power.3: Budget and/or sample size, power, MDES calculation for...

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

Budget and/or sample size, power, MDES calculation for three-level CRTs detecting main effects

Description

This function can calculate required budget for desired power, power or minimum detectable effect size (MDES) under fixed budget for three-level cluster randomized trials (CRTs). It also can perform conventional power analyses (e.g., required sample size, power, and MDES calculation).

Usage

power.3(
  cost.model = TRUE,
  expr = NULL,
  constraint = NULL,
  sig.level = 0.05,
  two.tailed = TRUE,
  d = NULL,
  power = NULL,
  m = NULL,
  n = NULL,
  J = NULL,
  K = NULL,
  p = NULL,
  icc2 = NULL,
  icc3 = NULL,
  r12 = NULL,
  r22 = NULL,
  r32 = NULL,
  q = NULL,
  c1 = NULL,
  c2 = NULL,
  c3 = NULL,
  c1t = NULL,
  c2t = NULL,
  c3t = NULL,
  dlim = NULL,
  powerlim = NULL,
  Klim = NULL,
  mlim = NULL,
  rounded = TRUE
)

Arguments

cost.model	Logical; power analyses accommodating costs and budget (e.g., required budget for desired power, power/MDES under fixed budget) if TRUE, otherwise conventional power analyses (e.g., required sample size, power, or MDES calculation); default value is TRUE.
expr	Returned objects from function od.3; default is NULL; if expr is specified, parameter values of icc2, icc3, r12, r22, r32, c1, c2, c3, c1t, c2t, c3t, p, n, and J used or solved in function od.3 will be passed to the current function; only the values of p, n, and/or J that specified or solved in function od.3 can be overwritten if constraint is specified.
constraint	Specify the constrained values of p, n, and/or J in list format to overwrite those from expr; default is NULL.
sig.level	Significance level or type I error rate, default value is 0.05.
two.tailed	Logical; two-tailed tests if TRUE, otherwise one-tailed tests; default value is TRUE.
d	Effect size.
power	Statistical power.
m	Total budget.
n	The level-1 sample size per level-2 unit.
J	The level-2 sample size per level-3 unit.
K	The total level-3 sample size.
p	The proportion of level-3 clusters/units assigned to treatment.
icc2	The unconditional intraclass correlation coefficient (ICC) at level 2.
icc3	The unconditional intraclass correlation coefficient (ICC) at level 3.
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.
q	The number of covariates at level 3.
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.
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.
dlim	The range for solving the root of effect size (d) numerically, default value is c(0, 5).
powerlim	The range for solving the root of power (power) numerically, default value is c(1e-10, 1 - 1e-10).
Klim	The range for searching the root of level-3 sample size (K) numerically, default value is c(4, 1e+10).
mlim	The range for searching the root of budget (m) numerically, default value is the costs sampling Klim level-3 units across treatment conditions or c(4 * Kcost, 1e+10 * Kcost) with Kcost = ((1 - p) * (c1 * n * J + c2 * J + c3) + p * (c1t * n * J + c2t * J + c3t)).
rounded	Logical; round the values of p, n/J that are from functions od.3 to two decimal places and integer, respectively if TRUE, otherwise no rounding; default value is TRUE.

Value

Required budget (and/or required level-3 sample size), statistical power, or MDES depending on the specification of parameters. The function also returns the function name, design type, and parameters used in the calculation.

References

Shen, Z., & Kelcey, B. (2020). Optimal sample allocation under unequal costs in cluster-randomized trials. Journal of Educational and Behavioral Statistics, 45(4): 446–474. <https://doi.org/10.3102/1076998620912418>

Examples

# Unconstrained optimal design
  myod1 <- od.3(icc2 = 0.2, icc3 = 0.1, r12 = 0.5, r22 = 0.5, r32 = 0.5,
              c1 = 1, c2 = 5, c3 = 25, c1t = 1, c2t = 50, c3t = 250)
  myod1$out # output  # n = 7.9, J = 3.2, p = 0.28

# ------- Power analyses by default considering costs and budget -------
# Required budget and sample size
  mym.1 <- power.3(expr = myod1, d = 0.2, q = 1, power = 0.8)
  mym.1$out  # m = 16032, K = 97.3
  #mym.1$par  # parameters and their values used for the function
# Or, equivalently, specify every argument in the function
  mym.1 <- power.3(d = 0.2, power = 0.8, q = 1,
                 icc2 = 0.2, icc3 = 0.1, r12 = 0.5, r22 = 0.5, r32 = 0.5,
                 c1 = 1, c2 = 5, c3 = 25, c1t = 1, c2t = 50, c3t = 250,
                 n = 8, J = 3, p = 0.28)
# Required budget and sample size with constrained p
  mym.2 <- power.3(expr = myod1, d = 0.2, q = 1, power = 0.8,
                 constraint = list(p = 0.5))
  mym.2$out  # m = 19239, K = 78.8
# Required budget and sample size with constrained p and J
  mym.3 <- power.3(expr = myod1, d = 0.2, q = 1, power = 0.8,
                 constraint = list(p = 0.5, J = 20))
  mym.3$out  # m = 39774, K = 46.9

# Power calculation
  mypower <- power.3(expr = myod1, q = 1, d = 0.2, m = 16032)
  mypower$out  # power = 0.80
# Power calculation under constrained p (p = 0.5)
  mypower.1 <- power.3(expr = myod1, q = 1, d = 0.2, m = 16032,
                 constraint = list(p = 0.5))
  mypower.1$out  # power = 0.72

# MDES calculation
  mymdes <- power.3(expr = myod1, q = 1, power = 0.80, m = 16032)
  mymdes$out  # d = 0.20


# ------- Conventional power analyses with cost.model = FALSE-------
# Required sample size
  myK <- power.3(cost.model = FALSE, expr = myod1, d = 0.2, q = 1, power = 0.8)
  myK$out  # K = 97.3
  #myK$par  # parameters and their values used for the function
# Or, equivalently, specify every argument in the function
  myK <- power.3(cost.model = FALSE, d = 0.2, power = 0.8, q = 1,
                  icc2 = 0.2, icc3 = 0.1, r12 = 0.5, r22 = 0.5, r32 = 0.5,
                  n = 8, J = 3, p = 0.28)

# Power calculation
  mypower1 <- power.3(cost.model = FALSE, expr = myod1, K = 97, d = 0.2, q = 1)
  mypower1$out  # power = 0.80

# MDES calculation
  mymdes1 <- power.3(cost.model = FALSE, expr = myod1, K = 97, power = 0.8, q = 1)
  mymdes1$out  # d = 0.20

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