implements the De Vielder approximation

Description

DV computes the De Vielder approximation whose goal is to identify the first two moments of a general case of the first model where p(x) is unknown to the first two moments of the specific case of the first model where p(x) = 1- exp(-mu *x)

Usage

DV(T)

Arguments

Value

a vector of lambda and mu of the De Vielder method

Author(s)

Christophe Dutang and Julie Barthes

Examples

T<-c(12.9622796,  1.4146460,  1.3146761, 14.9147353,  7.5131105,  
8.5130874, 6.5943351, 10.6954653, 14.1000977, 12.4673316,  2.7185478,  
9.6297777, 10.0930441,  0.6270543, 26.7937074,  7.6082447)
res<-DV(T)

plots a survival function with a Kaplan Meier variant

Description

plots the survival function of patients knowing censored data. Model : a variant of Kaplan-Meier's model

Usage

KM(fileName, toplot = TRUE, header = TRUE)

Arguments

Value

No values returned, just plot the survival function and the theoretical distribution of our model with exponential stays and a constant side effect probability

Author(s)

Christophe Dutang and Julie Barthes

Examples

#KM("data.rda",TRUE,TRUE)

make an array of bias, variance and R for different distribution and estimators

Description

this function prints an array of the bias, variance, risk constants R and CR for three estimators (parametric, non parametric and De Vielder) with different side effect probability for p

Usage

Table(file, nb = 10, mod)

Arguments

Value

Null.

Author(s)

Christophe Dutang and Julie Barthes

Examples

#Table("d.rda",100,3)

# plot the following result 
#[1] "arg2Exp"
#           nonpar           par
#bias 4.407856e-02 -3.503516e-06
#var  6.001352e-05  1.972828e-05
#R    9.405885e-02  4.997679e-02
#CR   8.492920e+00  1.455619e+01
#[1] "arg2Cst"
#           nonpar          par
#bias 1.575410e-02 4.573187e-04
#var  1.714712e-05 5.675577e-06
#R    3.242554e-02 1.712875e-02
#CR   2.197198e+01 4.066553e+01
#[1] "arg2Comp"
#           nonpar           par
#bias 3.247060e-02 -5.558817e-05
#var  4.621880e-05  1.006148e-05
#R    6.880894e-02  3.628275e-02
#CR   1.101930e+01  1.967524e+01
#[1] "arg2Gamma"
#           nonpar           par
#bias 1.832645e-02 -7.552530e-04
#var  2.267637e-05  7.363311e-06
#R    3.778277e-02  1.870107e-02
#CR   1.911443e+01  3.773611e+01
#[1] "arg2Lnorm"
#           nonpar          par
#bias 4.556463e-02 1.017082e-03
#var  7.013414e-05 3.104221e-05
#R    1.005464e-01 5.599889e-02
#CR   8.101552e+00 1.318976e+01
#[1] "arg2Unif"
#           nonpar          par
#bias 2.514426e-02 2.598740e-04
#var  3.878331e-05 1.073282e-05
#R    5.236710e-02 2.748271e-02
#CR   1.408411e+01 2.580822e+01
#[1] "arg2Weib"
#           nonpar          par
#bias 4.588473e-03 1.540856e-04
#var  5.405285e-06 1.589171e-06
#R    9.367470e-03 4.933083e-03
#CR   7.709814e+01 1.468196e+02
#

test the adequation of a random variable to the exponential distribution

Description

In order to test the adequation of a random variable, this function plot the probabilit plot with reference distribution exponential of the variable and calculates the Kolmogorov Smirnov test.

Usage

adequadExp(T, toplot = FALSE)

Arguments

Value

a list of the following components

Author(s)

Christophe Dutang and Julie Barthes

Examples

## Not run: 
T <- c(12.9622796,  1.4146460,  1.3146761, 14.9147353,  7.5131105,  
8.5130874, 6.5943351, 10.6954653, 14.1000977, 12.4673316,  2.7185478,  
9.6297777, 10.0930441,  0.6270543, 26.7937074,  7.6082447)
adequadExp(T,TRUE)

## End(Not run)

compute the bias, variance of the De Vielder approximation

Description

calcErrorDV computes the risk constant R with the De Vielder estimator and its bias and variance.

Usage

calcErrorDV(file, nb = 10, disXi, disP, plot = TRUE)

Arguments

Value

a list of the following components

Author(s)

Christophe Dutang and Julie Barthes

Examples

## Not run: 
arg1Exp<-list(rangen=rexp,nbparam=1,param=list(1/3));
arg2Exp<-list(disfun=pexp,nbparam=1,param=list(1/5));
res<-calcErrorDV("data.rda",25,arg1Exp,arg2Exp,TRUE)

## End(Not run)

compute the bias, variance of the non parametric estimator

Description

calcErrorNonParam computes the risk constant R with the non parametric estimator and its bias and variance.

Usage

calcErrorNonParam(file, nb = 10, disXi, disP, plot = TRUE)

Arguments

Value

a list of the following components

Author(s)

Christophe Dutang and Julie Barthes

Examples

#arg1Exp<-list(rangen=rexp,nbparam=1,param=list(1/3));
#arg2Exp<-list(disfun=pexp,nbparam=1,param=list(1/5));


#res<-calcErrorNonParam("data.rda",25,arg1Exp,arg2Exp,TRUE)

compute the bias, variance of the non parametric estimator

Description

calcErrorNonParam computes the risk constant R with the non parametric estimator and its bias and variance.

Usage

calcErrorParam(file, nb = 10, disXi, disP, plot = TRUE)

Arguments

Value

a list of the following components

Author(s)

Christophe Dutang and Julie Barthes

Examples

#arg1Exp<-list(rangen=rexp,nbparam=1,param=list(1/3));
#arg2Exp<-list(disfun=pexp,nbparam=1,param=list(1/5));


#res<-calcErrorNonParam("data.rda",25,arg1Exp,arg2Exp,TRUE)

compute the De Vielder estimator

Description

compute the De Vielder estimator, in other words, do the same function as DV but returns more details about this estimator whereas DV only compute the lambda and mu of the De Vielder method

Usage

estimDV(fileName, toplot = TRUE, header = TRUE, ks = FALSE)

Arguments

Value

a list of the following components

Author(s)

Christophe Dutang and Julie Barthes

Examples

#res<-estimDV("data.rda",TRUE,TRUE)

compute the parametric estimation

Description

estimParam compute the parametric estimation of the first model on the input file containing the stay duration Xi and the side effect reporting Zi. this estimator of R (and not mu) is the smallest root of the equation (*) : P(Zi=0)E[exp(-RXi)/Zi=0]=1

Usage

estimNonParam(fileName, toplot = TRUE, header = TRUE, ks = FALSE, DV = FALSE)

Arguments

Value

a list of the following components

Author(s)

Christophe Dutang and Julie Barthes

Examples

#res<-estimDV("data.rda",TRUE,TRUE)

compute the parametric estimation

Description

estimParam compute the parametric estimation of the first model on the input file containing the stay duration Xi and the side effect reporting Zi. this estimator of mu is the estimator of maximum likelihood of the random variable Zi / Xi=x. the risk constant R is given by the equation (star) R=mu.

Usage

estimParam(fileName, toplot = TRUE, header = TRUE, ks = FALSE, DV = FALSE)

Arguments

Value

a list of the following components

Author(s)

Christophe Dutang and Julie Barthes

Examples

#res<-estimDV("data.rda",TRUE,TRUE)

plot the histogram of the variable T

Description

plot of the random variable T and the equivalent function (t->CR*exp(-R*t)). in some cases, there are also plotted the theoretical and the De Vielder functions

Usage

histo(X, disXi = NULL, disP = NULL, plotDV = FALSE)

Arguments

Value

a NULL object.

Author(s)

Christophe Dutang and Julie Barthes

Examples

#use mainSimul to make the first argument
arg1Exp <- list(rangen=rexp,nbparam=1,param=list(1/3));
arg1Bin <- list(rangen=rbinom,nbparam=2,param=list(1,1/20));
arg1Unif <- list(rangen=runif,nbparam=2,param=list(0,20));
arg1Lnorm <- list(rangen=rlnorm,nbparam=2,param=list(1/4,1));

arg2Exp <- list(disfun=pexp,nbparam=1,param=list(1/5));
arg2Cst <- list(disfun=pcst <- function(x,p) p ,nbparam=1,param=list(1/3));
arg2Comp <- list(disfun=pcomp <- function(x,mu1,mu2,mu3)
{1-1/3*exp(-mu1* x)-1/2*exp(-mu2 *x)-1/6*exp(-mu3 *x)}
,nbparam=3,param=list(1/3,1/5,1/10));
arg2Gamma <- list(disfun=pgamma,nbparam=2,param=list(3,1/3));
arg2Lnorm <- list(disfun=plnorm,nbparam=2,param=list(1/20,2));

T <- mainSimul(100,100,arg1Exp,arg2Exp)

histo(T,arg1Exp,arg2Exp)

simulate many times the first model and calculate the risk constant

Description

main simulates nbBed times the first model with the function simul and calculates the risk constant R and CR by solving the renewal equation (star). this renewal equation is only valid if the Xi forms a poisson process. R and CR are defined such that the equivalent survival function is CR *exp(-R*x).

Usage

mainSimul(nbBed, nbPatient, disXi, disP, toplot = FALSE, calc = TRUE)

Arguments

Details

make simulation and estimation on the sample

Value

Describe the value returned If it is a LIST, use

Author(s)

Christophe Dutang and Julie Barthes

Examples

arg1Exp <- list(rangen=rexp,nbparam=1,param=list(1/3));
arg1Bin <- list(rangen=rbinom,nbparam=2,param=list(1,1/20));
arg1Unif <- list(rangen=runif,nbparam=2,param=list(0,20));
arg1Lnorm <- list(rangen=rlnorm,nbparam=2,param=list(1/4,1));

arg2Exp <- list(disfun=pexp,nbparam=1,param=list(1/5));
arg2Cst <- list(disfun=pcst <- function(x,p) p ,nbparam=1,param=list(1/3));
arg2Comp <- list(disfun=pcomp <- function(x,mu1,mu2,mu3)
{1-1/3*exp(-mu1* x)-1/2*exp(-mu2 *x)-1/6*exp(-mu3 *x)}
,nbparam=3,param=list(1/3,1/5,1/10));
arg2Gamma <- list(disfun=pgamma,nbparam=2,param=list(3,1/3));
arg2Lnorm <- list(disfun=plnorm,nbparam=2,param=list(1/20,2));

T <- mainSimul(100,100,arg1Exp,arg2Exp)

simulate many times the second model

Description

main simulates nbBed times the second model with the function simul

Usage

mainSimul2(nbBed, nbPatient, disXi, disYi, toplot = FALSE)

Arguments

Details

If necessary, more details than the description above

Value

return a list of the following components

Author(s)

Christophe Dutang and Julie Barthes

Examples

arg1ExpMod2 <- list(rangen=rexp,nbparam=1,param=list(1/2));
arg1BinMod2 <- list(rangen=rbinom,nbparam=2,param=list(1,1/20));
arg1UnifMod2 <- list(rangen=runif,nbparam=2,param=list(0,20));
arg1LnormMod2 <- list(rangen=rlnorm,nbparam=2,param=list(1/4,1));

arg2ExpMod2 <- list(rangen=rexp,nbparam=1,param=list(1/5));
# arg2-cst <- list(rangen=pcst <- function(x,p) p ,nbparam=1,param=list(1/10));
arg2GammaMod2 <- list(rangen=rgamma,nbparam=2,param=list(3,1/5));

T <- mainSimul2(100,100,arg1ExpMod2,arg2ExpMod2)

create a sample of the first model stored in a file

Description

make a sample of the first model, that is to say simulate the sequence of the random variables Xi (stay duration) and the sequence of Zi (side effect reporting)

Usage

makeSample(file, nbPatient, disXi, disP)

Arguments

Value

a NULL object.

Author(s)

Christophe Dutang and Julie Barthes

Examples

arg1Exp<-list(rangen=rexp,nbparam=1,param=list(1/3));

arg2Exp<-list(disfun=pexp,nbparam=1,param=list(1/5));

makeSample("mydata.rda",200,arg1Exp,arg2Exp)

create a sample of the second model stored in a file

Description

make a sample of the first model, that is to say simulate the sequence of the random variables Xi (stay duration) the sequence of Yi (exposure time) and the sequence of Zi (side effect reporting)

Usage

makeSample2(file, nbPatient, disXi, disYi)

Arguments

Value

a NULL object.

Author(s)

Christophe Dutang and Julie Barthes

Examples

arg1ExpMod2<-list(rangen=rexp,nbparam=1,param=list(1/2));
arg1BinMod2<-list(rangen=rbinom,nbparam=2,param=list(1,1/20));
arg1UnifMod2<-list(rangen=runif,nbparam=2,param=list(0,20));
arg1LnormMod2<-list(rangen=rlnorm,nbparam=2,param=list(1/4,1));

arg2ExpMod2<-list(rangen=rexp,nbparam=1,param=list(1/5));
# arg2-cst<-list(rangen=pcst<-function(x,p) p ,nbparam=1,param=list(1/10));
arg2GammaMod2<-list(rangen=rgamma,nbparam=2,param=list(3,1/5));


makeSample2("thedata.rda",200,arg1ExpMod2,arg2ExpMod2)

simulate the first model of the hospital risk

Description

simul simulate the first model of the hospital that is to say simulating the sequence of variables Xi (which follow the disxi distribution passed as an argument) and the sequence of Zi (where the probability of succes p is passed as an argument) simul returns T the vector of durations between two declared side effects

Usage

simul(nbPatient, disXi, disP, toplot = TRUE)

Arguments

Value

T the vector of durations between two declared side effects

Note

further notes

Author(s)

Christophe Dutang and Julie Barthes

See Also

simul2

Examples

arg1Exp <- list(rangen=rexp,nbparam=1,param=list(1/3));
arg1Bin <- list(rangen=rbinom,nbparam=2,param=list(1,1/20));
arg1Unif <- list(rangen=runif,nbparam=2,param=list(0,20));
arg1Lnorm <- list(rangen=rlnorm,nbparam=2,param=list(1/4,1));

arg2Exp <- list(disfun=pexp,nbparam=1,param=list(1/5));
arg2Cst <- list(disfun=pcst <- function(x,p) p ,nbparam=1,param=list(1/3));
arg2Comp <- list(disfun=pcomp <- function(x,mu1,mu2,mu3)
{1-1/3*exp(-mu1* x)-1/2*exp(-mu2 *x)-1/6*exp(-mu3 *x)}
,nbparam=3,param=list(1/3,1/5,1/10));
arg2Gamma <- list(disfun=pgamma,nbparam=2,param=list(3,1/3));
arg2Lnorm <- list(disfun=plnorm,nbparam=2,param=list(1/20,2));

T <- simul(100,arg1Exp,arg2Exp)
T <- simul(100,arg1Bin,arg2Cst)
T <- simul(100,arg1Unif,arg2Comp)
T <- simul(100,arg1Lnorm,arg2Gamma)

simulate the second model of the hospital risk

Description

simul simulate the first model of the hospital that is to say simulating the sequence of variables Xi (which follow the disxi distribution passed as an argument) and the sequence of Zi (where the probability of succes p is passed as an argument) simul returns T the vector of durations between two declared side effects

Usage

simul2(nbPatient, disXi, disYi, toplot = TRUE)

Arguments

Value

T the vector of durations between two declared side effects

Author(s)

Christophe Dutang and Julie Barthes

Examples

arg1Exp<-list(rangen=rexp,nbparam=1,param=list(1/2));
arg2Exp<-list(rangen=rexp,nbparam=1,param=list(1/20));
T<-simul2(100,arg1Exp,arg2Exp)