od.1.111: Optimal sample allocation calculation for single-level randomized controlled trials (RCTs) investigating mediation effects (1-1-1)

Description

The optimal design of single-level RCTs probing mediation effects is to identify the optimal sample allocation that use the minimum budget to achieve a fixed level of statistical power. The optimal design parameter is the proportion of individuals/units to be assigned to the experimental condition. This function identifies the optimal p.

Usage

od.1.111(
  a = NULL,
  b = NULL,
  c1 = NULL,
  c1t = NULL,
  m = NULL,
  r.yx = 0,
  r.mx = 0,
  r.mw = 0,
  q.a = 0,
  q.b = 0,
  test = "joint",
  p = NULL,
  n = NULL,
  tol = 1e-11,
  power = 0.8,
  d.p = c(0.1, 0.5),
  sig.level = 0.05,
  two.tailed = TRUE,
  plim = c(0.01, 0.99),
  varlim = c(0, 0.001),
  plab = NULL,
  varlab = NULL,
  vartitle = NULL,
  nlim = c(6, 1e+06),
  verbose = TRUE,
  max.value = Inf,
  max.iter = 300,
  e = 1e-10,
  n.of.ants = 10,
  n.of.archive = 20,
  q = 1e-04,
  xi = 0.5
)

Value

Unconstrained or constrained optimal sample allocation p). The function also returns statistical power, function name, design type, and parameters used in the calculation.

Arguments

a: The treatment effect on the mediator.
b: The within-treatment correlation between the outcome and the mediator.
c1: The cost of sampling an individual in the control group.
c1t: The cost of sampling an individual in the treated group.
m: Total budget.
r.yx: The within-treatment correlation between the outcome and the covariate(s) in the outcome model.
r.mx: The within-treatment correlation between the mediator and the covariate(s) in the outcome model.
r.mw: The within-treatment correlation between the mediator and the covariate(s) in the mediator model.
q.a: The number of covariates at the mediator model (except the treatment indicator), the default value is zero.
q.b: The number of covariates in the outcome model (except the treatment indicator and the mediator), the default value is zero.
test: The type of test will be used to detect mediation effects. The default is the joint significance test (i.e., test = "joint", "Joint","JOINT"). Another choice is the Sobel test by specifying the argument as test = "sobel", "Sobel", or "SOBEL".
p: The proportion of level-4 clusters/units to be assigned to treatment.
n: Total number of individuals in the experimental study, the default value is NULL.
tol: convergence tolerance.
power: Statistical power specified, default is .80.
d.p: The initial sampling domains for p. Default is c(0.10, 0.50).
sig.level: Significance level or type I error rate, default value is 0.05.
two.tailed: Two tailed test, the default value is TRUE.
plim: The plot range for p, default value is c(0, 1).
varlim: The plot range for variance, default value is c(0, 0.05).
plab: The plot label for p , default value is "Proportion of Individuals in Treatment: p".
varlab: The plot label for variance, default value is "Variance".
vartitle: The title of variance plot, default value is NULL.
nlim: The interval/range used to numerically solve for n, the default values are c(6, 1e7).
verbose: Print out evaluation process if TRUE, default is TRUE.
max.value: Maximal value of optimization when used as the stopping criterion. Default is infinite.
max.iter: Maximal number of function evaluations when used as the stopping criterion. Default is 200.
e: Maximum error value used when solution quality used as the stopping criterion, default is 1e-10.
n.of.ants: Number of ants used in each iteration after the initialization stage, the default value is 10.
n.of.archive: Size of the solution archive, default is 20.
q: Locality of the search (0,1), default is 0.0001.
xi: Convergence pressure (0, Inf), suggested: (0, 1), default is 0.5.

Examples

Run this code

myod <- od.1.111(a = .3, b = .5, c1 = 10, c1t = 100)
myod

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