# LogisticIndepBeta-class: No initialization function Standard logistic model with prior... In crmPack: Object-Oriented Implementation of CRM Designs

 LogisticIndepBeta-class R Documentation

## No initialization function Standard logistic model with prior in form of pseudo data

### Description

This is a class for the two-parameter logistic regression DLE model with prior expressed in form of pseudo data. This model describe the relationhship of the binary DLE (dose-limiting events) responses and the dose levels. More specifically, this DLE model reprsents the relationship of the probabilities of the occurrence of a DLE with their corresponding dose levels in log scale. This model is specified as

p(d_{(j)})= \frac{exp(φ_1+φ_2 log(d_{(j)}))}{1+exp(φ_1+φ_2 log(d_{(j)}))}

for any dose j where p(d_{(j)}) is the probability of the occurrence of a DLE at dose j. The two parameters of this model is the intercept φ_1 and the slope φ_2 It inherits all slots from ModelTox class.

### Details

The pseudo data can be interpreted as as if we obtain some observations before the trial starts. These pseudo data can be used to express our prior, the initial beliefs for the model parameter(s). The pseudo data are expressed in the following way. First, fix at least two dose levels which are Then ask for experts' opinion how many subjects are to be treated at each of these dose levels and the number of subjects observed with DLE are observed. At each dose level, the number of subjects observed with a DLE divided by the total number of subjects treated is the probability of the occurrence of a DLE at that particular dose level. The probabilities of the occurrence of a DLE based on these pseudo data are independent Beta distributions. Therefore, the joint prior probability density function of all these probabilities can be obtained. Hence, by a change of variable, the joint prior probability density function of the two parameters in this model can also be obtained. In addition, a conjugate joint perior density function of the two paramaters in the model is used. For details about the form of all these joint prior and posterior probability density function, please refers to Whitehead and Willamson (1998).

When expressing the pseudo data, binDLE,DLEdose and DLEweights are used. The binDLE represents the number of subjects observed with DLE. Note that, since the imaginary nature of the pseudo data, the number of subjects observed wtih DLE is not necesssary to be integer(s) but any scalar value. The DLEdose represents the dose levels at which the pseudo DLE responses (binDLE) are observed. The DLEweights represents the total number of subjects treated. Since at least two DLE pseudo responses are needed to obtain prior modal estimates (same as the maximum likelihood estimates) for the model parameters. binDLE, DLEdose and DLEweights must all be vectors of at least length 2. Since given one pseudo DLE responses, the number of subjects observed with a DLE relates to at which dose level they are treated and the total number of of subjects treated at this dose level. Therefore, each of the elements in any of the vectors of binDLE, DLEdose and DLEweights must have a corresponding elements in the other two vectors. A set of three values with one of each in the vectors of binDLE, DLEdose and DLEweights. In this model, each of these three values must be specified in the same position as in each of the vector of binDLE, DLEdose and DLEweights. The order of the values or elements in one of the vector binDLE, DLEdose and DLEweights must corresponds to the values or elements specified in the other two vectors.

### Slots

binDLE

represents the vector of pseudo DLE responses. This must be at least f length 2 and the order of its elements must corresponds to values specified in DLEdose and DLEweights. (see details from above)

DLEdose

represents the vector of the corresponding dose levels observed at each of the pseudo DLE responses (binDLE). This mus be at least of length 2 and the order of its elements must corresponds to values specified in binDLE and DLEweights. (see details from above)

DLEweights

refers to the total number of subjects treated at each of the pseudo dose level (DLEdose). This must be of length of at least 2 and the oreder of its elements must corresponds to values specified in binDLE and DLEdose. (see details from above)

phi1

refers the intercept of the model. This slot is used in output to display the resulting prior or posterior modal estimate of the intercept obtained based on the pseudo data and (if any) observed data/responses.

phi2

refers to slope of the model. This slot is used in output to display the resulting prior or posterior modal estimate of the slope obtained based on the pseudo data and (if any) the observed data/responses.

Pcov

refers to the covariance matrix of the intercept (phi1) and the slope parameters (phi2) of the model. This is used in output to display the resulting prior and posterior covariance matrix of phi1 and phi2 obtained, based on the pseudo data and (if any) the observed data and responses. This slot is needed for internal purposes.

### Examples

##Obtain prior modal estimates given the pseudo data.
##First we used an empty data set such that only the dose levels under investigations are given.
##In total, 12 dose levels are under investigation ranging from 25 to 300 mg with increments of 25
##(i.e 25, 50, 75, ..., 300).
emptydata<- Data(doseGrid=seq(25,300,25))

##specified our data set is the empty data
data<-emptydata
## Given the pseudo data such that
## Fix two dose level 25 and 300 mg and specified in (DLEdose slot).
## Total number of subjects treated in each of these levels is 3, specified in (DLEweights slot).
## The number of subjects observed with a DLE is 1.05 at dose 25 mg and 1.8 at dose 300 mg,
## and specified in (binDLE slot).
## the data set we used in the emptydata set, and specified in (data slot).
## Then to modal estimates of the model parameters.
model<-LogisticIndepBeta(binDLE=c(1.05,1.8),DLEweights=c(3,3),DLEdose=c(25,300),data=data)

##using a data set (see data -class example specification) with observed DLE responses
##to obtain posterior modal estimates.
##for the model given the pseudo data

data<-Data(x=c(25,50,50,75,100,100,225,300),y=c(0,0,0,0,1,1,1,1),
doseGrid=seq(25,300,25))

model<-LogisticIndepBeta(binDLE=c(1.05,1.8),DLEweights=c(3,3),DLEdose=c(25,300),data=data)



crmPack documentation built on Sept. 3, 2022, 1:05 a.m.