Table 4.

Sample sizes using the Schoenfeld formula when the effect size is defined using ‘Hazard Ratio at t_avg (average of median survival times in the two study arms) vs Proposed Method (when the assumption of ‘Relative Time’ is valid) for various scenarios with type I error rate of 5% and Nominal Power of 80% for one-sided test with accrual time = 12 months, follow-up time = 12 months, and r=1.

Design features of the proposed method			# Events/ Sample Size: Proposed method vs Schoenfeld formula		Empirical Power of two methods when data is simulated under proposed method
Control arm Shape parameter β0	Effect Size User Input	True HR calculated at ${\mathit{t}}_{\mathit{a}\mathit{v}\mathit{g}}=\frac{{\mathit{t}}_{\mathit{m}\mathit{e}\mathit{d},\mathit{C}}+{\mathit{t}}_{\mathit{m}\mathit{e}\mathit{d},\mathit{E}}}{2}$ $\mathbf{H}\mathbf{R}=\frac{{\mathit{\beta }}_1{{\mathit{\theta }}_0}^{{\mathit{\beta }}_0}}{{\mathit{\beta }}_0{{\mathit{\theta }}_1}^{{\mathit{\beta }}_1}}{{\mathit{t}}_{\mathit{a}\mathit{v}\mathit{g}}}^{{\mathit{\beta }}_1-{\mathit{\beta }}_0}$	Proposed Method	Schoenfeld using HR at tavg as effect size	Proposed Method	Cox model (without an interaction term)
β0=0.25	p1=0.10; p2=0.90; RT[p1]=1.52; RT[p2]=1.98	HR = 0.8479	601/991	455/751	80.77%	80.46%
	p1=0.10; p2=0.90; RT[p1]=2.00; RT[p2]=1.50	HR = 0.8984	722/1182	1079/1766	79.28%	79.41%
β0=0.50	p1=0.10; p2=0.90; RT[p1]=1.52; RT[p2]=1.98	HR = 0.7211	154/216	116/164	81.47%	82.49%
	p1=0.10; p2=0.90; RT[p1]=2.00; RT[p2]=1.50	HR = 0.8054	177/244	265/366	79.25%	76.90%
β0=0.75	p1=0.10; p2=0.90; RT[p1]=1.52; RT[p2]=1.98	HR = 0.6150	70/87	53/67	81.48%	83.36%
	p1=0.10; p2=0.90; RT[p1]=2.00; RT[p2]=1.50	HR = 0.7202	77/93	115/140	78.26%	73.26%
β0=1.00	p1=0.10; p2=0.90; RT[p1]=1.52; RT[p2]=1.98	HR = 0.5258	41/46	30/35	81.90%	84.37%
	p1=0.10; p2=0.90; RT[p1]=2.00; RT[p2]=1.50	HR = 0.6423	43/47	64/71	79.06%	71.31%
β0=1.25	p1=0.10; p2=0.90; RT[p1]=1.52; RT[p2]=1.98	HR = 0.4507	27/29	20/22	82.28%	84.80%
	p1=0.10; p2=0.90; RT[p1]=2.00; RT[p2]=1.50	HR = 0.5712	27/27	40/42	79.10%	69.81%
β0=1.50	p1=0.10; p2=0.90; RT[p1]=1.52; RT[p2]=1.98	HR = 0.3872	19/20	14/15	81.77%	83.60%
	p1=0.10; p2=0.90; RT[p1]=2.00; RT[p2]=1.50	HR = 0.5064	18/19	27/28	80.67%	70.66%
β0=0.25	p1=0.25; p2=0.75; RT[p1]=1.50; RT[p2]=1.667	HR = 0.8764	933/1525	711/1163	80.58%	80.49%
	p1=0.25; p2=0.75; RT[p1]=1.667; RT[p2]=1.50	HR = 0.9076	953/1552	1317/2146	79.69%	79.59%
β0=0.50	p1=0.25; p2=0.75; RT[p1]=1.50; RT[p2]=1.667	HR = 0.7696	238/329	181/251	81.08%	82.62%
	p1=0.25; p2=0.75; RT[p1]=1.667; RT[p2]=1.50	HR = 0.8225	235/321	325/446	78.99%	76.60%
β0=0.75	p1=0.25; p2=0.75; RT[p1]=1.50; RT[p2]=1.667	HR = 0.6770	108/131	82/101	81.22%	83.98%
	p1=0.25; p2=0.75; RT[p1]=1.667; RT[p2]=1.50	HR = 0.7443	103/123	142/171	78.75%	74.53%
β0=1.00	p1=0.25; p2=0.75; RT[p1]=1.50; RT[p2]=1.667	HR = 0.5966	62/69	47/53	81.40%	84.80%
	p1=0.25; p2=0.75; RT[p1]=1.667; RT[p2]=1.50	HR = 0.6724	57/63	79/87	79.54%	73.52%
β0=1.25	p1=0.25; p2=0.75; RT[p1]=1.50; RT[p2]=1.667	HR = 0.5266	40/43	31/34	81.01%	85.05%
	p1=0.25; p2=0.75; RT[p1]=1.667; RT[p2]=1.50	HR = 0.6063	36/38	50/53	79.67%	71.90%
β0=1.50	p1=0.25; p2=0.75; RT[p1]=1.50; RT[p2]=1.667	HR = 0.4656	29/30	21/22	80.93%	84.96%
	p1=0.25; p2=0.75; RT[p1]=1.667; RT[p2]=1.50	HR = 0.5458	25/25	34/35	79.15%	70.35%