A package for computing the boundaries for sequential generalized likelihood ratio test for pre-licensure vaccine studies

Description

This package is an implementation of the methodology of Shih, Lai, Heyse, and Chen (to appear in Statistics in Medicine) for computing Generalized Likelihood Ratio test boundaries for pre-licensure vaccine studies

Details

The package provides several functions. The function glrSearch computes boundaries for testing a given p_0 versus p_1 (specified as a two-dimensional vector) given a significance level \alpha and a type II error \beta. The function computeBoundary computes the boundary in terms of a more understandable and usable quantity, such as the number of adverse events in a pre-licensure vaccine study for example. It takes as input a set of given boundaries for the GLR statistic. The third function is plotBoundary which also takes the same arguments as computeBoundary and produces a plot. The last two functions can make use of statistics computed previously for the problem, which can be specified as an argument; otherwise, the statistics are computed from scratch.

Author(s)

Balasubramanian Narasimhan with input from Tze Lai and Mei-Chiung Shih. Maintainer: Balasubramanian Narasimhan <naras@stat.stanford.edu>

References

“Sequential Generalized Likelihood Ratio Tests for Vaccine Safety Evaluation” doi: 10.1002/sim.4036.

Examples

library(sglr)
result <- glrSearch(p=c(.5, .75), alpha=0.05, beta=0.10)
## print(result)  ## large amounts of output possible!
result[1:3]

A function to compute the boundary of the decision region in terms of the number of adverse events (AEs) of interest, such as vaccine AEs.

Description

This function computes the boundary of the decision region in a manner that can be employed in the field, as a table, for example. See section 4.2 of the reference below.

Usage

computeBoundary(b1, b0, p, glrTables = NULL, tol=1e-7)

Arguments

Details

This essentially computes the probabilities of hitting the boundaries using a recursion.

Value

Author(s)

Balasubramanian Narasimhan

References

“Sequential Generalized Likelihood Ratio Tests for Vaccine Safety Evaluation” doi: 10.1002/sim.4036.

See Also

See Also glrSearch

Examples

computeBoundary(b1=2.8, b0=3.3, p=c(.5, .75))

This function searches through a space of design boundaries (scalar values a and b) to find values that achieve close to specified type I and type II errors for the sequential generalized likelihood ratio test of p0 versus p1 (specified respectively as vector of length 2) in pre-licensure vaccine trials

Description

The search through the space of b_1 (corresponds to b_1 in paper) and b_0 (corresponds to b_0 in paper) is greedy initially. Then refinements to the boundary are made by adjusting the boundaries by the step-size. It is entirely possible that the step-size is so small that a maximum number of iterations can be reached. Depending on how close p_0 and p_1 are the memory usage can grow significantly. The process is computationally intensive being dominated by a recursion deep in the search.

Usage

glrSearch(p, alpha, beta, stepSize = 0.5, tol = 1e-7,
          startB1 = log(1/beta), startB0 = log(1/alpha),
          maxIter = 25, gridIt = FALSE, nGrid = 5, verbose = FALSE)

Arguments

Details

One should not use this code without a basic understanding of the Shih, Lai, Heyse and Chen paper cited below, particularly the section on the pre-licensure vaccine trials.

As the search can be computationally intensive, the program needs to use some variables internally by reference, particularly large tables that stay constant.

In our experiments, starting off with the default step size has usually worked, but in other cases the step size and the maximum number of iterations may need to be adjusted.

Value

Author(s)

Balasubramanian Narasimhan

References

“Sequential Generalized Likelihood Ratio Tests for Vaccine Safety Evaluation” doi: 10.1002/sim.4036.

Examples

library(sglr)
result <- glrSearch(p=c(.5, .75), alpha=0.05, beta=0.10)

result <- glrSearch(p=c(.5, .75), alpha=0.05, beta=0.10, verbose=TRUE)

result <- glrSearch(p=c(.5, .75), alpha=0.05, beta=0.10, gridIt=TRUE)
print(result$alphaTable)
print(result$betaTable)

## takes a while
result <- glrSearch(p=c(.5, 2/3), alpha=0.05, beta=0.10)
print(names(result))

##result <- glrSearch(p=c(.5, 2/3), alpha=0.05, beta=0.10, gridIt=TRUE)
##print(result$alphaTable)
##print(result$betaTable)

A function to plot the boundary of the decision region

Description

This function attempts to plot the boundary of the decision region, but currently falls flat. Will be rewritten.

Usage

plotBoundary(b1, b0, p, glrTables = NULL, tol = 1e-7,
             legend  =FALSE, textXOffset = 2, textYSkip = 2)

Arguments

Details

This essentially computes the recursion and the probabilities of hitting the boundaries and returns a ggplot2 object

Value

A ggplot2 object

Author(s)

Balasubramanian Narasimhan

See Also

See Also glrSearch

Examples

plotBoundary(b1=2.8, b0=3.3, p=c(.5, .75))