EffFlexi-class: Class for the efficacy model in flexible form for prior...
In 0liver0815/onc-crmpack-test: Object-Oriented Implementation of CRM Designs

Description Details Slots Examples

This is a class where a flexible form is used to describe the relationship between the efficacy responses and the dose levels. This flexible form aims to capture different shape for the dose-efficacy curve and the mean efficacy responses at each dose level are estimated using MCMC. In addition, the first (RW1) or second order (RW2) random walk model can be used for smoothing data. That is the random walk model is used to model the first or the second order difference of the mean efficacy responses to its neighboring dose levels of their mean efficacy responses. The flexible form is specified as

\mathbf{W}\vert\boldsymbol{β_w}, σ^2 \sim Normal (\mathbf{X}_w \boldsymbol{β_w}, σ^2 \mathbf{I})

where \mathbf{W} represent the column vector of the efficacy responses, \boldsymbol{β_w} is th column vector of the mean efficacy responses for all dose levels, \mathbf{X_w} is the design matrix with entries I_{i(j)} which gives a value 1 if subject i is allocated to dose j. The σ^2 (sigma2) is the variance of the efficacy responses which can be either fixed or from an inverse gamma distribution.

The RW1 model is given as

β_{W,(j)} - β_{W,(j-1)} \sim Normal(0, σ^{2}_{β_{W}})

where β_{W,(j)} is the mean efficacy responses at dose j For the RW2 is given as

β_{W,(j-2)} - 2 β_{W,(j-1)} + β_{W,(j)} \sim Normal(0, σ^{2}_{β_{W}})

The variance parameter σ^{2}_{β_{W}}. The variance σ^{2}_{β_{W}} (sigma2betaW) will be the same at all dose levels and can either be fixed or assigned an inverse gamma prior distribution.

The Eff and Effdose are the pseudo efficacy responses and dose levels at which these pseudo efficacy responses are observed at. (see more details for Effloglog class) Eff and Effdose must be vector of at least length 2. The values or elements in vectors Eff or Effdose must put in the same position with its corresponding value in the other vector. The sigma2 is the prior variance of the flexible efficacy form. The variance is either specified with a single scalar value (fixed) or positive scalar value have to be specified for the a shape and b slope parameter for th inverse gamma distribution. Similarly, sigma2betaW is the prior variance of the random walk model which can be specified with a single scalar (fixed) value or specifying positive scalar values for the shape a and rate b parameters for the inverse gamma distributions. This model will output the updated value or the updated values of the parameters of the inverse gamma distributions for sigma^2 (sigma2) and σ^2_{β_W} (sigma2betaW)

Eff: the pseudo efficacy responses. A vector of at least length 2 with the elements here and its corresponding value in Effdose must be specified in the same position. (see details above)
Effdose: the dose levels at which the pseudo efficacy responses are observed. This is a vector of at least length 2 and the elements here and its corresponding value in Eff must be specified in the same position. (see details from above)
sigma2: the prior variance of the flexible efficacy form. It can be specified with a single positive scalar or specifying a, the shape and b, the rate parameter of the inverse gamma distribution. (see details from above)
sigma2betaW: the prior variance of the random walk model for the mean efficacy responses. A single positive scalar can be specified or specifying a, the shape and b, the rate parameter of the inverse gamma distribution (see details from above)
useFixed: a list of with logical value to each of the parameters sigma2 and sigma2betaw indicating whether a fixed value is used or not; this slot is needed for internal purposes and not to be touched by the user.
useRW1: for specifying the random walk model for the mean efficacy responses; if TRUE, first order random walk model is used, otherwise the second-order random walk model.
designW: is the design matrix for the efficacy responses. If only the pseudo efficacy responses are used, this will be the design matrix of the pseudo efficacy responses. If there are some observed efficacy responses available. It will be the design matrix based on both the pseudo and the observed efficacy responses.
RWmat: is the the difference matrix for the random walk model. This slot is needed for internal purposes and not to be touched by the user.
RWmatRank: is the rank of the difference matrix. This slot is needed for internal purposes and not to be touched by the user.

##Obtain prior estimates for the EffFlexi (efficacy model) given the pseudo data.
##First define an empty data set by only define the dose levels used in the study
## 12 dose levels are usesd from 25 to 300 mg with increments of 25.
emptydata<-DataDual(doseGrid=seq(25,300,25))
data<-emptydata
## define the pseudo data as first fixed 2 dose levels 25 and 300 mg and
## specified in (Effdose slot).
## Then the efficacy responses observed at these two dose levels are 1.223 and 2.513 and
## specified in (Eff slot).
## The prior variance of the pseudo efficacy responses. This can be either a fixed value of
## specifying the shape (a) and the rate (b) parameters for the inverse gamma distribution
## in (sigma2 slot). The prior variance of the random walk model which can be a fixed value or
## two value for the shape (a) and rate (b) parameter of the inverse gamma distribution in
## (sigma2betaW slot). The data are specified in (data slot)


Effmodel<- EffFlexi(Eff=c(1.223, 2.513),Effdose=c(25,300),
                    sigma2=c(a=0.1,b=0.1),sigma2betaW=c(a=20,b=50),
                    smooth="RW2",data=data)

##Obtain estimates from the model given some observed responses
## first specified the data
data<-DataDual(x=c(25,50,50,75,100,100,225,300),y=c(0,0,0,0,1,1,1,1),
               w=c(0.31,0.42,0.59,0.45,0.6,0.7,0.6,0.52),
               doseGrid=seq(25,300,25))

Effmodel<- EffFlexi(Eff=c(1.223, 2.513),Effdose=c(25,300),
                    sigma2=c(a=0.1,b=0.1),sigma2betaW=c(a=20,b=50),
                    smooth="RW2",data=data)