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. Author manuscript; available in PMC: 2022 Oct 1.
Published in final edited form as: Biom J. 2021 Jul 17;63(7):1406–1433. doi: 10.1002/bimj.202000043

Table 1.

Event size/Sample size (given by d/n) for Proposed method (equal allocation ratio) with α=0.05, one-sided test, 80% power, accrual time 12 months, follow-up time 12 months - for varying combinations of Control-Arm shape parameter β0 and effect size definitions (RT[p1] and RT[p2]) with p1=0.10, p2=0.90 and p1=0.25, p2=0.75 compared to Event Size/Sample size from Piece-wise Linear (Lakatos) method for varying number ‘m’ of equally spaced intervals

Control arm Shape β0 Time Quantiles at which the effect size is defined
p1=0.10, p2=0.90 p1=0.25, p2=0.75
RT(p1)=1.52, RT(p2)=1.98 RT(p1)=2.00, RT(p2)=1.50 RT(p1)=1.500, RT(p2)=1.667 RT(p1)=1.667, RT(p2)=1.500
Proposed Method Piecewise Linear (Lakatos) method Proposed Method Piecewise Linear (Lakatos) method Proposed Method Piecewise Linear (Lakatos) method Proposed Method Piecewise Linear (Lakatos) method
β 1 d/n #m d/n β 1 d/n #m d/n β 1 d/n #m d/n β 1 d/n #m d/n
β0 =0.25 β1 =0.2448 601/991 m=2
m=3
m=4
m=6
m=12		 629/1044
618/1021
612/1010
607/1001
603/994		 β1 =0.2560 722/1182 m=2
m=3
m=4
m=6
m=12		 904/1488
871/1428
852/1396
832/1361
809/1323		 β1 =0.2459 933/1525 m=2
m=3
m=4
m=6
m=12		 978/1608
959/1572
949/1554
941/1539
935/1528		 β1 =0.2543 953/1552 m=2
m=3
m=4
m=6
m=12		 1176/1926
1134/1853
1111/1812
1086/1764
1058/1723
β0 =0.50 β1 =0.4795 154/216 m=2
m=3
m=4
m=6
m=12		 160/228
152/214
148/209
146/205
144/202		 β1 =0.5247 177/244 m=2
m=3
m=4
m=6
m=12		 262/366
237/329
226/312
216/298
207/285		 β1 =0.4838 238/329 m=2
m=3
m=4
m=6
m=12		 249/348
235/327
229/318
224/311
222/307		 β1 =0.5174 235/321 m=2
m=3
m=4
m=6
m=12		 339/470
307/424
293/403
280/384
269/369
β0 =0.75 β1 =0.7047 70/87 m=2
m=3
m=4
m=6
m=12		 77/97
69/86
66/82
64/79
63/78		 β1 =0.8064 77/93 m=2
m=3
m=4
m=6
m=12		 142/175
117/142
107/130
100/121
95/115		 β1 =0.7141 108/131 m=2
m=3
m=4
m=6
m=12		 120/148
106/130
102/124
98/119
96/117		 β1 =0.7898 103/123 m=2
m=3
m=4
m=6
m=12		 183/223
150/182
138/167
129/156
123/148
β0 =1.00 β1 =0.9211 41/46 m=2
m=3
m=4
m=6
m=12		 50/58
41/48
38/44
37/42
36/41		 β1 =1.1029 43/47 m=2
m=3
m=4
m=6
m=12		 104/118
74/83
65/72
59/65
55/61		 β1 =0.9371 62/69 m=2
m=3
m=4
m=6
m=12		 79/90
63/72
59/66
56/63
54/61		 β1 =1.0720 57/63 m=2
m=3
m=4
m=6
m=12		 134/151
96/106
84/92
76/84
72/79
β0 =1.25 β1 =1.1290 27/29 m=2
m=3
m=4
m=6
m=12		 40/44
30/33
27/29
25/27
24/26		 β1 =1.4150 27/27 m=2
m=3
m=4
m=6
m=12		 95/102
55/59
45/48
40/42
37/38		 β1 =1.1532 40/43 m=2
m=3
m=4
m=6
m=12		 64/70
46/50
40/44
38/40
36/38		 β1 =1.3645 36/38 m=2
m=3
m=4
m=6
m=12		 123/132
71/75
58/61
51/54
47/49
β0 =1.50 β1 =1.3291 19/20 m=2
m=3
m=4
m=6
m=12		 36/39
24/26
21/23
19/20
18/19		 β1 =1.7440 18/19 m=2
m=3
m=4
m=6
m=12		 106/111
45/47
35/36
29/30
26/27		 β1 =1.3628 29/30 m=2
m=3
m=4
m=6
m=12		 61/65
38/40
32/33
29/30
27/28		 β1 =1.6680 25/25 m=2
m=3
m=4
m=6
m=12		 140/145
59/61
45/46
38/39
34/34
β0 =2.00 β1 =1.7073 11/12 m=2
m=3
m=4
m=6
m=12		 45/47
19/19
16/17
14/14
12/13		 β1 =2.4586 10/10 m=2
m=3
m=4
m=6
m=12		 325/330
33/34
25/25
19/19
15/15		 β1 =1.7633 17/17 m=2
m=3
m=4
m=6
m=12		 91/94
29/30
24/25
20/21
17/18		 β1 =2.3102 14/14 m=2
m=3
m=4
m=6
m=12		 227/229
45/46
33/33
25/25
20/20