. Author manuscript; available in PMC: 2019 Apr 23.

Published in final edited form as: Stat Med. 2017 Aug 16;36(26):4121–4140. doi: 10.1002/sim.7421

TABLE 5.

Sample size comparisons for proportional time (PT) approach (true) versus piecewise exponential model (PEM) and cure rate (CR) model

PT model (Δ_PT assumed true)		Piecewise Exponential PE model		Cure Rate Mixture CRM model (EL = Exponential-Logit, WL = Weibul-Logit, CL = Cox-Logit)
Simulation Scenarios	Power/N_Total	Calculation Parameters	Power/N_Total	Calculation Parameters	Power/N_Total
λ = −1.9930	0.8/ 142	m_std = 9	0.8/ N_LR = 408,	π₀ = π₁ = 0.1335,	0.8/ N_WLR = 258, N_SLR = 238
σ = 1.414		m_new = 9	N_G = 220, N_TW = 282	λ₀ = 0.3641,
a = 12, f = 36	0.9/ 194	a = 12	0.9/ N_LR = 564,	ω = −0.6931,	0.9/ N_WLR = 356, N_SLR = 330
d = 0.77, Δ_PT = 2		f = 36	N_G = 304, N_TW = 390	a = 12, f = 36, EL
λ = −0.2	0.8/ 232	m_std = 15	0.8/ N_LR = 230,	π₀ = π₁ = 0.1988,	0.8/ N_WLR = 360, N_SLR = 378
σ = 1.8830		m_new = 11	N_G = 212, N_TW = 218	λ₀ = 0.1456,
a = 12, f = 48	0.9/ 324	a = 12	0.9/ N_LR = 316,	ω = −0.6931,	0.9/ N_WLR = 498, N_SLR = 524
d = 0.63, Δ_PT = 2		f = 48	N_G = 306, N_TW = 300	a = 12, f = 48, EL
λ = 1.5,	0.8/ 48	m_std = 15	0.8/ N_LR = 62,	π₀ = π₁ = 0.0001,	0.8/ N_WLR = 76, N_SLR = 72
σ = 0.85		m_new = 11	N_G = 92, N_TW = 74	λ₀= 1.1985,
a = 1, f = 2.5	0.9/ 62	a = 1	0.9/ N_LR = 86,	ω = −0.6066,	0.9/ N_WLR = 104, N_SLR = 98
d = 1, Δ_PT = 2		f = 2.5	N_G = 128, N_TW = 102	a = 1, f = 2.5, CL
λ = 2	0.8/ 232	m_std = 9	0.8/ N_LR = 304,	π₀ = π₁ = 0.0001,	0.8/ N_WLR = 622, N_SLR = 618
σ = 2		m_new = 11	N_G = 932, N_TW = 544	λ₀ = 0.6274,
a = 2, f = 8	0.9/ 312	a = 2	0.9/ N_LR = 422,	ω = −0.2006,	0.9/ N_WLR = 862, N_SLR = 856
d = 1, Δ_PT = 1.1		f = 8	N_G = 1290, N_TW = 754	a = 2, f = 8, CL
λ = 0.9717	0.8; 70	m_std = 9	0.8/ N_LR = 80,	π₀ = π₁ = 0.0547	0.8/ N_WLR = 90, N_SLR = 76
σ = 0.1606		m_new = 8	N_G = 72, N_TW =	λ₀ = 0.2567, β = 3.8956
a = 0, f = 1.5	0.9; 96	a = 0	740.9/ N_LR = 110,	ω = −0.7431	0.9/ N_WLR = 126, N_SLR = 104
d = 0.80		f = 1.5	N_G = 98, N_TW = 102	a = 0, f = 1.5, WL
λ = 0.5559	0.8; 134	m_std = 4	0.8/ N_LR = 138,	π₀ = π₁ = 0.0464,	0.8/ N_WLR = 155, N_SLR = 147
σ = 2.0396		m_new = 7	N_G = 144, N_TW = 134	λ₀= 1.3645, β = 1.8475	0.9/ N_WLR = 214, N_SLR = 203
a = 6, f = 15	0.9; 186	a = 6	0.9/ N_LR = 190,	ω = −0.6010,
d = 0.5, Δ_PT = 2.5		f = 18	N_G = 198, N_TW = 184	a = 6, f = 15, WL

For PE model: N_LR, N_G, and N_TW represent the sample size calculations using the Logrank, Gehan, and Taroneware options; m_std and m_new represent the number of intervals for the standard and new treatment groups, respectively, such that the shape of the survival curve for the 2 groups is approximated as much as possible.

For CR model (following Xiong and Wu¹⁹), N_WLR and N_SLR are the sample sizes calculated using the weighted logrank and the standard logrank test, respectively; π₀ and π₁ are the cured proportions in the standard and new treatment arms, respectively; λ₀ is the constant hazard rate in the standard treatment arm; and ω is the log hazards ratio comparing the new treatment to the standard treatment arm.