(n) > 1, the length is taken to be the number required.

Details

The asymmetric normal distribution has the following density
f(x)=(2τ(1−τ)/π/σ)/(1−τ+τ)exp⁡(−∣(τ−(x<=μ))∣∗(x−μ)2/σ2)f(x) = (2\sqrt{\tau(1-\tau)/\pi}/\sigma)/(\sqrt{1-\tau} + \sqrt{\tau)}\exp(-|(\tau - (x <= \mu))|*(x - \mu)^2/\sigma^2) The cdf is derived by integration of the distribution function by using the integrate function.

Value

dasynorm gives the density, pasynorm gives the distribution function, qasynorm gives the quantile function, and rasynorm generates random deviates.

Corresponds to the normal distribution for τ=0.5\tau = 0.5.

The length of the result is determined by n for rasynorm, and is the maximum of the lengths of the numerical arguments for the other functions.

The numerical arguments other than n are recycled to the length of the result.

Examples

hist(rasynorm(1000))

qg <- qasynorm(0.1, 1, 2, 0.5)

pasynorm(qg, 1, 2, 0.5)

ax <- c(1:1000)/100-5
plot(ax,dasynorm(ax), type = 'l')

Estimate confidence intervals and standard errors for the mode regression fit

Description

Performs bootstrap on the modreg object.

Usage

boot.modreg(
  reg,
  nboot,
  level = 0.95,
  newdata = NULL,
  bw = c("variable", "fixed"),
  quiet = FALSE,
  terms = NULL,
  seed = NULL
)

Arguments

reg

an object of class modreg (output of the modreg function)
nboot

number of bootstrap replications
level

confidence level
newdata

Should be a data frame containing all the variables needed for predictions. If supplied, confidence intervals are calculated for the corresponding predictions.
bw

Either "variable" or "fix", determining if the bandwidth of the original fit should be used for the bootstrap fits (fix) or if the bandwith should be recalculated (variable).
quiet

if TRUE, printing of the status is suppressed
terms

character scalar. If supplied, uses this term for confidence intervals of the prediction
seed

the seed to use

Details

A nonparametric residual bootstrap is performed to calculate standard errors of parameters and confidence intervals. More details can be found in Seipp et al. (2022). newdata can be supplied to get confidence intervals for specific predictions. terms can be specified to calculate confidence interval for the contribution of one covariate (useful for P-splines). variable bandwidth is the default, which has higher coverage than fix, but is computationally much more demanding. A seed can be supplied to guarantee a reproducible result.

Value

a list with the following elements

confpredict

data frame, the confidence intervals for the predictions.
confparams

data frame, the confidence intervals and standard errors for the parametric regression coefficients.
level

confidence level
na

scalar, stating the number of NA bootstrap repetitions.
seed

scalar, the used seed.

References

Seipp, A., Uslar, V., Weyhe, D., Timmer, A., & Otto-Sobotka, F. (2022). Flexible Semiparametric Mode Regression for Time-to-Event Data. Manuscript submitted for publication.

Examples

data(colcancer)
colcancer80 <- colcancer[1:80, ]

# linear mode regression
regL <- modreg(Surv(logfollowup, death) ~ sex + age, data = colcancer80)

# bootstrap with a fixed bandwidth and 3 iterations, chosen to speed up the function. 
# Should in practice be much more than 3 iterations.
btL <- boot.modreg(regL, 3, bw = "fixed", level = 0.9, seed = 100)

# coefficients, SE and confidence intervals
cbind(coef(regL), btL$confparams)


## confidence inverval for smooth effect / predictions

reg <- modreg(Surv(logfollowup, death) ~ sex + s(age, bs = "ps"), data = colcancer80, 
              control = modreg.control(tol_opt = 10^-2, tol_opt2 = 10^-2, tol = 10^-3))
ndat <- data.frame(sex = rep(colcancer80$sex[1], 200), age = seq(50, 90, length = 200))

# iterations should in practice be much more than 2!
bt <- boot.modreg(reg, 2, bw = "fixed", newdata = ndat, terms = "s(age)", seed = 100)

pr <- predict(reg, newdata = ndat, type = "terms", terms = "s(age)")[, 1]

plot(ndat$age, pr, ylim = c(-0.75, 1.5), type = "l", xlab = "age", ylab = "s(age)")
lines(ndat$age, bt$confpredict$lower, lty = 2)
lines(ndat$age, bt$confpredict$upper, lty = 2)

Colon Cancer Dataset

Description

A dataset describing colon cancer patients. The data is based on real data from a hospital-based cancer registry but many values are changed to ensure anonymity. Each row is a single case, while the columns represent patients' health conditions and physical parameters.

Usage

data("colcancer")

Format

A data.frame with 546 observations with colon cancer cases. The 12 columns describe different parameters of patients' conditions.

Details

The columns of the data set are:

  • followup. numeric. Follow-up time since surgery in days. The time the patient was observed.

  • logfollowup. numeric. The follow-up time, but logarithmic.

  • death. integer. Indicates whether the patient died. If death occured it is set to 1, otherwise 0.

  • sex. factor. Level: "f", "m". The sex of the patient. In this case "f" stands for female, and "m" represents male patients.

  • LNE. numeric. The number of examined lymph nodes.

  • LNR. numeric, ranges from 0 to 1. The number of cancerous lymph nodes divided by the total number (LNE).

  • pUICC. factor. Levels: "I", "II", "III", "IV". Pathological cancer stage. The UICC staging system was used.

  • CTX. factor. Levels: "0", "1". Chemotherapy (no / yes)

  • ASA.score. factor. Levels: "mild", "severe". An ASA score smaller than 3 is considered a mild general illness, 3 or greater is considered a severe general illness. The ASA scoring system of patients was originally proposed by the American Society of Anesthesiologists.

  • R.status factor. Level: "0", "12". Residual tumor after surgery. 0 stands for no residual tumor. 12 stands either for microscopic (R1) or macroscopic residues (R2).

  • preexisting.cancer. integer. If there was a history of cancer before the colon cancer. Set to 1 if there has been a cancer in the past and to 0 if not.

  • age. numeric. The age of the patient in years.

Expectile regression for right censored event times using an auxiliary likelihood

Description

Estimate a set of conditional expectiles or quantiles with semiparametric predictors in accelerated failure time models. For the estimation, the asymmetric loss functions are reformulated into auxiliary likelihoods.

Usage

expectreg.aft(
   formula,
   data = NULL,
   smooth = c("cvgrid", "aic", "bic", "lcurve", "fixed"), 
   lambda = 1, 
   expectiles = NA, ci = FALSE)

qureg.aft(
   formula, 
   data = NULL, 
   smooth = c( "cvgrid", "aic", "bic", "lcurve", "fixed"), 
   lambda = 1, 
   quantiles = NA, 
   ci = FALSE)

Arguments

formula

An R formula object consisting of the response variable, '~' and the sum of all effects that should be taken into consideration. Each semiparametric effect has to be given through the function rb. The response needs to be a call of Surv.
data

Optional data frame containing the variables used in the model, if the data is not explicitely given in the formula.
smooth

There are different smoothing algorithms that tune lambda to prevent overfitting. Caution, the currently implemented smoothing algorithms can take a long time. Cross validation is done with a grid search ('cvgrid'). The function can also use a supplied fixed penalty ('fixed'). The numerical minimisation is also possible with AIC or BIC as score ('aic', 'bic'). The L-curve ('lcurve') is a new 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. The option may be set to 'density' for the calculation of a dense set of expectiles that enhances the use of cdf.qp and cdf.bundle afterwards.
ci

Whether a covariance matrix for confidence intervals and a summary is calculated.
quantiles

Quantiles for which the regression should be performed.

Details

For expectile regression, the LAWS loss function

S=∑i=1nwi(p)(yi−μi(p))2S = \sum_{i=1}^{n}{ w_i(p)(y_i - \mu_i(p))^2}

with

wi(p)=p1(yi>μi(p))+(1−p)1(yi<μi(p))w_i(p) = p 1_{(y_i > \mu_i(p))} + (1-p) 1_{(y_i < \mu_i(p))}

is repackaged into the asymmetric normal distribution. Then, an accelerated failure time model is estimated. This function is based on the 'expectreg' package and uses the same functionality to include semiparametric predictors.

For quantile regression, the loss function is replaced with a likelihood from the asymmetric laplace distribution.

Value

An object of class 'expectreg', which is basically a list consisting of:

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\phi for kriging.

design

Complete design matrix.

bases

Bases components of each covariate.

fitted

Fitted values y^\hat{y}.

covmat

Covariance matrix, estimated when ci = TRUE.

diag.hatma

Diagonal of the hat matrix. Used for model selection criteria.

data

Original data

smooth_orig

Unchanged original type of smoothing.

plot, predict, resid, fitted, effects and further convenient methods are available for class 'expectreg'.

Author(s)

Fabian Otto-Sobotka
Carl von Ossietzky University Oldenburg
https://uol.de

See Also

expectreg.ipc, expectreg.ls

Examples

data(colcancer)
ex <- c(0.05, 0.2, 0.5, 0.8, 0.95)
c100 <- colcancer[1:100,]
exfit <- expectreg.aft(Surv(logfollowup, death) ~ LNE, data = c100, expectiles = ex, smooth="f")
coef(exfit)

qu1 <- qureg.aft(Surv(logfollowup, death) ~ LNE + sex, data=c100, smooth="fixed")
coef(qu1)

## Not run: 

# takes some time
qu2 <- qureg.aft(Surv(logfollowup, death) ~ rb(LNE) + sex, data=colcancer[1:200,])

## End(Not run)

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\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)

The Gumbel Distribution.

Description

Density, distribution function, quantile function and random generation for the gumbel distribution with the two parameters location and scale.

Usage

dgumbel(x, location = 0, scale = 1)
pgumbel(q, location = 0, scale = 1)
qgumbel(p, location = 0, scale = 1)
rgumbel(n, location = 0, scale = 1)

Arguments

q

vector of quantiles.
location

location parameter and mode of the distribution.
scale

scaling parameter, has to be positive.
x

vector of locations.
p

vector of probabilities.
n

number of observations. If length(n)>1length(n) > 1, the length is taken to be the number required.

Details

The gumbel distribution has the following density and cdf
f(x)=(1/scale)∗exp((x−location)/scale−exp((x−location)/scale))f(x) = (1/scale)*exp((x - location)/scale - exp((x - location)/scale)), F(x)=1−exp(−exp((x−location)/scale))F(x) = 1 - exp(- exp((x - location)/scale)). The mode of the distribution is location, the variance is π2/6∗scale\pi^{2/6} * \code{scale}.

Value

dgumbel gives the density, pgumbel gives the distribution function, qgumbel gives the quantile function, and rgumbel generates random deviates.

The length of the result is determined by n for rgumbel, and is the maximum of the lengths of the numerical arguments for the other functions.

The numerical arguments other than n are recycled to the length of the result.

References

Collett, D. (2015). Modelling survival data in medical research, chapter 6. CRC press.

Examples

hist(rgumbel(1000))

qg <- qgumbel(0.1, 1, 2)

pgumbel(qg, 1, 2)

ax <- c(1:1000)/100-5
plot(ax,dgumbel(ax), type = 'l')

Methods for fitted modreg model

Description

Methods for modreg objects returned by the mode regression function.

Usage

## S3 method for class 'modreg'
coefficients(object, ...)

## S3 method for class 'modreg'
coef(object, ...)

## S3 method for class 'modreg'
print(x, ...)

## S3 method for class 'modreg'
summary(object, ...)

Arguments

...

further arguments passed to or from other methods
x, object

A modreg object

Value

coef returns a named numerical vector with coefficients

Mode-regression for right-censored data

Description

This function implements semiparametric kernel-based mode regression for right-censored or full data.

Usage

modreg(
  formula,
  data = NULL,
  bw = c("Pseudo", "Plugin"),
  lambda = NULL,
  KMweights = NULL,
  control = NULL
)

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.
data

A data set on which the regression should be performed on. It should consist of columns that have the names of the specific variables defined in formula. If NULL, the function will look for the data in the environment given by the formula argument.
bw

String, either "Pseudo", "Plugin" or a fixed numerical value. This determines how bandwidth should be estimated. "Plugin" only recommended for uncensored linear mode regression.
lambda

Penalty term for penalized splines. Will be estimated if NULL.
KMweights

numerical vector, should be the same length as the response. Inverse probability of censoring weights can be provided here. They will be calculated if NULL.
control

A call to control. Various control parameters can be supplied here.

Details

Fits mode regression in an iteratively weighted least squares approach. A detailed description of the approach and algorithm can be found in Seipp et al. (2022). In short, kernel-based mode regression leads to minimization of weighted least squares, if the normal kernel is assumed. We use gam for estimation in each iteration. Mode regression is extended to right-censored time-to event data with inverse probability of censoring weights. Hyperparameters (bandwidth, penalty) are determined with a pseudo-likelihood approach for bw = "Pseudo". For "Plugin", plug-in bandwidth selection is performed, as described in Yao and Li (2014). However, this is only justified for uncensored data and mode regression with linear covariate trends or known transformations.

The event time has to be supplied using the Surv function. Positive event times with multiplicative relationships should be logarithmized beforehand. Nonlinear trends can be estimated with P-splines, indicated by using s(covariate, bs = "ps"). This will be passed down to gam, which is why the same notation is used. Other smooth terms are not tested yet. The whole gam object will be returned but standard errors and other information are not valid. boot.modreg can be used for calculation of standard errors and confidence intervals.

Value

This function returns a list with the following properties:

reg

object of class gam. Should be interpreted with care.
bw

The used bandwidth.
converged

logical. Whether or not the iteratively weighted least squares algorithm converged.
iterations

the number of iterations of the final weighted least squares fit
cova

Covariance matrix. Only supplied in case of linear terms and plug-in bandwidth.
KMweights

double vector. Weights used.
called

list. The arguments that were provided.
aic

Pseudo AIC.
pseudologlik

Pseudo log-likelihood.
edf

Effective degrees of freedom
delta

vector. Indicating whether an event has occured (1) or not (0) in the input data.
response

vector with response values
hp_opt

Summary of hyperparameter estimation.

References

Seipp, A., Uslar, V., Weyhe, D., Timmer, A., & Otto-Sobotka, F. (2022). Flexible Semiparametric Mode Regression for Time-to-Event Data. Manuscript submitted for publication.
Yao, W., & Li, L. (2014). A new regression model: modal linear regression. Scandinavian Journal of Statistics, 41(3), 656-671.

Examples

data(colcancer)
colcancer80 <- colcancer[1:80, ]

# linear trend
regL <- modreg(Surv(logfollowup, death) ~ sex + age, data = colcancer80)
summary(regL)

# mode regression with P-splines. Convergence criteria are changed to speed up the function
reg <- modreg(Surv(logfollowup, death) ~ sex + s(age, bs = "ps"), data = colcancer80, 
control = modreg.control(tol_opt = 10^-2, tol_opt2 = 10^-2, tol = 10^-3))
summary(reg)
plot(reg)

# with a fixed penalty
reg2 <- modreg(Surv(logfollowup, death) ~ sex + s(age, bs = "ps"), data = colcancer80, lambda = 0.1)

# for linear effects and uncensored data, we can use the plug-in bandwidth
regP <- modreg(age ~ sex, data = colcancer, bw = "Plugin")

Setting fitting values for modreg.

Description

This is an internal function of package dirttee which allows control of the numerical options for fitting mode regression. Typically, users will want to modify the defaults if model fitting is slow or fails to converge.

Usage

modreg.control(
  StartInterval = sqrt(3),
  nStart = 11,
  nInterim = NULL,
  maxit = 100,
  itInterim = 10,
  tol = 10^-4,
  tol_bw_plugin = 10^-3,
  maxit_bw_plugin = 10,
  maxit_penalty_plugin = 10,
  tol_penalty_plugin = 10^-3,
  tol_regopt = tol * 100,
  tol_opt = 10^-3,
  maxit_opt = 200,
  tol_opt2 = 10^-3,
  maxit_opt2 = 200
)

Arguments

StartInterval

Starting values are based on an estimate for the mean and an interval around it. The interval is +−StartInterval∗σ+-\code{StartInterval} * \sigma. Default is 3\sqrt{3}.
nStart

Number of starting values, considered in the first iteration. Default is 11.
nInterim

Probably has little impact on speed and result. After itInterim weighted least squares iterations, the number of estimates is reduced from nStart to nInterim estimates. Default is 5.
maxit

Maximum number of iterations for the weighted least squares algorithm. Default is 100.
itInterim

Probably has little impact on speed and result. After itInterim weighted least squares iterations, the number of estimates is reduced from nStart to nInterim estimates. Default is 10.
tol

Convergence criterion for the weighted least squares algorithm. Default is 10^-4.
tol_bw_plugin

Convergence criterion for bandwidth selection in the "Plugin" method. Default is 10^-3.
maxit_bw_plugin

Maximum number of iterations for bandwidth selection in the "Plugin" method. Default is 10.
maxit_penalty_plugin

Maximum number of iterations for penalty selection in the "Plugin" method. Default is 10.
tol_penalty_plugin

Convergence criterion for penalty selection in the "Plugin" method. Default is 10^-3.
tol_regopt

Weighted least squares are recalculated for hyperparameter optimization. This is the convergence criterion within this optimization. Default is tol * 100.
tol_opt

Convergence criterion for the first hyperparameter optimizion. Can be increased to reduce compuation time. Default is 10^-3.
maxit_opt

Maximum number of iterations for the first hyperparameter optimizion. Can be lowered to reduce compuation time. Default is 200.
tol_opt2

Convergence criterion for the second hyperparameter optimizion. Default is 10^-3.
maxit_opt2

Maximum number of iterations for the second hyperparameter optimizion. Default is 200.

Details

The algorithm is described in Seipp et al. (2022). To increase the speed of the algorithm, adapting tol and maxit_opt/maxit_opt2 and other penalty / hyperparameter optimization parameters are a good starting point.

Value

A list with the arguments as components

References

Seipp, A., Uslar, V., Weyhe, D., Timmer, A., & Otto-Sobotka, F. (2022). Flexible Semiparametric Mode Regression for Time-to-Event Data. Manuscript submitted for publication.
Yao, W., & Li, L. (2014). A new regression model: modal linear regression. Scandinavian Journal of Statistics, 41(3), 656-671.

Plot regression terms for modreg objects

Description

Plots smooth components of a fitted modreg object.

Usage

## S3 method for class 'modreg'
plot(x, ...)

Arguments

x

The object to plot, must be of class modreg.
...

Additional arguments to pass to plot.gam.

Details

This function is a wrapper for plot.gam. It displays term plots of smoothed variables. Optionally produces term plots for parametric model components as well. Standard errors will not be displayed but can be estimated by boot_modreg.

Value

The functions main purpose is its side effect of generating plots. It also silently returns a list of the data used to produce the plots, which can be used to generate customized plots.

Examples

data(colcancer)
# mode regression with P-splines. Convergence criteria are changed to speed up the function
reg <- modreg(Surv(logfollowup, death) ~ sex + s(age, bs = "ps"), data = colcancer[1:70, ], 
control = modreg.control(tol_opt = 10^-2, tol_opt2 = 10^-2, tol = 10^-3))
plot(reg)

Prediction from a fitted modreg model

Description

Takes a fitted modreg object produced by modreg and produces predictions. New sets of covariates can by supplied through newdata.

Usage

## S3 method for class 'modreg'
predict(object, ...)

Arguments

object

The object to plot, must be of class modreg.
...

Additional arguments to pass to predict.gam.

Details

This function is a wrapper for predict.gam.

Value

A vector or matrix of predictions. For type = "terms" this is a matrix with a column per term.

Examples

data(colcancer)
colcancer70 <- colcancer[1:70, ]

mc <- modreg.control(tol_opt = 10^-2, tol_opt2 = 10^-2, 
tol = 10^-3)
reg <- modreg(Surv(logfollowup, death) ~ sex + s(age, bs = "ps"), data = 
colcancer70, control = mc)
ndat <- data.frame(sex = rep(colcancer70$sex[1], 200), age = seq(50, 90, length = 200))
pr <- predict(reg, newdata = ndat)

Inverse probability of censoring weights

Description

Computes inverse probability of censoring weights.

Usage

weightsKM(y, delta)

Arguments

y

numerical vector with right-censored follow-up times
delta

numerical vector, same length as y, 1 indicates an event while 0 indicates censoring

Details

Inverse probability of censoring weights are calculated by dividing the event indicator by the Kaplan-Meier estimator of the censoring time. This leads to zero weights for censored observations, while every uncensored event receives a weight larger than 1, representing several censored observations. In the redistribute-to-the-right approach, the last observation always receives a positive weight such that no weight will be lost. Further details can be found in Seipp et al. (2021).

Value

A data frame with 2 coloumns. The first column consists of usual inverse probability of censoring weights. For the second column, IPC weights modified in a redistribute-to-the-right approach are given.

References

Seipp, A., Uslar, V., Weyhe, D., Timmer, A., & Otto-Sobotka, F. (2021). Weighted expectile regression for right-censored data. Statistics in Medicine, 40(25), 5501-5520.

Examples

data(colcancer)
kw <- weightsKM(colcancer$logfollowup, colcancer$death)