# refine_decision_rectangles: Adaptive Enrichment Design Optimization Using Sparse Linear... In mrosenblum/AdaptiveDesignOptimizerSparseLP: Two-Stage, Two Population, Adaptive Enrichment Design Optimizer Using Sparse Linear Programming

## Description

Adaptive Enrichment Design Optimization Using Sparse Linear Programming

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```refine_decision_rectangles( subpopulation.1.proportion = 0.5, stage.1.sample.sizes = c(50, 50), stage.2.sample.sizes.per.enrollment.choice = matrix(c(50, 50, 0, 0, 150, 0, 0, 150), nrow = 4, ncol = 2, byrow = TRUE, dimnames = list(c(), c("Subpopulation1Stage2SampleSize", "Subpopulation2Stage2SampleSize"))), discretization.parameter = c(1, 1, 10), list.of.rectangles.dec = c(), LP.iteration = 1, round.each.decision.rectangle.to.integer = FALSE, set.rectangles.with.identically.valued.neighbors.and.split.others = TRUE, sln ) ```

## Arguments

 `subpopulation.1.proportion` Proportion of overall population in subpopulation 1. Must be between 0 and 1. `stage.1.sample.sizes` Vector with 2 entries representing stage 1 sample sizes for subpopulations 1 and 2, respectively `stage.2.sample.sizes.per.enrollment.choice` Matrix with number.choices.end.of.stage.1 rows and 2 columns, where the (i,j) entry represents the stage 2 sample size under enrollment choice i for subpopulation j. `discretization.parameter` vector with 3 elements representing initial discretization of decision region, rejection regions, and grid representing Type I error constraints `list.of.rectangles.dec` list of rectangles representing decision region partition, encoded as a list with each element of the list having fields \$lower_boundaries (pair of real numbers representing coordinates of lower left corner of rectangle), \$upper_boundaries (pair of real numbers representing upper right corner of rectangle), \$allowed_decisions (subset of stage.2.sample.sizes.per.enrollment.choice representing which decisions allowed if first stage z-statistics are in corresponding rectangle; default is entire list stage.2.sample.sizes.per.enrollment.choice), \$preset_decision (indicator of whether the decision probabilities are hard-coded by the user; default is 0), \$d_probs (empty unless \$preset_decision==1, in which case it is a vector representing the probabilities of each decision); if list.or.rectangles.dec is empty, then a default partition is used based on discretization.parameter. `LP.iteration` positive integer used in file name to store output; can be used to avoid overwriting previous computations `round.each.decision.rectangle.to.integer` TRUE/FALSE indicator of whether decision probabilities encoded in list.of.rectangles.dec should be rounded to integer values `set.rectangles.with.identically.valued.neighbors.and.split.others` TRUE/FALSE indicator of whether decision probabilities encoded in list.of.rectangles.dec should be modified for use in next iteration `sln` solution to linear program computed previously

## Value

4 element list containing optimized designs from four classes (with increasing complexity):

A refined partition of the decision rectangles is constructed and returned.

## Author(s)

Michael Rosenblum, Ethan Fang, Han Liu

mrosenblum/AdaptiveDesignOptimizerSparseLP documentation built on Feb. 13, 2020, 12:59 p.m.