Package 'OWEA'

Design Generator for Three Models

Description

Construct optimal approximate designs as well as efficient exact designs for crossover model with subject dropout, crossover model with proportional residual effect, and interference model.

Usage

design(
  model = c("dropout", "proportional", "interference"),
  n,
  opt,
  t,
  p,
  ...,
  max_iter = 40
)

Arguments

model	an model indicator, must be one of 'dropout', 'proportional', or 'interference'.
n	Positive Integer, total number of observations needed.
opt	Integer. optimal criterion indicator, opt = 0 means D-opt, opt = 1 means A-opt
t	Positive interger,number or levels of treatment, the default coding is integer from 1 to t
p	Numeric, number of periods for crossover model or number of blocks for intereference model
...	other necessary control parameters required by specific model For crossover with dropout, drop, a numeric vector of dropout mechanism For crossover proportional, lambda,value of proportion cofficient in proportional model and sigma, assumed covariance matrix. For interference model, sigma, assumed covariance matrix.
max_iter	a positive integer. Controls maximum iteration time of exchange. Default is 40.

Value

A S3 object of one of classes 'dropout', 'proportional' or 'interference'.

model	the model name
n	total number of observations of exact design
opt	optimal criterion
t	number of levels of treaments
p	number of periods or plots in a block
...	other inputs
initial_design	a randomly chosen design as a starting point for newton's method
exact_design	an exact design rounded from approximate design
approx_design	optimal approximate design
verify_equivalence	result of general equivalence theorem, the last entry is the value of directional derivative
time	computing time for approximate design

See Also

eff, effLB, summary

Examples

# NOTE: max_iter is usually set to 40. 
# Here max_iter = 5 is for demenstration only.
# crossover dropout model
## D-optimal

example1 <- design('dropout',10,0,3,3,drop=c(0,0,0.5), max_iter = 5)
summary(example1)
eff(example1) # efficiency from rounding
effLB(example1) # obtain lower bound of efficiency

## A-optimal
design('dropout',10,1,3,3,drop=c(0,0,0.5), max_iter = 5)


# proportional model
## D-optimal
design('proportional',10,0,3,3, sigma = diag(1,3),tau = matrix(sqrt(1+3),
    nrow=3, ncol=1),lambda = 0.2, max_iter = 5)

## A-optimal
design('proportional',10,1,3,3, sigma = diag(1,3), tau = matrix(sqrt(1+3),
    nrow=3, ncol=1),lambda = 0.2, max_iter = 5)


# interference model
## D-optimal
design('interference',10,0,3,3, sigma = diag(1,3), max_iter = 5)

## A-optimal
design('interference',10,1,3,3, sigma = diag(1,3), max_iter = 5)

---

Shiny App for design function

Description

A function to launch graphical interface to design function.

Usage

design_app()

Examples

## Not run: 
design_app() # lauching the app.
## End(Not run)

---

Efficiency generic function

Description

A generic function that returns the effciency for either exact designs to approximate designs or exact design to a given design

Usage

eff(exact_design, ex = NULL)

## Default S3 method:
eff(exact_design, ex = NULL)

## S3 method for class 'dropout'
eff(exact_design, ex = NULL)

## S3 method for class 'proportional'
eff(exact_design, ex = NULL)

## S3 method for class 'interference'
eff(exact_design, ex = NULL)

Arguments

exact_design	A S3 object returned by design function.
ex	Matrix. Design to be compared to. Default is NULL.

Value

Numeric. Relatve Efficiency.

If ex is given	return relative effciency by $\Phi_{example}/\Phi_{exact\_design};$
If ex is missing	return relative efficiency by $\Phi_{approx\_design}/\Phi_{exact\_design}.$

See Also

see examples in design.

---

Lower Bound Efficiency for Crossover-Dropout Model

Description

The function take S3 object of class 'dropout' as input and return its lower bound of efficiency of exact design.

Usage

effLB(exact_design)

Arguments

exact_design

A object of class returned by design function.

Value

A list of relavent numerics.

optimal	Optimal Criterion
lower.bound	Lower Bound of the exact design
optimal.value	The value of objective function at optimal approxiamte design

See Also

see examples in design.

---

Generic function for information matrix.

Description

Returns a information matrix for a given design

Usage

infor_design(design, t, ...)

## Default S3 method:
infor_design(design, t)

## S3 method for class 'dropout'
infor_design(design, t, ...)

## S3 method for class 'interference'
infor_design(design, t, ...)

## S3 method for class 'proportional'
infor_design(design, t, ...)

Arguments

design	Matrix. A design, each row is a design point with weight or repetition on the last entry.
t	Numeric. Number of levels of treatments.
...	Other control parameter to be passed to methods

Value

An information matrix.

---

OWEA: A package for optimal designs by implementing optimal weight exchange algorithm.

Description

The OWEA package provides relizations for three models: crossover with subject dropout, crossover with proportional first order residual, and interference model

Key functions

design, design_app, eff, effLB, summary

---

Summary method for S3 object

Description

Return summary info for S3 object return by design function.

Usage

## S3 method for class 'dropout'
summary(object, ...)

## S3 method for class 'proportional'
summary(object, ...)

## S3 method for class 'interference'
summary(object, ...)

Arguments

object	A S3 object of class 'dropout', 'proportional', or 'interference'.
...	other control parameters, but usually not necessary.

Value

A list of key info.

exact_design	exact design and its repetitions
approximate_design	approximate design and its weights
computing_time	computing time for approximate design

See Also

see examples in design.

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