LogisticIndepBeta

LogisticIndepBeta is the class for the two-parameters logistic regression dose-limiting events (DLE) model with prior expressed in form of pseudo data. This model describes the relationship between the binary DLE responses and the dose levels. More specifically, it represents the relationship of the probabilities of the occurrence of a DLE for corresponding dose levels in log scale. This model is specified as $$p(x) = exp(phi1 + phi2 * log(x)) / (1 + exp(phi1 + phi2 * log(x)))$$ where \(p(x)\) is the probability of the occurrence of a DLE at dose \(x\). The two parameters of this model are the intercept \(phi1\) and the slope \(phi2\). The LogisticIndepBeta inherits all slots from ModelTox class.

In the context of pseudo data, the following three arguments are used, binDLE, DLEdose and DLEweights. The DLEdose represents fixed dose levels at which the pseudo DLE responses binDLE are observed. DLEweights represents total number of subjects treated per each dose level in DLEdose. The binDLE represents the number of subjects observed with DLE per each dose level in DLEdose. Hence, all these three vectors must be of the same length and the order of the elements in any of the vectors binDLE, DLEdose and DLEweights must be kept, so that an element of a given vector corresponds to the elements of the remaining two vectors (see the example for more insight). Finally, since at least two DLE pseudo responses are needed to obtain prior modal estimates (same as the maximum likelihood estimates) for the model parameters, the binDLE, DLEdose and DLEweights must all be vectors of at least length 2.

Usage

LogisticIndepBeta(binDLE, DLEdose, DLEweights, data)

.DefaultLogisticIndepBeta()

Arguments

binDLE

(numeric)
the number of subjects observed with a DLE, the pseudo DLE responses, depending on dose levels DLEdose. Elements of binDLE must correspond to the elements of DLEdose and DLEweights.

DLEdose

(numeric)
dose levels for the pseudo DLE responses. Elements of DLEdose must correspond to the elements of binDLE and DLEweights.

DLEweights

(numeric)
the total number of subjects treated at each of the dose levels DLEdose, pseudo weights. Elements of DLEweights must correspond to the elements of binDLE and DLEdose.

data

(Data)
the input data to update estimates of the model parameters.

Details

The pseudo data can be interpreted as if we obtain some observations before the trial starts. It can be used to express our prior, i.e. the initial beliefs for the model parameters. The pseudo data is expressed in the following way. First, fix at least two dose levels, then ask for experts' opinion on how many subjects are to be treated at each of these dose levels and on the number of subjects observed with a DLE. 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 this pseudo data are independent and they follow 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 prior density function of the two parameters in the model is used. For details about the form of all these joint prior and posterior probability density functions, please refer to Whitehead and Willamson (1998).

Slots

binDLE

(numeric)
a vector of total numbers of DLE responses. It must be at least of length 2 and the order of its elements must correspond to values specified in DLEdose and DLEweights.

DLEdose

(numeric)
a vector of the dose levels corresponding to It must be at least of length 2 and the order of its elements must correspond to values specified in binDLE and DLEweights.

DLEweights

(integer)
total number of subjects treated at each of the pseudo dose level DLEdose. It must be at least of length 2 and the order of its elements must correspond to values specified in binDLE and DLEdose.

phi1

(number)
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

(number)
the 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

(matrix)
refers to the 2x2 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.

Note

Typically, end users will not use the .DefaultLogisticIndepBeta() function.

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))

# Fix two dose levels 25 and 300 mg (DLEdose).
# Total number of subjects treated in each of these levels is 3, (DLEweights).
# The number of subjects observed with a DLE is 1.05 at dose 25 mg and 1.8 at dose 300 mg (binDLE).
my_model1 <- LogisticIndepBeta(
  binDLE = c(1.05, 1.8),
  DLEdose = c(25, 300),
  DLEweights = c(3, 3),
  data = emptydata
)

# Use observed DLE responses to obtain posterior modal estimates.
my_data <- Data(
  x = c(25, 50, 50, 75, 100, 100, 225, 300),
  y = c(0, 0, 0, 0, 1, 1, 1, 1),
  doseGrid = emptydata@doseGrid
)
#> Used default patient IDs!
#> Used best guess cohort indices!

my_model2 <- LogisticIndepBeta(
  binDLE = c(1.05, 1.8),
  DLEdose = c(25, 300),
  DLEweights = c(3, 3),
  data = my_data
)