# Relative efficiency (RE) calculation Calculate the relative efficiency (RE) between two designs, it returns same results as those from function `rpe`. ```r re(od, subod, rounded = TRUE, verbose = TRUE) ``` ## Arguments - `od`: Returned object of first design (e.g., unconstrained optimal design) from function `od.1`, `od.2`, `od.3`, `od.4`, `od.2m`, `od.3m`, or `od.4m`. - `subod`: Returned object of second design (e.g., constrained optimal design) from function `od.1`, `od.2`, `od.3`, `od.4`, `od.2m`, `od.3m`, or `od.4m`. - `rounded`: Logical; round the values of `p`, `n`/`J`/`K` that are from functions to two decimal places and integer, respectively if TRUE, no rounding if FALSE; default is TRUE. - `verbose`: Logical; print the value of relative efficiency if TRUE, otherwise not; default is TRUE. ## Returns Relative efficiency value. ## Examples ```r # Unconstrained optimal design of 2-level CRT #---------- myod1 <- od.2(icc = 0.2, r12 = 0.5, r22 = 0.5, c1 = 1, c2 = 5, c1t = 1, c2t = 50, varlim = c(0.01, 0.02)) # Constrained optimal design with n = 20 myod2 <- od.2(icc = 0.2, r12 = 0.5, r22 = 0.5, c1 = 1, c2 = 5, c1t = 1, c2t = 50, n = 20, varlim = c(0.005, 0.025)) # Relative efficiency (RE) myre <- re(od = myod1, subod= myod2) myre$re # RE = 0.88 # Constrained optimal design with p = 0.5 myod2 <- od.2(icc = 0.2, r12 = 0.5, r22 = 0.5, c1 = 1, c2 = 5, c1t = 1, c2t = 50, p = 0.5, varlim = c(0.005, 0.025)) # Relative efficiency (RE) myre <- re(od = myod1, subod= myod2) myre$re # RE = 0.90 # Unconstrained optimal design of 3-level CRT #---------- 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, varlim = c(0.005, 0.025)) # Constrained optimal design with J = 20 myod2 <- od.3(icc2 = 0.2, icc3 = 0.1, r12 = 0.5, r22 = 0.5, r32 = 0.5, J = 20, c1 = 1, c2 = 5, c3 = 25, c1t = 1, c2t = 50, c3t = 250, varlim = c(0, 0.025)) # Relative efficiency (RE) myre <- re(od = myod1, subod= myod2) myre$re # RE = 0.53 # Unconstrained optimal design of 4-level CRT #--------- myod1 <- od.4(icc2 = 0.2, icc3 = 0.1, icc4 = 0.05, r12 = 0.5, r22 = 0.5, r32 = 0.5, r42 = 0.5, c1 = 1, c2 = 5, c3 = 25, c4 = 125, c1t = 1, c2t = 50, c3t = 250, c4t = 2500, varlim = c(0, 0.01)) # Constrained optimal design with p = 0.5 myod2 <- od.4(icc2 = 0.2, icc3 = 0.1, icc4 = 0.05, r12 = 0.5, p = 0.5, r22 = 0.5, r32 = 0.5, r42 = 0.5, c1 = 1, c2 = 5, c3 = 25, c4 = 125, c1t = 1, c2t = 50, c3t = 250, c4t = 2500, varlim = c(0, 0.01)) # Relative efficiency (RE) myre <- re(od = myod1, subod= myod2) myre$re # RE = 0.78 ``` ## References (1) 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. (2) Shen, Z., & Kelcey, B. (in press). Optimal sample allocation in multisite randomized trials. The Journal of Experimental Education. (3) Shen, Z., & Kelcey, B. (in press). Optimal sampling ratios in three-level multisite experiments. Journal of Research on Educational Effectiveness.

re function