od.2m.111 {odr}

Optimal sample allocation calculation for two-level multisite-randomized trials investigating mediation effects with individual-level mediators (1-1-1)

Description

The optimal design of two-level multisite-randomized trials (MRTs) probing mediation effects with individual-level mediators, for the Sobel test, is to calculate the optimal sample allocation that minimizes the variance of a mediation effect under a fixed budget. For the joint significance test, it is to identify the optimal sample allocation that requires the minimum budget to achieve certain power level. The optimal design parameters include the level-1 sample size per level-2 unit (n) and the proportion of level-1 individuals/units to be assigned to treatment (p). This function solves the optimal n and/or p with and without a constraint.

Usage

od.2m.111(
  a = NULL,
  b = NULL,
  icc.m = NULL,
  icc = NULL,
  c1 = NULL,
  c1t = NULL,
  c2 = NULL,
  m = NULL,
  r12m = 0,
  r22m = 0,
  r12 = 0,
  omega = 0.01,
  q.a = 0,
  q.b = 3,
  test = "joint",
  n = NULL,
  p = NULL,
  iter = 100,
  tol = 1e-11,
  power = 0.8,
  d.p = c(0.1, 0.5),
  d.n = c(5, 50),
  sig.level = 0.05,
  two.tailed = TRUE,
  plots = TRUE,
  nlim = c(4, 100),
  plim = c(0.01, 0.99),
  varlim = c(0, 0.001),
  nlab = NULL,
  plab = NULL,
  varlab = NULL,
  vartitle = NULL,
  Jlim = c(3, 1e+05),
  verbose = TRUE,
  max.value = Inf,
  max.iter = 300,
  e = 1e-10,
  n.of.ants = 10,
  n.of.archive = 50,
  q = 1e-04,
  xi = 0.5,
  plot.by = list(n = "n", p = "p")
)

Arguments

a

The treatment effect on the mediator.

b

The within treatment correlation between the outcome and the mediator.

icc.m

The intraclass correlation coefficient for the mediator.

icc

The unconditional intraclass correlation coefficient (ICC) in population or in each treatment condition.

c1

The cost of sampling one level-1 unit in control condition.

c1t

The cost of sampling one level-1 unit in treatment condition.

c2

The cost of sampling one level-2 unit.

m

Total budget.

r12m

The proportion of within treatment mediator variance at the level one explained by covariates.

r22m

The proportion of treatment-by-site variance explained by covariates.

r12

The proportion of within treatment individual-level outcome variance explained by covariates.

omega

The treatment-by-site variance of the outcome.

q.a

The number of covariates at the individual level of the mediator model (except the treatment indicator).

q.b

The number of covariates in the outcome model (except the treatment indicator and the mediator).

test

The type of test will be used to detect mediation effects. Default is the joint significance test (i.e., test = "joint"). Another choice is the Sobel test by specifying the argument as test = "sobel".

n

The level-1 sample size per level-2 unit.

p

The proportion of level-1 units to be assigned to treatment.

iter

number of iteration used for solving roots in the Sobel test.

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).

d.n

The initial sampling domain for n. Default is c(4, 500).

sig.level

Significance level or type I error rate, default value is 0.05.

two.tailed

Logical; two-tailed tests if TRUE, otherwise one-tailed tests; default value is TRUE.

plots

Logical, provide variance plots if TRUE, otherwise not; default value is TRUE.

nlim

The plot range for n, default value is c(2, 50).

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).

nlab

The plot label for n, default value is "Level-1 Sample Size: n".

plab

The plot label for p, default value is "Proportion Level-3 Units in Treatment: p".

varlab

The plot label for variance, default value is "Variance".

vartitle

The title of variance plot, default value is NULL.

Jlim

The range for J to search for a numerical solution. Default is c(3, 10e4).

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 of power analysis for calculating required budget, default value is 10.

n.of.archive

Size of the solution archive, default is 100.

q

Locality of the search (0,1), default is 0.0001.

xi

Convergence pressure (0, Inf), suggested: (0, 1), default is 0.5.

plot.by

Plot the variance by n, J, K and/or p; default value is plot.by = list(n = "n", J = "J", K = 'K', p = "p").

Value

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