Type:	Package
Title:	Nonparametric Estimation of the Distribution of Gap Times for Recurrent Events
Version:	1.1
Date:	2023-08-09
Description:	Provides estimates for the bivariate and trivariate distribution functions and bivariate and trivariate survival functions for censored gap times. Two approaches, using existing methodologies, are considered: (i) the Lin's estimator, which is based on the extension the Kaplan-Meier estimator of the distribution function for the first event time and the Inverse Probability of Censoring Weights for the second time (Lin DY, Sun W, Ying Z (1999) <doi:10.1093/biomet/86.1.59> and (ii) another estimator based on Kaplan-Meier weights (Una-Alvarez J, Meira-Machado L (2008) https://w3.math.uminho.pt/~lmachado/Biometria_conference.pdf). The proposed methods are the landmark estimators based on subsampling approach, and the estimator based on weighted cumulative hazard estimator. The package also provides nonparametric estimator conditional to a given continuous covariate. All these methods have been submitted to be published.
License:	GPL-3
Depends:	R (≥ 3.5.0)
Imports:	survival, KernSmooth, graphics, stats, utils, methods
RoxygenNote:	7.2.1
Encoding:	UTF-8
LazyLoad:	yes
LazyData:	yes
NeedsCompilation:	yes
Suggests:	rmarkdown, knitr
VignetteBuilder:	knitr
Packaged:	2023-08-09 09:13:50 UTC; asus
Author:	Gustavo Soutinho [aut, cre], Luis Meira-Machado [aut], Artur Araujo [ctb], Ana Moreira [ctb]
Maintainer:	Gustavo Soutinho <gustavosoutinho@sapo.pt>
Repository:	CRAN
Date/Publication:	2023-08-09 10:30:05 UTC

Estimation of the conditional distribution function of the response, given the covariate under random censoring.

Description

Computes the conditional survival probability P(T > y|Z = z)

Usage

Beran(time, status, covariate, delta, x, y, kernel = "gaussian", bw, 
lower.tail = FALSE)

Arguments

Details

Possible options for argument window are "gaussian", "epanechnikov", "tricube", "boxcar", "triangular", "quartic" or "cosine"

Value

Vector with the estimation of the conditional distribution function of the response, given the covariate under random censoring.

Author(s)

Gustavo Soutinho and Luis Meira-Machado

References

R. Beran. Nonparametric regression with randomly censored survival data. Technical report, University of California, Berkeley, 1981.

Examples

data("bladder4state")
b3state<-multidf(gap1=bladder4state$y1, event1=bladder4state$d1, 
                 gap2=bladder4state$y2, status=bladder4state$d2, 
                 size=bladder4state$size)

head(b3state[[1]])

##P(T>y|size=3)
library(KernSmooth)

obj0 <- b3state[[1]]

h <- dpik(obj0$size)
Beran(time = obj0$time, status = obj0$status, covariate =obj0$size, x = 3, 
y = 50, bw = h)

##P(T<=y|size=3)
Beran(time = obj0$time, status = obj0$status, covariate =obj0$size, x = 3,
 y = 50, bw = h,
lower.tail = TRUE)

Inverse probability of censoring weighting estimator for the bivariate distribution function.

Description

Provides estimates for the bivariate distribution function based on the Inverse Probability of Censoring Weighting estimator (IPCW).

Usage

IPCWdf(object, x, y, covariate, cov.value, bw, window = "gaussian")

Arguments

Value

Vector with the IPWC estimates for the bivariate distribution function.

Author(s)

Gustavo Soutinho and Luis Meira-Machado.

Gustavo Soutinho and Luis Meira-Machado

References

de Una-Alvarez, J. and Meira-Machado, L. (2008). A simple estimator of the bivariate distribution function for censored gap times, Statistics and Probability Letters 78, 2440-2445.

See Also

KMWdf, LDMdf, LINdf and WCHdf.

Examples

data("bladder4state")

b3state<-multidf(gap1=bladder4state$y1, event1=bladder4state$d1, 
                 gap2=bladder4state$y2, status=bladder4state$d2, 
                 size=bladder4state$size)         

b3size<-multidf(gap1=bladder3$t1, event1=bladder3$d1, 
                gap2=bladder3$t2-bladder3$t1,status=bladder4state$d2, 
                size=bladder3$size)  

library(KernSmooth)

IPCWdf(object=b3state, x=13, y=15, covariate="size", cov.value=3, 
       window = "gaussian")
       
IPCWdf(object=b3state, x=13, y=15, covariate="size", bw=2, cov.value=3, 
       window = "gaussian")

IPCWdf(object=b3size, x=13, y=15, covariate="size", cov.value=3, 
       window = "gaussian")
       
IPCWdf(object=b3size, x=13, y=15, covariate="size", bw=2, cov.value=3, 
       window = "gaussian")

Kaplan-Meier product-limit estimate of survival

Description

This function provides survival estimates using the product-limit Kaplan-Meier estimator.

Usage

KM(time, status, t)

Arguments

Value

Vector with Kaplan-Meier estimate of survival.

Author(s)

Gustavo Soutinho and Luis Meira-Machado

References

E. Kaplan and P. Meier. Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53:457-481, 1958.

Examples

require(survival)
data("bladder4state")

obj<- multidf(gap1=bladder4state$y1, event1=bladder4state$d1, 
              gap2=bladder4state$y2, status=bladder4state$d2, 
              size=bladder4state$size) 
              
obj2<-obj[[1]]
KM(time = obj2$time, status = obj2$status, t = 20)
fit <- survfit(Surv(obj2$time, obj2$status) ~ 1, data = obj2)
summary(fit, time = 20)$surv

Kaplan-Meier weights

Description

This function returns a vector with the Kaplan-Meier weights.

Usage

KMW(time, status)

Arguments

Value

Vector with Kaplan-Meier weights.

Author(s)

Gustavo Soutinho and Luis Meira-Machado

References

E. Kaplan and P. Meier. Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53:457-481, 1958.

Examples

data("bladder4state")

obj<- multidf(gap1=bladder4state$y1, event1=bladder4state$d1, 
              gap2=bladder4state$y2, status=bladder4state$d2, 
             size=bladder4state$size) 
             
obj2<-obj[[1]]
kmw <- KMW(time = obj2$time, status = obj2$status)
require(survival)
bladder.surv <- survfit(Surv(time, status) ~ 1, obj2)
times <- summary(bladder.surv)$time
surv <- summary(bladder.surv)$surv
nevent <- summary(bladder.surv)$n.event
p <- match(obj2$time, times)
kmw2 <- -diff(c(1, surv))/nevent
kmw2 <- kmw2[p]*obj2$status
kmw2[is.na(kmw2)] <- 0
all.equal(kmw, kmw2)

Kaplan-Meier Weighted estimator for three gap times distribution function.

Description

Provides estimates for three gap times distribution function based on Kaplan-Meier Weights (KMW).

Usage

KMW3df(object, x, y, z)

Arguments

Value

Vector with the Kaplan-Meier Weighted estimates for three gapes times distribution function.

Author(s)

Gustavo Soutinho and Luis Meira-Machado

References

de Una-Alvarez J, Meira Machado LF (2008). "A Simple Estimator of the Bivariate Distribution Function for Censored Gap Times", Statistical and Probability Letters, 78, 2440-2445.

Davison, A.C. and Hinkley, D.V. (1997) "Bootstrap Methods and Their Application", Chapter 5. Cambridge University Press.

See Also

LDM3df, LIN3df and WCH3df.

Examples

data("bladder5state")
b4state<-multidf(gap1=bladder5state$y1, event1=bladder4state$d1, 
                 gap2=bladder5state$y2, event2=bladder4state$d2,
                 gap3=bladder5state$y3, status=bladder4state$d3)
                 
head(b4state)[[1]]

KMW3df(b4state, x=13, y=20, z=40)

b4<-multidf(gap1=bladder4$t1, event1=bladder4$d1, 
            gap2=bladder4$t2-bladder4$t1, event2=bladder4$d2,
            gap3=bladder4$t3-bladder4$t2, status=bladder4state$d3)

KMW3df(b4, x=13, y=20, z=40)

Kaplan-Meier Weighted estimator for the bivariate distribution function.

Description

Provides estimates for the bivariate distribution function based on Kaplan-Meier Weights (KMW).

Usage

KMWdf(object, x, y)

Arguments

Value

Vector with the Kaplan-Meier weights estimates for the bivariate distribution function.

Author(s)

Gustavo Soutinho and Luis Meira-Machado

References

de Una-Alvarez J, Meira Machado LF (2008). "A Simple Estimator of the Bivariate Distribution Function for Censored Gap Times", Statistical and Probability Letters, 78, 2440-2445.

Davison, A.C. and Hinkley, D.V. (1997) "Bootstrap Methods and Their Application", Chapter 5. Cambridge University Press.

See Also

IPCWdf, LDMdf, LINdf and WCHdf.

Examples

data("bladder4state")

b3state<-multidf(gap1=bladder4state$y1, event1=bladder4state$d1, 
                 gap2=bladder4state$y2, status=bladder4state$d2, 
                 size=bladder4state$size)
                 
KMWdf(b3state, x=13, y=20)

Landmark estimator for three gap times distribution function.

Description

Provides estimates for three gap times distribution function based on landmarking. The extension of the landmark estimator (LDM) to three gap times is a consequence of Bayes' theorem.

Usage

LDM3df(object, x, y, z)

Arguments

Value

Vector with the Landmark estimates for three gap times distribution function.

Author(s)

Gustavo Soutinho and Luis Meira-Machado

References

van Houwelingen, H.C. (2007). Dynamic prediction by landmarking in event history analysis, Scandinavian Journal of Statistics, 34, 70-85.

Kaplan, E. and Meier, P. (1958). Nonparametric Estimation from Incomplete Observations, Journal of the American Statistical Association 53(282), 457-481.

See Also

LDM3df, LIN3df and WCH3df.

Examples

data("bladder5state")
b4state<-multidf(gap1=bladder5state$y1, event1=bladder4state$d1, 
                 gap2=bladder5state$y2, event2=bladder4state$d2,
                 gap3=bladder5state$y3, status=bladder4state$d3)
                 
head(b4state)[[1]]

LDM3df(b4state, x=13, y=20, z=40)

b4<-multidf(gap1=bladder4$t1, event1=bladder4$d1, 
            gap2=bladder4$t2-bladder4$t1, event2=bladder4$d2,
            gap3=bladder4$t3-bladder4$t2, status=bladder4state$d3)

LDM3df(b4,x=13,y=20,z=40)

Landmark estimator for the bivariate distribution function

Description

Provides estimates for the bivariate distribution function based on Bayes' theorem and Kaplan-Meier survival function. This approach is also named as landmarking.

Usage

LDMdf(object, x, y)

Arguments

Value

Vector with the Landmark estimates for the bivariate distribution function.

Author(s)

Gustavo Soutinho and Luis Meira-Machado

References

van Houwelingen, H.C. (2007). Dynamic prediction by landmarking in event history analysis, Scandinavian Journal of Statistics, 34, 70-85.

Kaplan, E. and Meier, P. (1958). Nonparametric Estimation from Incomplete Observations, Journal of the American Statistical Association 53(282), 457-481.

See Also

IPCWdf, KMWdf, LINdf and WCHdf.

Examples

b3state<-multidf(gap1=bladder4state$y1, event1=bladder4state$d1, 
                 gap2=bladder4state$y2, status=bladder4state$d2, 
                 size=bladder4state$size)
                 
LDMdf(b3state, x=13, y=20)

Lin's estimator for three gap times distribution function.

Description

Provides estimates for three gap times distribution function based on the extension the Lin's estimator.

Usage

LIN3df(object, x, y, z)

Arguments

Value

Vector with the Lin's estimates for three gapes times distribution function.

Author(s)

Gustavo Soutinho and Luis Meira-Machado

References

Lin, D. Y., Sun, W. and Ying, Z. (1999). Nonparametric estimation of the gap time distributions for serial events with censored data, Biometrika 86, 59-70.

See Also

LDM3df, KMW3df and WCH3df.

Examples

data("bladder5state")
b4state<-multidf(gap1=bladder5state$y1, event1=bladder4state$d1, 
                 gap2=bladder5state$y2, event2=bladder4state$d2,
                 gap3=bladder5state$y3, status=bladder4state$d3)
                 
head(b4state)[[1]]

LIN3df(b4state, x=13, y=20, z=40)

b4<-multidf(gap1=bladder4$t1, event1=bladder4$d1, 
            gap2=bladder4$t2-bladder4$t1, event2=bladder4$d2,
            gap3=bladder4$t3-bladder4$t2, status=bladder4state$d3)

LIN3df(b4, x=13, y=20, z=40)

Lin's estimator for the bivariate distribution function.

Description

Provides estimates for the bivariate distribution function based on the extension the Kaplan-Meier estimator of the distribution function for the first event time and the Inverse Probability of Censoring Weights for the second time.

Usage

LINdf(object, x, y)

Arguments

Value

Vector with the Lin's estimates for the bivariate distribution function.

Author(s)

Gustavo Soutinho and Luis Meira-Machado

References

Lin, D. Y., Sun, W. and Ying, Z. (1999). Nonparametric estimation of the gap time distributions for serial events with censored data, Biometrika 86, 59-70.

See Also

IPCWdf, LDMdf, KMWdf and WCHdf.

Examples

b3state<-multidf(gap1=bladder4state$y1, event1=bladder4state$d1, 
                 gap2=bladder4state$y2, status=bladder4state$d2, 
                 size=bladder4state$size)
             
LINdf(b3,x=13,y=20)

Nadaraya-Watson weights

Description

Computes the Nadaraya-Watson weights.

Usage

NWW(covariate, x, kernel = "gaussian", bw)

Arguments

Details

Possible options for argument window are "gaussian", "epanechnikov", "tricube", "boxcar", "triangular", "quartic" or "cosine".

Value

A vector with Nadaraya-Watson weights.

Author(s)

Gustavo Soutinho and Luis Meira-Machado

Examples

b3state<-multidf(gap1=bladder4state$y1, event1=bladder4state$d1, 
                 gap2=bladder4state$y2, status=bladder4state$d2, 
                 size=bladder4state$size)
                 
obj0 <- b3state[[1]]

NWW(covariate = obj0$size, x=3, kernel = "gaussian", bw = 3)

Weighted cumulative hazard estimator for three gap times distribution function.

Description

Provides estimates for three gap times distribution function based on Weighted cumulative hazard estimator (WCH).

Usage

WCH3df(object, x, y, z)

Arguments

Value

Vector with the Weighted cumulative hazard estimates for three gap times distribution function.

Author(s)

Gustavo Soutinho and Luis Meira-Machado

References

Wang, M.C. and Wells, M.T. (1998). Nonparametric Estimation of successive duration times under dependent censoring, Biometrika 85, 561-572.

See Also

KMW3df, LIN3df and LDM3df.

Examples

data("bladder5state")

b4state<-multidf(gap1=bladder5state$y1, event1=bladder4state$d1, 
                 gap2=bladder5state$y2, event2=bladder4state$d2,
                 gap3=bladder5state$y3, status=bladder4state$d3)
                 
head(b4state)[[1]]

WCH3df(b4state, x=13, y=20, z=40)

b4<-multidf(gap1=bladder4$t1, event1=bladder4$d1, 
            gap2=bladder4$t2-bladder4$t1, event2=bladder4$d2,
            gap3=bladder4$t3-bladder4$t2, status=bladder4state$d3)
              
WCH3df(b4, x=13, y=20, z=40)

Weighted cumulative hazard estimator for the bivariate distribution function

Description

Provides estimates for the bivariate distribution function based on Weighted cumulative hazard estimator (WCH).

Usage

WCHdf(object, x, y)

Arguments

Value

Vector with the Weighted cumulative hazard estimates for the bivariate distribution function.

Author(s)

Gustavo Soutinho and Luis Meira-Machado

References

Wang, M.C. and Wells, M.T. (1998). Nonparametric Estimation of successive duration times under dependent censoring, Biometrika 85, 561-572.

See Also

IPCWdf, KMWdf, LINdf and LDMdf.

Examples

data("bladder3")

b3<-multidf(gap1=bladder3$t1, event1=bladder3$d1, 
            gap2=bladder3$t2-bladder3$t1,status=bladder4state$d2)  

head(b3[[1]])
WCHdf(b3,x=13,y=20)

b3

Description

b3 data set.

Usage

data("b3")

Format

A data frame with 85 observations on the following 4 variables. Below a brief description is given for each of these variables.

time1

First time or censoring time.

time

The total time of the process.

event1

Indicator of the first time; 0 if the first time is censored and 1 otherwise.

status

Censoring indicator of the survival time of the process; 0 if the total time is censored and 1 otherwise.

Examples

data(b3)
head(b3)

b3size

Description

b3size data set.

Usage

data("b3size")

Format

A data frame with 85 observations on the following 5 variables. Below a brief description is given for each of these variables.

time1

First time or censoring time.

time

The total time of the process

event1

Indicator of the first time; 0 if the first time is censored and 1 otherwise.

status

Censoring indicator of the survival time of the process; 0 if the total time is censored and 1 otherwise.

size

Values of covariate size.

Examples

data(b3size)

b3state

Description

b3state data set.

Usage

data("b3state")

Format

A data frame with 85 observations on the following 4 variables. Below a brief description is given for each of these variables.

time1

First time or censoring time.

time

The total time of the process.

event1

Indicator of the first time; 0 if the first time is censored and 1 otherwise.

status

Censoring indicator of the survival time of the process; 0 if the total time is censored and 1 otherwise.

Examples

data(b3state)
str(b3state)

b3state2

Description

b3state2 data set

Usage

data("b3state2")

Format

A data frame with 85 observations on the following 5 variables. Below a brief description is given for each of these variables.

time1

First time or censoring time.

time

The total time of the process

event1

Indicator of the first time; 0 if the first time is censored and 1 otherwise.

status

Censoring indicator of the survival time of the process; 0 if the total time is censored and 1 otherwise.

size

Values of covariate size.

Examples

data(b3state2)
str(b3state2)

b4

Description

b4 data set.

Usage

data("b4")

Format

A data frame with 85 observations on the following 6 variables. Below a brief description is given for each of these variables.

time1

First time or censoring time.

time2

Second time.

time

The total time of the process

event1

Indicator of the first time; 0 if the first time is censored and 1 otherwise.

event2

Indicator of the second time; 0 if the first time is censored and 1 otherwise.

status

Censoring indicator of the survival time of the process; 0 if the total time is censored and 1 otherwise.

Examples

data(b4)
head(b4)

b4state

Description

b4state data set.

Usage

data("b4state")

Format

A data frame with 85 observations on the following 6 variables. Below a brief description is given for each of these variables.

time1

First time or censoring time.

time2

Second time.

time

The total time of the process

event1

Indicator of the first time; 0 if the first time is censored and 1 otherwise.

event2

Indicator of the second time; 0 if the first time is censored and 1 otherwise.

status

Censoring indicator of the survival time of the process; 0 if the total time is censored and 1 otherwise.

Examples

data(b4state)
## maybe str(b4state) ; plot(b4state) ...

bladder3

Description

bladder3-description

Usage

data("bladder3")

Format

A data frame with 85 observations on the following 6 variables.

t1

First time or censoring time.

d1

Indicator of the first time; 0 if the first time is censored and 1 otherwise.

t2

The total time of the process

d2

Censoring indicator of the survival time of the process; 0 if the total time is censored and 1 otherwise.

rx

Values of covariate rx.

size

Values of covariate size.

Examples

data(bladder3)
str(bladder3) 

bladder3state

Description

bladder3state data set.

Usage

data("bladder3state")

Format

A data frame with 85 observations on the following 7 variables.

id

Identification number.

y1

First gap time.

d1

Indicator of the first gap time; 0 if the first time is censored and 1 otherwise.

y2

Second gap time.

d2

Censoring indicator of the second gap time; 0 if the total time is censored and 1 otherwise.

rx

Values of covariate rx.

size

Values of covariate size.

Examples

data(bladder3state)
str(bladder3state)

bladder4

Description

bladder4 data set.

Usage

data("bladder4")

Format

A data frame with 85 observations on the following 8 variables.

t1

First time or censoring time.

d1

Indicator of the first time; 0 if the first time is censored and 1 otherwise.

t2

Second time or censoring time.

d2

Indicator of the second time; 0 if the first time is censored and 1 otherwise.

t3

The total time of the process.

d3

Censoring indicator of the survival time of the process; 0 if the total time is censored and 1 otherwise.

rx

Values of covariate rx.

size

Values of covariate size.

Examples

data(bladder4)

bladder4state

Description

bladder4state data set.

Usage

data("bladder4state")

Format

A data frame with 85 observations on the following 9 variables.

id

Identification number.

y1

First gap time.

d1

Indicator of the first gap time; 0 if the first time is censored and 1 otherwise.

y2

Second gap time.

d2

Censoring indicator of the second gap time; 0 if the total time is censored and 1 otherwise.

y3

Third gap time.

d3

Censoring indicator of the third gap time; 0 if the total time is censored and 1 otherwise.

rx

Values of covariate rx.

size

Values of covariate size.

Examples

data(bladder4state)

bladder5

Description

bladder5 data set.

Usage

data("bladder5")

Format

A data frame with 85 observations on the following 10 variables.

t1

First time or censoring time.

d1

Indicator of the first time; 0 if the first time is censored and 1 otherwise.

t2

Second time or censoring time.

d2

Indicator of the second time; 0 if the first time is censored and 1 otherwise.

t3

Third time or censoring time.

d3

Indicator of the third time; 0 if the first time is censored and 1 otherwise.

t4

The total time of the process

d4

Censoring indicator of the survival time of the process; 0 if the total time is censored and 1 otherwise.

rx

Values of covariate rx.

size

Values of covariate size.

Examples

data(bladder5)

bladder5state

Description

bladder5state data set.

Usage

data("bladder5state")

Format

A data frame with 85 observations on the following 11 variables.

id

Identification number.

y1

First gap time.

d1

Indicator of the first gap time; 0 if the first time is censored and 1 otherwise.

y2

Second gap time.

d2

Censoring indicator of the second gap time; 0 if the total time is censored and 1 otherwise.

y3

Third gap time.

d3

Censoring indicator of the third gap time; 0 if the total time is censored and 1 otherwise.

y4

Fourth gap time.

d4

Censoring indicator of the fourth gap time; 0 if the total time is censored and 1 otherwise.

rx

Values of covariate rx.

size

Values of covariate size.

Examples

data(bladder5state)

Create a multidf object

Description

Creates a "multidf" object, usually used as a response variable in a model formula.

Usage

multidf(gap1, gap2, gap3=NULL, event1, status, event2=NULL, ...)

Arguments

Details

Arguments in this function must be introduced in the following order: gap1, event1, gap2 and status, where gap1 and gap2 are ordered event times and event1 and status their corresponding indicator statuses. Other arguments can be also added. These should consider intermediate times and corresponding censoring indicators or covariates.

Value

An object of class "multidf". "multidf" objects are implemented as a single data frame.

Author(s)

Gustavo Soutinho and Luis Meira-Machado

Examples

library(survivalREC)
data("bladder4state")

b3state<-multidf(gap1=bladder4state$y1, event1=bladder4state$d1, 
                 gap2=bladder4state$y2, status=bladder4state$d2, 
                 size=bladder4state$size) 

head(b3state[[1]])

class(b3state)

b4state<-multidf(gap1=bladder4state$y1, event1=bladder4state$d1, 
                 gap2=bladder4state$y2, event2=bladder4state$d2,
                 gap3=bladder4state$y3, status=bladder4state$d3, 
                 size=bladder4state$size)

head(b4state[[1]])

Plot methods for a multidf object

Description

Provides the plots for the bivariate distribution function and marginal distribution of the second time.

Usage

## S3 method for class 'multidf'
plot(x, t1, method = "KMW", type = "s", ...)

Arguments

Value

No value is returned.

Author(s)

Gustavo Soutinho and Luis Meira-Machado

References

de Una-Alvarez, J. and Meira-Machado, L. (2008). A simple estimator of the bivariate distribution function for censored gap times, Statistics and Probability Letters 78, 2440-2445.

Davison, A.C. and Hinkley, D.V. (1997) "Bootstrap Methods and Their Application", Chapter 5. Cambridge University Press.

van Houwelingen, H.C. (2007). Dynamic prediction by landmarking in event history analysis, Scandinavian Journal of Statistics, 34, 70-85. Kaplan, E. and Meier, P. (1958). Nonparametric Estimation from Incomplete Observations, Journal of the American Statistical Association 53(282), 457-481.

See Also

KMWdf, LDMdf, LINdf and WCHdf.

Examples

data("bladder4state")

b3state<-multidf(gap1=bladder4state$y1, event1=bladder4state$d1, 
                 gap2=bladder4state$y2, status=bladder4state$d2, 
                 size=bladder4state$size)

head(b3state[[1]])

KMWdf(b3state,x=13,y=20)
LDMdf(b3state,x=13,y=20)
LINdf(b3state,x=13,y=20)
WCHdf(b3state,x=13,y=20)

plot(x=b3state, t1=3, method="KMW", type = "s")
plot(x=b3state, t1=3, method="LIN", type = "s")
plot(x=b3state, t1=3, method="WCH", type = "s")
plot(x=b3state, t1=3, method="LANDMARK", type = "s")