RCT Operating Characteristics
oc_rct.RdFunction for calculating the operating characteristics of the RCT Bayesian designs in setting 3 and 4 for early gating.
oc_rct( N_c, N_e, delta, delta_power, confidence, e_a = 0.5, e_b = 0.5, c_a = 0.5, c_b = 0.5, h_a = 0.5, h_b = 0.5, RR_h = NULL, N_h = NULL, w = NULL, trues = seq(0, 1, 0.01), plot = T, legend = T, legend.pos = "topleft" )
Arguments
| N_c | Sample Size in the control group. Can be either a single value or a vector, but needs to be the same length as N_e. |
|---|---|
| N_e | Sample Size in the experimental group. Can be either a single value or a vector, but needs to be the same length as N_c. |
| delta | Required superiority to make a "GO" decision. Corresponds to \(\delta\). |
| delta_power | Superiority, at which decision power will be evaluated. Corresponds to \(\bar{\delta}\). |
| confidence | Required confidence to make "GO" decision. Corresponds to \(\gamma\). |
| e_a | Alpha parameter of Beta Prior Distribution for the experimental response rate. Corresponds to \(\alpha_e\). Default is \(\frac{1}{2}\). |
| e_b | Beta parameter of Beta Prior Distribution for the experimental response rate. Corresponds to \(\beta_e\). Default is \(\frac{1}{2}\). |
| c_a | Alpha parameter of Beta Prior Distribution for the control response rate. Corresponds to \(\alpha_c\). Default is \(\frac{1}{2}\). |
| c_b | Beta parameter of Beta Prior Distribution for the control response rate. Corresponds to \(\beta_c\). Default is \(\frac{1}{2}\). |
| h_a | Alpha parameter of Beta Prior Distribution for the historical control response rate. Corresponds to \(\alpha_h\). Only needs to be specified, if RR_h, N_h and w are also specified. Default is \(\frac{1}{2}\). |
| h_b | Beta parameter of Beta Prior Distribution for the historical control response rate. Corresponds to \(\beta_h\). Only needs to be specified, if RR_h, N_h and w are also specified. Default is \(\frac{1}{2}\). |
| RR_h | Historical control response rate. Corresponds to \(p_h\). If specified together with N_h and w, function will use setting 4 from pdf. |
| N_h | Historical control sample size. Corresponds to \(n_h\). If specified together with RR_h and w, function will use setting 4 from pdf. |
| w | Level of dynmaic borrowing. Corresponds to \(w\). |
| trues | Sequence of true control response rates and experimental response rates, at which the Probability to Go will be computed. Default is seq(0,1,0.01) to ensure continuous plots and accurate results. |
| plot | Plots yes or no. Default is TRUE. |
| legend | Logical; whether or not to include legend in plot. Default is TRUE. |
| legend.pos | Position of legend. Default is "topleft". |
Value
A matrix containing the decision power and decision alpha with respect to the true control response rate.
Examples
# Setting 3 oc_rct( N_c = 25, N_e = 25, delta = 0.08, delta_power = 0.13, confidence = 0.6 )#> Dec. Alpha Dec. Power True control RR #> [1,] 0.0000 0.4123 0.00 #> [2,] 0.0001 0.4222 0.01 #> [3,] 0.0009 0.4301 0.02 #> [4,] 0.0032 0.4364 0.03 #> [5,] 0.0071 0.4415 0.04 #> [6,] 0.0124 0.4457 0.05 #> [7,] 0.0187 0.4492 0.06 #> [8,] 0.0257 0.4521 0.07 #> [9,] 0.0330 0.4546 0.08 #> [10,] 0.0405 0.4567 0.09 #> [11,] 0.0479 0.4586 0.10 #> [12,] 0.0551 0.4602 0.11 #> [13,] 0.0621 0.4616 0.12 #> [14,] 0.0687 0.4629 0.13 #> [15,] 0.0751 0.4640 0.14 #> [16,] 0.0811 0.4650 0.15 #> [17,] 0.0868 0.4659 0.16 #> [18,] 0.0922 0.4668 0.17 #> [19,] 0.0973 0.4675 0.18 #> [20,] 0.1021 0.4682 0.19 #> [21,] 0.1067 0.4688 0.20 #> [22,] 0.1110 0.4693 0.21 #> [23,] 0.1150 0.4699 0.22 #> [24,] 0.1188 0.4703 0.23 #> [25,] 0.1223 0.4707 0.24 #> [26,] 0.1257 0.4711 0.25 #> [27,] 0.1288 0.4715 0.26 #> [28,] 0.1318 0.4718 0.27 #> [29,] 0.1345 0.4721 0.28 #> [30,] 0.1371 0.4724 0.29 #> [31,] 0.1395 0.4726 0.30 #> [32,] 0.1418 0.4728 0.31 #> [33,] 0.1439 0.4731 0.32 #> [34,] 0.1459 0.4732 0.33 #> [35,] 0.1477 0.4734 0.34 #> [36,] 0.1494 0.4735 0.35 #> [37,] 0.1510 0.4737 0.36 #> [38,] 0.1524 0.4738 0.37 #> [39,] 0.1538 0.4739 0.38 #> [40,] 0.1550 0.4739 0.39 #> [41,] 0.1561 0.4740 0.40 #> [42,] 0.1570 0.4740 0.41 #> [43,] 0.1579 0.4741 0.42 #> [44,] 0.1587 0.4741 0.43 #> [45,] 0.1593 0.4741 0.44 #> [46,] 0.1599 0.4741 0.45 #> [47,] 0.1603 0.4740 0.46 #> [48,] 0.1607 0.4740 0.47 #> [49,] 0.1609 0.4739 0.48 #> [50,] 0.1611 0.4739 0.49 #> [51,] 0.1611 0.4738 0.50 #> [52,] 0.1611 0.4737 0.51 #> [53,] 0.1609 0.4735 0.52 #> [54,] 0.1607 0.4734 0.53 #> [55,] 0.1603 0.4732 0.54 #> [56,] 0.1599 0.4731 0.55 #> [57,] 0.1593 0.4728 0.56 #> [58,] 0.1587 0.4726 0.57 #> [59,] 0.1579 0.4724 0.58 #> [60,] 0.1570 0.4721 0.59 #> [61,] 0.1561 0.4718 0.60 #> [62,] 0.1550 0.4715 0.61 #> [63,] 0.1538 0.4711 0.62 #> [64,] 0.1524 0.4707 0.63 #> [65,] 0.1510 0.4703 0.64 #> [66,] 0.1494 0.4699 0.65 #> [67,] 0.1477 0.4693 0.66 #> [68,] 0.1459 0.4688 0.67 #> [69,] 0.1439 0.4682 0.68 #> [70,] 0.1418 0.4675 0.69 #> [71,] 0.1395 0.4668 0.70 #> [72,] 0.1371 0.4659 0.71 #> [73,] 0.1345 0.4650 0.72 #> [74,] 0.1318 0.4640 0.73 #> [75,] 0.1288 0.4629 0.74 #> [76,] 0.1257 0.4616 0.75 #> [77,] 0.1223 0.4602 0.76 #> [78,] 0.1188 0.4586 0.77 #> [79,] 0.1150 0.4567 0.78 #> [80,] 0.1110 0.4546 0.79 #> [81,] 0.1067 0.4521 0.80 #> [82,] 0.1021 0.4492 0.81 #> [83,] 0.0973 0.4457 0.82 #> [84,] 0.0922 0.4415 0.83 #> [85,] 0.0868 0.4364 0.84 #> [86,] 0.0811 0.4301 0.85 #> [87,] 0.0751 0.4222 0.86 #> [88,] 0.0687 0.4123 0.87 #> [89,] 0.0621 0.0000 0.88 #> [90,] 0.0551 0.0000 0.89 #> [91,] 0.0479 0.0000 0.90 #> [92,] 0.0405 0.0000 0.91 #> [93,] 0.0330 0.0000 0.92 #> [94,] 0.0257 0.0000 0.93 #> [95,] 0.0187 0.0000 0.94 #> [96,] 0.0124 0.0000 0.95 #> [97,] 0.0071 0.0000 0.96 #> [98,] 0.0032 0.0000 0.97 #> [99,] 0.0009 0.0000 0.98 #> [100,] 0.0001 0.0000 0.99 #> [101,] 0.0000 0.0000 1.00# Setting 4 oc_rct( N_c = 25, N_e = 25, delta = 0.08, delta_power = 0.13, confidence = 0.6, RR_h = 0.5, N_h = 50, w = 0.3 )#> Dec. Alpha Dec. Power True control RR #> [1,] 0.0000 0.4123 0.00 #> [2,] 0.0001 0.4222 0.01 #> [3,] 0.0009 0.4300 0.02 #> [4,] 0.0032 0.4362 0.03 #> [5,] 0.0071 0.4410 0.04 #> [6,] 0.0124 0.4445 0.05 #> [7,] 0.0187 0.4466 0.06 #> [8,] 0.0257 0.4473 0.07 #> [9,] 0.0330 0.4464 0.08 #> [10,] 0.0404 0.4441 0.09 #> [11,] 0.0476 0.4402 0.10 #> [12,] 0.0545 0.4348 0.11 #> [13,] 0.0610 0.4281 0.12 #> [14,] 0.0668 0.4203 0.13 #> [15,] 0.0719 0.4116 0.14 #> [16,] 0.0763 0.4023 0.15 #> [17,] 0.0798 0.3926 0.16 #> [18,] 0.0826 0.3827 0.17 #> [19,] 0.0844 0.3727 0.18 #> [20,] 0.0856 0.3628 0.19 #> [21,] 0.0860 0.3531 0.20 #> [22,] 0.0859 0.3437 0.21 #> [23,] 0.0852 0.3346 0.22 #> [24,] 0.0842 0.3259 0.23 #> [25,] 0.0829 0.3177 0.24 #> [26,] 0.0813 0.3101 0.25 #> [27,] 0.0796 0.3030 0.26 #> [28,] 0.0778 0.2966 0.27 #> [29,] 0.0759 0.2909 0.28 #> [30,] 0.0740 0.2860 0.29 #> [31,] 0.0722 0.2819 0.30 #> [32,] 0.0704 0.2786 0.31 #> [33,] 0.0688 0.2762 0.32 #> [34,] 0.0672 0.2748 0.33 #> [35,] 0.0659 0.2742 0.34 #> [36,] 0.0647 0.2747 0.35 #> [37,] 0.0637 0.2762 0.36 #> [38,] 0.0630 0.2787 0.37 #> [39,] 0.0625 0.2824 0.38 #> [40,] 0.0624 0.2872 0.39 #> [41,] 0.0626 0.2933 0.40 #> [42,] 0.0631 0.3007 0.41 #> [43,] 0.0640 0.3095 0.42 #> [44,] 0.0654 0.3196 0.43 #> [45,] 0.0672 0.3312 0.44 #> [46,] 0.0695 0.3442 0.45 #> [47,] 0.0724 0.3586 0.46 #> [48,] 0.0759 0.3743 0.47 #> [49,] 0.0800 0.3913 0.48 #> [50,] 0.0849 0.4094 0.49 #> [51,] 0.0905 0.4285 0.50 #> [52,] 0.0969 0.4484 0.51 #> [53,] 0.1041 0.4688 0.52 #> [54,] 0.1121 0.4895 0.53 #> [55,] 0.1209 0.5102 0.54 #> [56,] 0.1305 0.5307 0.55 #> [57,] 0.1409 0.5506 0.56 #> [58,] 0.1518 0.5698 0.57 #> [59,] 0.1633 0.5878 0.58 #> [60,] 0.1751 0.6045 0.59 #> [61,] 0.1872 0.6196 0.60 #> [62,] 0.1994 0.6329 0.61 #> [63,] 0.2114 0.6442 0.62 #> [64,] 0.2230 0.6534 0.63 #> [65,] 0.2341 0.6605 0.64 #> [66,] 0.2445 0.6653 0.65 #> [67,] 0.2538 0.6679 0.66 #> [68,] 0.2620 0.6683 0.67 #> [69,] 0.2688 0.6667 0.68 #> [70,] 0.2740 0.6632 0.69 #> [71,] 0.2775 0.6580 0.70 #> [72,] 0.2793 0.6513 0.71 #> [73,] 0.2791 0.6433 0.72 #> [74,] 0.2771 0.6343 0.73 #> [75,] 0.2732 0.6244 0.74 #> [76,] 0.2675 0.6137 0.75 #> [77,] 0.2601 0.6022 0.76 #> [78,] 0.2511 0.5897 0.77 #> [79,] 0.2409 0.5759 0.78 #> [80,] 0.2295 0.5608 0.79 #> [81,] 0.2172 0.5440 0.80 #> [82,] 0.2042 0.5254 0.81 #> [83,] 0.1906 0.5053 0.82 #> [84,] 0.1766 0.4842 0.83 #> [85,] 0.1623 0.4630 0.84 #> [86,] 0.1476 0.4430 0.85 #> [87,] 0.1327 0.4257 0.86 #> [88,] 0.1176 0.4123 0.87 #> [89,] 0.1023 0.0000 0.88 #> [90,] 0.0871 0.0000 0.89 #> [91,] 0.0721 0.0000 0.90 #> [92,] 0.0578 0.0000 0.91 #> [93,] 0.0444 0.0000 0.92 #> [94,] 0.0324 0.0000 0.93 #> [95,] 0.0222 0.0000 0.94 #> [96,] 0.0138 0.0000 0.95 #> [97,] 0.0075 0.0000 0.96 #> [98,] 0.0033 0.0000 0.97 #> [99,] 0.0009 0.0000 0.98 #> [100,] 0.0001 0.0000 0.99 #> [101,] 0.0000 0.0000 1.00
