Lp: Likelihood functions

In UBCRM: Functions to Simulate and Conduct Dose-Escalation Phase I Studies

Likelihood functions

Description

Lp is the likelihood function for the power model psy(s,a)=s^exp(a). Lt is the likelihood function for the hyperbolic tangent model psy(s,a)= ((tanh(s)+1)/2)**a. Ll is the likelihood function for the logistic model psy(s,a) = exp(3+a*s)/(1+exp(3+a*s)).

Usage

Lp(a, data, sgl)
Lt(a, data, sgl)
Ll(a, data, sgl)

Arguments

a	Parameter.
data	CRM dataframe with a CreData() structure.
sgl	Dose level singleton.

Details

# Power model Lp<- function(a, data, sgl) npt<- data$npt ndlt<- data$ndlt sapply(a,FUN=function(a)prod((psip(sgl,a)^ndlt)*((1-psip(sgl,a))^(npt-ndlt))))

# Hyperbolic tangent model Lt<- function(a, data, sgl) npt<- data$npt ndlt<- data$ndlt sapply(a,FUN=function(a)prod((psit(sgl,a)^ndlt)*((1-psit(sgl,a))^(npt-ndlt))))

# Logistic model Ll<- function(a, data, sgl) npt<- data$npt ndlt<- data$ndlt sapply(a,FUN=function(a)prod((psil(sgl,a)^ndlt)*((1-psil(sgl,a))^(npt-ndlt))))

Value

Numeric value of the computed likelihood.

Author(s)

Benjamin Esterni, Baboukar Mane. Unite de Biostatistique et de Methodologie, Institut Paoli-Calmettes, Marseille, France.

References

O'Quigley J., Pepe M., Fisher L. (1990). Continual Reassessment Method: a practical design for Phase I clinical trials in cancer. Biometrics 46, 33-48.

O'Quigley J., Shen LZ. (1996). Continual Reassessment Method: a likelihood approach. Biometrics 52, 673-684.

Paoletti X., Kramar A. (2009). A comparison of model choices for the Continual Reassessment Method in phase I cancer trials. Statistics in Medecine 28, 3012-3028.

Chamorey Emmanuel. (2009). Methodologie des essais de phase precoce en cancerologie: evolution des schemas et apport de la pharmacologie. These.

Garret-Mayer Elizabeth. (2006). The Continual Reassessment Method for dose-finding studies: a tutorial. Clinical Trials: 57-71.

UBCRM documentation built on May 17, 2022, 1:07 a.m.