od.2.221 {odr}

Optimal sample allocation calculation for two-level CRTs probing mediation effects with cluster-level mediators

Description

The optimal design of two-level cluster randomized trials (CRTs) probing mediation effects with cluster-level mediators is to 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-2 clusters/groups to be assigned to treatment (p). This function solves the optimal n and/or p with and without a constraint.

Usage

od.2.221(
  a = NULL,
  b = NULL,
  n = NULL,
  p = NULL,
  icc = NULL,
  c1 = NULL,
  c1t = NULL,
  c2 = NULL,
  c2t = NULL,
  m = NULL,
  r2m = 0,
  r.yx = 0,
  r.mw = 0,
  r.yw = 0,
  q.a = 0,
  q.b = 0,
  test = "joint",
  tol = 1e-11,
  power = 0.8,
  d.p = c(0.1, 0.5),
  d.n = c(2, 100),
  sig.level = 0.05,
  two.tailed = TRUE,
  Jlim = c(max(q.a, q.b) + 4, 1e+06),
  verbose = TRUE,
  nrange = c(1.5, 10000),
  max.value = Inf,
  max.iter = 300,
  e = 1e-10,
  n.of.ants = 10,
  n.of.archive = 50,
  q = 1e-04,
  xi = 0.5
)

Arguments

a

The treatment effect on the mediator.

b

The within treatment correlation between the outcome and the mediator at the cluster level.

n

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

p

The proportion of level-2 clusters/units to be assigned to treatment.

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 in control condition.

c2t

The cost of sampling one level-2 unit in treatment condition.

m

Total budget.

r2m

The proportion of mediator variance explained by covariates in the mediator model.

r.yx

The correlation between the outcome and the covariate at the individual level.

r.mw

The correlation between the mediator and the covariate at the cluster level.

r.yw

The correlation between the outcome and the covariate at the cluster level.

q.a

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

q.b

The number of covariates in the outcome model at the cluster level (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"). The other choice is the Sobel test by specifying the argument as test = "sobel".

tol

convergence tolerance.

power

Statistical power specified. The default value is .80.

d.p

The initial sampling domains for p. Default is c(0.1, 0.5).

d.n

The initial sampling domain for n. Default is c(2, 100).

sig.level

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

two.tailed

Two tailed test, the default value is TRUE.

Jlim

The range for J to solve for a numerical solution. Default is c(max(q.a, q.b)+4, 1e6).

verbose

Print out evaluation process if TRUE, default is TRUE.

nrange

The range of the individual-level sample size per cluster that used to exclude unreasonable values. Default value is c(1.5, 10000).

max.value

Maximal value of optimization when used as the stopping criterion. Default is -Inf.

max.iter

Maximal number of function evaluations when used as the stopping criterion.

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.

Value

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