od.4: Optimal sample allocation calculation for four-level CRTs...

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

Optimal sample allocation calculation for four-level CRTs detecting main effects

Description

The optimal design of four-level cluster randomized trials (CRTs) is to calculate the optimal sample allocation that minimizes the variance of treatment effect under fixed budget, which is approximately the optimal sample allocation that maximizes statistical power under a fixed budget. The optimal design parameters include the level-1 sample size per level-2 unit (n), the level-2 sample size per level-3 unit (J), the level-3 sample size per level-4 unit (K), and the proportion of level-4 clusters/groups to be assigned to treatment (p). This function solves the optimal n, J, K and/or p with and without constraints.

Usage

od.4(
  n = NULL,
  J = NULL,
  K = NULL,
  p = NULL,
  icc2 = NULL,
  icc3 = NULL,
  icc4 = NULL,
  r12 = NULL,
  r22 = NULL,
  r32 = NULL,
  r42 = NULL,
  c1 = NULL,
  c2 = NULL,
  c3 = NULL,
  c4 = NULL,
  c1t = NULL,
  c2t = NULL,
  c3t = NULL,
  c4t = NULL,
  m = NULL,
  plots = TRUE,
  plot.by = NULL,
  nlim = NULL,
  Jlim = NULL,
  Klim = NULL,
  plim = NULL,
  varlim = NULL,
  nlab = NULL,
  Jlab = NULL,
  Klab = NULL,
  plab = NULL,
  varlab = NULL,
  vartitle = NULL,
  verbose = TRUE,
  iter = 100,
  tol = 1e-10
)

Arguments

n	The level-1 sample size per level-2 unit.
J	The level-2 sample size per level-3 unit.
K	The level-3 sample size per level-4 unit.
p	The proportion of level-4 clusters/units to be assigned to treatment.
icc2	The unconditional intraclass correlation coefficient (ICC) at level 2.
icc3	The unconditional intraclass correlation coefficient (ICC) at level 3.
icc4	The unconditional intraclass correlation coefficient (ICC) at level 4.
r12	The proportion of level-1 variance explained by covariates.
r22	The proportion of level-2 variance explained by covariates.
r32	The proportion of level-3 variance explained by covariates.
r42	The proportion of level-4 variance explained by covariates.
c1	The cost of sampling one level-1 unit in control condition.
c2	The cost of sampling one level-2 unit in control condition.
c3	The cost of sampling one level-3 unit in control condition.
c4	The cost of sampling one level-4 unit in control condition.
c1t	The cost of sampling one level-1 unit in treatment condition.
c2t	The cost of sampling one level-2 unit in treatment condition.
c3t	The cost of sampling one level-3 unit in treatment condition.
c4t	The cost of sampling one level-4 unit in treatment condition.
m	Total budget, default value is the total costs of sampling 60 level-4 units across treatment conditions.
plots	Logical, provide variance plots if TRUE, otherwise not; default value is TRUE.
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").
nlim	The plot range for n, default value is c(2, 50).
Jlim	The plot range for J, default value is c(2, 50).
Klim	The plot range for K, 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".
Jlab	The plot label for J, default value is "Level-2 Sample Size: J".
Klab	The plot label for K, default value is "Level-3 Sample Size: K".
plab	The plot label for p, default value is "Proportion Level-4 Units in Treatment: p".
varlab	The plot label for variance, default value is "Variance".
vartitle	The title of variance plot, default value is NULL.
verbose	Logical; print the values of n, J, K, and p if TRUE, otherwise not; default value is TRUE.
iter	Number of iterations; default value is 100.
tol	Tolerance for convergence; default value is 1e-10.

Value

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

Examples

# Unconstrained optimal design #---------
  myod1 <- od.4(icc2 = 0.2, icc3 = 0.1, icc4 = 0.05,
              r12 = 0.5, r22 = 0.5, r32 = 0.5, r42 = 0.5,
              c1 = 1, c2 = 5, c3 = 25, c4 = 125,
              c1t = 1, c2t = 50, c3t = 250, c4t = 2500,
              varlim = c(0, 0.01))
  myod1$out # output
# Plots by p and K
  myod1 <- od.4(icc2 = 0.2, icc3 = 0.1, icc4 = 0.05,
              r12 = 0.5, r22 = 0.5, r32 = 0.5, r42 = 0.5,
              c1 = 1, c2 = 5, c3 = 25, c4 = 125,
              c1t = 1, c2t = 50, c3t = 250, c4t = 2500,
              varlim = c(0, 0.01), plot.by = list(p = 'p', K = 'K'))

# Constrained optimal design with p = 0.5 #---------
  myod2 <- od.4(icc2 = 0.2, icc3 = 0.1, icc4 = 0.05, p = 0.5,
              r12 = 0.5, r22 = 0.5, r32 = 0.5, r42 = 0.5,
              c1 = 1, c2 = 5, c3 = 25, c4 = 125,
              c1t = 1, c2t = 50, c3t = 250, c4t = 2500,
              varlim = c(0, 0.01))
  myod2$out
# Relative efficiency (RE)
  myre <- re(od = myod1, subod= myod2)
  myre$re # RE = 0.78

# Constrained optimal design with K = 20 #---------
  myod3 <- od.4(icc2 = 0.2, icc3 = 0.1, icc4 = 0.05,  K = 20,
              r12 = 0.5, r22 = 0.5, r32 = 0.5, r42 = 0.5,
              c1 = 1, c2 = 5, c3 = 25, c4 = 125,
              c1t = 1, c2t = 50, c3t = 250, c4t = 2500,
              varlim = c(0, 0.01))
  myod3$out
# Relative efficiency (RE)
  myre <- re(od = myod1, subod= myod3)
  myre$re # RE = 0.67

# Constrained n, J, K and p, no calculation performed #---------
  myod4 <- od.4(icc2 = 0.2, icc3 = 0.1, icc4 = 0.05,
              r12 = 0.5, n = 10, J = 10, K = 20, p = 0.5,
              r22 = 0.5, r32 = 0.5, r42 = 0.5,
              c1 = 1, c2 = 5, c3 = 25, c4 = 125,
              c1t = 1, c2t = 50, c3t = 250, c4t = 2500,
              varlim = c(0, 0.01))
  myod4$out
# Relative efficiency (RE)
  myre <- re(od = myod1, subod= myod4)
  myre$re # RE = 0.27

odr documentation built on Aug. 8, 2023, 5:13 p.m.