od.2.221m: Optimal sample allocation calculation for two-level CRTs...

In odr: Optimal Design and Statistical Power for Experimental Studies Investigating Main, Mediation, and Moderation Effects

Optimal sample allocation calculation for two-level CRTs probing moderation effects with cluster-level moderators

Description

The optimal design of two-level cluster randomized trials (CRTs) probing moderation effects with cluster-level moderators is to to identify the optimal sample allocation that requires the minimum budget to achieve a 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.2.221m(
  d = NULL,
  gamma = NULL,
  n = NULL,
  Q = NULL,
  p = NULL,
  icc = NULL,
  c1 = NULL,
  c1t = NULL,
  c2 = NULL,
  c2t = NULL,
  r12 = NULL,
  r22 = NULL,
  r12m = NULL,
  r22m = NULL,
  m = NULL,
  q.main = 0,
  q.mod = 0,
  tol = 1e-11,
  power.mod = 0.8,
  power.main = 0.8,
  d.p = c(0.5, 0.9),
  d.n = c(2, 1000),
  sig.level = 0.05,
  two.tailed = TRUE,
  Jlim = NULL,
  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

d	The standardized main or average treatment effect.
gamma	The standardized moderated treatment effect (i.e., regression coefficient of the interaction term of moderator and treatment).
n	The level-1 sample size per level-2 unit.
Q	The proportion of binary moderator that coded as 1.
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.
r12	The proportion of level-1 variance explained by covariates.
r22	The proportion of level-2 variance explained by covariates.
r12m	The proportion of outcome variance at the individual level explained by covariates in the model with the moderator.
r22m	The proportion of outcome variance at the cluster level explained by covariates in the model with the moderator.
m	Total budget.
q.main	The number of covariates in the outcome model testing main effects
q.mod	The number of cluster-level covariates in the model (except the treatment indicator, moderator, and the interaction term).
tol	convergence tolerance.
power.mod	Statistical power specified for moderation. The default value is .80.
power.main	Statistical power specified for the total/main effect. The default value is .80.
d.p	The initial sampling domains for p. Default is c(0.5, 0.9).
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.mod, q.main)+7, 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 function name, design type, and parameters used in the calculation.

odr documentation built on June 8, 2025, 10:50 a.m.