Continuous monitoring of clinical trials involving binary outcomes
   using Pocock-type boundaries (version 1.1)
          (c) Bahjat Qaqish (2004)

(Simulation-based calculations)
Defintions:
  K     = the maximum planned sample size
  THETA = the event probability
  PHI   = the desired probability of early stopping (hitting the boundary)
Input  K  THETA  PHI: 200 0.2 0.05
K     = 200
THETA = 0.2
PHI   = 0.05
PHI*  = 0.049206 = the actual probability of hitting the upper boundary
ALPHA = 0.00693154 = the pointwise stopping probability

The upper boundary is:
b[1] = 2
b[2] = 3
b[3] = 4
b[4] = 4
b[5] = 4
b[6] = 5
b[7] = 5
b[8] = 6
b[9] = 6
b[10] = 6
b[11] = 7
b[12] = 7
b[13] = 8
b[14] = 8
b[15] = 8
b[16] = 9
b[17] = 9
b[18] = 9
b[19] = 9
b[20] = 10
b[21] = 10
b[22] = 10
b[23] = 11
b[24] = 11
b[25] = 11
b[26] = 12
b[27] = 12
b[28] = 12
b[29] = 13
b[30] = 13
b[31] = 13
b[32] = 13
b[33] = 14
b[34] = 14
b[35] = 14
b[36] = 15
b[37] = 15
b[38] = 15
b[39] = 15
b[40] = 16
b[41] = 16
b[42] = 16
b[43] = 16
b[44] = 17
b[45] = 17
b[46] = 17
b[47] = 18
b[48] = 18
b[49] = 18
b[50] = 18
b[51] = 19
b[52] = 19
b[53] = 19
b[54] = 19
b[55] = 20
b[56] = 20
b[57] = 20
b[58] = 21
b[59] = 21
b[60] = 21
b[61] = 21
b[62] = 22
b[63] = 22
b[64] = 22
b[65] = 22
b[66] = 23
b[67] = 23
b[68] = 23
b[69] = 23
b[70] = 24
b[71] = 24
b[72] = 24
b[73] = 24
b[74] = 25
b[75] = 25
b[76] = 25
b[77] = 25
b[78] = 26
b[79] = 26
b[80] = 26
b[81] = 26
b[82] = 27
b[83] = 27
b[84] = 27
b[85] = 28
b[86] = 28
b[87] = 28
b[88] = 28
b[89] = 29
b[90] = 29
b[91] = 29
b[92] = 29
b[93] = 30
b[94] = 30
b[95] = 30
b[96] = 30
b[97] = 31
b[98] = 31
b[99] = 31
b[100] = 31
b[101] = 32
b[102] = 32
b[103] = 32
b[104] = 32
b[105] = 33
b[106] = 33
b[107] = 33
b[108] = 33
b[109] = 34
b[110] = 34
b[111] = 34
b[112] = 34
b[113] = 35
b[114] = 35
b[115] = 35
b[116] = 35
b[117] = 35
b[118] = 36
b[119] = 36
b[120] = 36
b[121] = 36
b[122] = 37
b[123] = 37
b[124] = 37
b[125] = 37
b[126] = 38
b[127] = 38
b[128] = 38
b[129] = 38
b[130] = 39
b[131] = 39
b[132] = 39
b[133] = 39
b[134] = 40
b[135] = 40
b[136] = 40
b[137] = 40
b[138] = 41
b[139] = 41
b[140] = 41
b[141] = 41
b[142] = 42
b[143] = 42
b[144] = 42
b[145] = 42
b[146] = 43
b[147] = 43
b[148] = 43
b[149] = 43
b[150] = 44
b[151] = 44
b[152] = 44
b[153] = 44
b[154] = 44
b[155] = 45
b[156] = 45
b[157] = 45
b[158] = 45
b[159] = 46
b[160] = 46
b[161] = 46
b[162] = 46
b[163] = 47
b[164] = 47
b[165] = 47
b[166] = 47
b[167] = 48
b[168] = 48
b[169] = 48
b[170] = 48
b[171] = 49
b[172] = 49
b[173] = 49
b[174] = 49
b[175] = 49
b[176] = 50
b[177] = 50
b[178] = 50
b[179] = 50
b[180] = 51
b[181] = 51
b[182] = 51
b[183] = 51
b[184] = 52
b[185] = 52
b[186] = 52
b[187] = 52
b[188] = 53
b[189] = 53
b[190] = 53
b[191] = 53
b[192] = 53
b[193] = 54
b[194] = 54
b[195] = 54
b[196] = 54
b[197] = 55
b[198] = 55
b[199] = 55
b[200] = 55

THETA   PHI*    E[Y]    SD[Y]   E[N]    SD[N]   E[Y/N]  SD[Y/N]

0.20    0.050   38.57   7.56    192.93  33.26   0.21    0.08
0.30    0.873   28.54   15.25   95.14   63.52   0.36    0.13
0.40    1.000   12.70   6.73    31.75   23.54   0.49    0.15
0.50    1.000   8.14    3.59    16.29   11.11   0.59    0.16
0.60    1.000   6.15    2.25    10.26   6.31    0.69    0.16
0.70    1.000   5.07    1.46    7.25    3.80    0.77    0.16
0.80    1.000   4.44    0.86    5.55    2.21    0.85    0.14
0.90    1.000   4.11    0.38    4.56    1.08    0.92    0.11

Defintions:
  Y    = the number of events, random, between 0 and N
  N    = the number of patients, random, between 1 and K
  PHI* = the actual probability of early stopping (hitting the boundary)
  E[ ]   denotes the expected value (mean)
  SD[ ]  denotes the standard deviation


The boundary has been written to file _bndry_.dat in a format
appropriate for reading into other supplied programs (e.g. cp3).
Date and time: Mon Jul 26 11:59:38 2004