od.2.221 | R Documentation |
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.
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
)
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. |
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.
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