od.2.221m {odr} | R Documentation |
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.