computeBoundary: A function to compute the boundary of the decision region in...

Description Usage Arguments Details Value Author(s) References See Also Examples

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

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

Arguments

b1

The acceptance boundary value (corresponds to the boundary b_1 in the appendix of reference)

b0

The rejection boundary value (corresponds to the boundary b_0 in the appendix of reference)

p

The vector of probabilities, (p_0, p_1) with p_0 < p_1.

glrTables

A previously computed set of likelihood functions, to speed up computation for the same hypothesis testing problem. Otherwise, it is computed ab initio, resulting in a longer running time.

tol

A numerical tolerance, defaults to 1e-7

Details

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

Value

upper

The upper boundary that indicates rejection of the null hypothesis

lower

The upper boundary that indicates acceptance of the null hypothesis

estimate

The estimated α and β values corresponding to the two boundaries

Author(s)

Balasubramanian Narasimhan

References

Mei-Chiung Shih, Tze Leung Lai, Joseph F. Heyse, and Jie Chen. Sequential Generalized Likelihood Ratio Tests for Vaccine Safety Evaluation (Statistics in Medicine, Volume 29, issue 26, p.2698-2708, 2010.)

Please also consult the website http://med.stanford.edu/biostatistics/ClinicalTrialMethodology/ for further developments.

See Also

See Also glrSearch

Examples

1
computeBoundary(b1=2.8, b0=3.3, p=c(.5, .75))

Example output

Loading required package: ggplot2
Loading required package: shiny
$upper
 [1] NA NA NA NA  5  6  7  8  9  9 10 11 11 12 13 13 14 15 15 16 17 17 18 19 19
[26] 20 21 21 22 22 23 24 24 25 25 26 27 27 28 29 29 30 30 31 32 32 33 33 34 34
[51] 35 36 36 37 37 38 39 39 40 40 41 42 42 43 43 44 44 45 46 46 47 47 48 48 49
[76] 50 50 51 51 52 52 53 54 54 55 55 56 56 57 58 58

$lower
 [1] NA NA  0  0  1  1  2  2  3  3  4  5  5  6  6  7  8  8  9 10 10 11 11 12 13
[26] 13 14 15 15 16 17 17 18 19 19 20 21 21 22 23 23 24 25 25 26 27 27 28 29 29
[51] 30 31 31 32 33 33 34 35 35 36 37 38 38 39 40 40 41 42 42 43 44 44 45 46 46
[76] 47 48 49 49 50 51 51 52 53 53 54 55 55 56 57 58

$estimate
     alpha       beta 
0.06045524 0.06606180 

sglr documentation built on May 1, 2019, 7:14 p.m.