msce_numerical {msce}

Numerical solution of the Multi-Stage Clonal Expansion Model

Description

This function aims to solve the general multi-stage model with piecewise constant parameters approximatively by integrating the characteristic equations with Euler's method. For sufficiently small time intervalls, this approximation often yields reasonable results. Small time intervals can either be provided explicitly with many columns in argument t. An alternative is the optional parameter innerSteps.

Usage

msce_numerical(t, parameterList, innerSteps = 1000L)

Arguments

t

Each element in a row of t defines the endpoint of a time interval. The first time interval starts at time 0. The last element is the time point for which hazard and survival function are evaluated. Elements in a row have to be in monotonously increasing order. In order to achieve a different number of time intervals for different rows, rows may start with an arbitrary number of zeros (i.e. time intervals of length zero).

parameterList

List of Matrices. Each list member has to be named. Allowed names are Nnu0, alphaX, gammaX, and nuX where X can be any positive integer value. The number of stages is deduced from nuX with the highest X. Matrices Nnu0 and successive nuX must be provided. Missing other matrices are assumed to be zero. For each matrix it has to hold that the number of columns must be equal to the ones in t. The number of rows can either equal to the number of rows in t, or only one row is provided, which then is applied to all rows of t.

Values in matrices Nnu0, alphaX, gammaX, nuX correspond to parameters for each time interval, see the figure and explanations in the package vignette. Here, Nnu0 is the product of N and \nu_0 and \gamma_X is defined by \alpha_X-\beta_X.

innerSteps

Positive integer. To improve accuracy, each time interval is internally divided into innerSteps time intervals of equal length. Defaults to 1000. Note, however, that even in the limit of infinite innerSteps, there will always be a finite discrepancy to the exact result.

Details

Value

The output list contains all used arguments of the parameterList and vectors of the model results for hazard and logarithm of the survival function for each row of the input.

See Also

tsce

Examples

t <-matrix(data=c(10,20,65,10,20,70),nrow=2,byrow=TRUE)
Nnu0 <- matrix(c(0.3,0.7,1),nrow = 1)
nu1  <- matrix(1e-6,nrow=1,ncol=3)
alpha1<- matrix(1,nrow=1,ncol=3)
gamma1<- matrix(c(0.13,0.13,0.13, 0.15,0.15,0.15),nrow=2,byrow=TRUE)
pars = list(Nnu0=Nnu0, nu1=nu1,alpha1=alpha1,gamma1=gamma1) 

msce_numerical(t,pars)