Table 2 Open in new tab Monte Carlo...

True	Working Model	Vaccine	All
		bias×100
x(t)	x(t)	–1.49			0.52	–0.39
	$x (t), x (0)$	0.64	–1.72		3.14	–1.03	–0.24
	$x (t), t$	–1.68		0.51	4.54	–1.53		–2.83
$x (t), x (0)$	$x (t), x (0)$	–0.6	–0.01		0.86	0.05	–0.55
	x(t)	–20.39			–149.88	–9.76
	x(0)		–57.45		65.6		–56.27
	$x (t), x (0), t$	–1.14	0.45	–1.47	1.15	–1.06	0.48	–2.75
$x (t), t$	$x (t), t$	–1.92		–1.62	5.66	–1.74		–3.79
	x(t)	–4.61			68.32	–14.72
	t			–154.61	68.32			–164.72
	$x (t), x (0), t$	–2.68	1.56	–3.6	3.59	–2.35	1.17	–5.51
		Variance
x(t)	x(t)	0.048			0.127	0.022
	$x (t), x (0)$	0.24	0.08		1.792	0.176	0.027
	$x (t), t$	0.053		1.373	0.719	0.052		0.288
$x (t), x (0)$	$x (t), x (0)$	0.086	0.235		1.644	0.03	0.169
	x(t)	0.047			0.149	0.022
	x(0)		0.132		1.518		0.126
	$x (t), x (0), t$	0.106	0.268	1.541	1.629	0.105	0.261	0.395
$x (t), t$	$x (t), t$	0.046		1.327	0.644	0.046		0.266
	x(t)	0.042			0.11	0.02
	t			0.042	0.11			0.02
	$x (t), x (0), t$	0.083	0.249	1.504	1.695	0.082	0.244	0.398

True	Working Model	Vaccine	All
		bias×100
x(t)	x(t)	–1.49			0.52	–0.39
	$x (t), x (0)$	0.64	–1.72		3.14	–1.03	–0.24
	$x (t), t$	–1.68		0.51	4.54	–1.53		–2.83
$x (t), x (0)$	$x (t), x (0)$	–0.6	–0.01		0.86	0.05	–0.55
	x(t)	–20.39			–149.88	–9.76
	x(0)		–57.45		65.6		–56.27
	$x (t), x (0), t$	–1.14	0.45	–1.47	1.15	–1.06	0.48	–2.75
$x (t), t$	$x (t), t$	–1.92		–1.62	5.66	–1.74		–3.79
	x(t)	–4.61			68.32	–14.72
	t			–154.61	68.32			–164.72
	$x (t), x (0), t$	–2.68	1.56	–3.6	3.59	–2.35	1.17	–5.51
		Variance
x(t)	x(t)	0.048			0.127	0.022
	$x (t), x (0)$	0.24	0.08		1.792	0.176	0.027
	$x (t), t$	0.053		1.373	0.719	0.052		0.288
$x (t), x (0)$	$x (t), x (0)$	0.086	0.235		1.644	0.03	0.169
	x(t)	0.047			0.149	0.022
	x(0)		0.132		1.518		0.126
	$x (t), x (0), t$	0.106	0.268	1.541	1.629	0.105	0.261	0.395
$x (t), t$	$x (t), t$	0.046		1.327	0.644	0.046		0.266
	x(t)	0.042			0.11	0.02
	t			0.042	0.11			0.02
	$x (t), x (0), t$	0.083	0.249	1.504	1.695	0.082	0.244	0.398

Table 2

Monte Carlo performance of the HF estimator for estimating Cox model parameter in standard trial, based on 1,000 simulations. Each setting has an average of 1778 (94) placebo(vaccine) cases. Immune responses are measured at day 0, month 6, and year 1 post-peak time point. For model with x(t) only, $β_{0} = - .5, β_{1} = - 1$ ⁠; for model with $x (t), x (0), β_{0} = 0.1, β_{1} = - .5, β_{2} = - .5$ ⁠; for model with $x (t), t, β_{0} = - 1.3, β_{1} = - 1, β_{3} = .5$ ⁠.

True	Working Model	Vaccine			All
True	Working Model	β₁	β₂	β₃	β₀	β₁	β₂	β₃
		bias×100
x(t)	x(t)	–1.49			0.52	–0.39
	$x (t), x (0)$	0.64	–1.72		3.14	–1.03	–0.24
	$x (t), t$	–1.68		0.51	4.54	–1.53		–2.83
$x (t), x (0)$	$x (t), x (0)$	–0.6	–0.01		0.86	0.05	–0.55
	x(t)	–20.39			–149.88	–9.76
	x(0)		–57.45		65.6		–56.27
	$x (t), x (0), t$	–1.14	0.45	–1.47	1.15	–1.06	0.48	–2.75
$x (t), t$	$x (t), t$	–1.92		–1.62	5.66	–1.74		–3.79
	x(t)	–4.61			68.32	–14.72
	t			–154.61	68.32			–164.72
	$x (t), x (0), t$	–2.68	1.56	–3.6	3.59	–2.35	1.17	–5.51
		Variance
x(t)	x(t)	0.048			0.127	0.022
	$x (t), x (0)$	0.24	0.08		1.792	0.176	0.027
	$x (t), t$	0.053		1.373	0.719	0.052		0.288
$x (t), x (0)$	$x (t), x (0)$	0.086	0.235		1.644	0.03	0.169
	x(t)	0.047			0.149	0.022
	x(0)		0.132		1.518		0.126
	$x (t), x (0), t$	0.106	0.268	1.541	1.629	0.105	0.261	0.395
$x (t), t$	$x (t), t$	0.046		1.327	0.644	0.046		0.266
	x(t)	0.042			0.11	0.02
	t			0.042	0.11			0.02
	$x (t), x (0), t$	0.083	0.249	1.504	1.695	0.082	0.244	0.398

True	Working Model	Vaccine			All
True	Working Model	β₁	β₂	β₃	β₀	β₁	β₂	β₃
		bias×100
x(t)	x(t)	–1.49			0.52	–0.39
	$x (t), x (0)$	0.64	–1.72		3.14	–1.03	–0.24
	$x (t), t$	–1.68		0.51	4.54	–1.53		–2.83
$x (t), x (0)$	$x (t), x (0)$	–0.6	–0.01		0.86	0.05	–0.55
	x(t)	–20.39			–149.88	–9.76
	x(0)		–57.45		65.6		–56.27
	$x (t), x (0), t$	–1.14	0.45	–1.47	1.15	–1.06	0.48	–2.75
$x (t), t$	$x (t), t$	–1.92		–1.62	5.66	–1.74		–3.79
	x(t)	–4.61			68.32	–14.72
	t			–154.61	68.32			–164.72
	$x (t), x (0), t$	–2.68	1.56	–3.6	3.59	–2.35	1.17	–5.51
		Variance
x(t)	x(t)	0.048			0.127	0.022
	$x (t), x (0)$	0.24	0.08		1.792	0.176	0.027
	$x (t), t$	0.053		1.373	0.719	0.052		0.288
$x (t), x (0)$	$x (t), x (0)$	0.086	0.235		1.644	0.03	0.169
	x(t)	0.047			0.149	0.022
	x(0)		0.132		1.518		0.126
	$x (t), x (0), t$	0.106	0.268	1.541	1.629	0.105	0.261	0.395
$x (t), t$	$x (t), t$	0.046		1.327	0.644	0.046		0.266
	x(t)	0.042			0.11	0.02
	t			0.042	0.11			0.02
	$x (t), x (0), t$	0.083	0.249	1.504	1.695	0.082	0.244	0.398

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