Table 1 Open in new tab Monte Carlo bias...

Design	Scenario	Feature	Data	β₀	β₁	β₂	β₃
Reference			All	–0.002	1.3e–4	–9e–5	–0.037
		Variance	Vaccine		0.161	0.331	1.707
			All	1.825	0.158	0.326	0.453
	2) No β₃	Bias	Vaccine		0.009	–0.009
			All	–0.005	0.014	–0.014
		Variance	Vaccine		0.128	0.281
			All	1.830	0.041	0.190
	3) No β₂ and β₃	Bias	Vaccine		0.002
			All	–0.034	0.009
		Variance	Vaccine		0.063
			All	0.246	0.030
	4) Add X(T)	Bias	Vaccine		–0.005	0.007	–0.032
			All	–0.007	–0.003	0.005	–0.036
		Variance	Vaccine		0.129	0.302	1.682
			All	1.774	0.125	0.290	0.396
B.	5) $β_{1}, β_{2}, β_{3}$ together	Bias	Vaccine		–0.020	0.012	–0.108
Few Events			All	–0.014	–0.022	0.015	–0.111
		Variance	Vaccine		0.479	1.081	6.523
			All	6.510	0.458	1.055	1.518
C.	6) $β_{1}, β_{2}, β_{3}$ together	Bias	Vaccine		–0.002	0.002	–0.013
Placebo Vx			All	–0.009	–0.002	0.003	–0.023
		Variance	Vaccine		0.157	0.296	0.461
			All	1.434	0.157	0.296	0.430
	7) No β₃	Bias	Vaccine		0.001	–0.0003
			All	–0.012	0.005	–0.003
		Variance	Vaccine		0.042	0.161
			All	1.423	0.036	0.152
	8) No β₂ and β₃	Bias	Vaccine		0.0002
			All	–0.012	0.002
		Variance	Vaccine		0.029
			All	0.240	0.025

Design

Scenario

Feature

Data

β₀

β₁

β₂

β₃

β_{1}, β_{2}, β_{3}

together

Bias

Vaccine

5e–4

–1e–5

–0.031

Reference

All

–0.002

1.3e–4

–9e–5

–0.037

Variance

Vaccine

0.161

0.331

1.707

All

1.825

0.158

0.326

0.453

2) No β₃

Bias

Vaccine

0.009

–0.009

All

–0.005

0.014

–0.014

Variance

Vaccine

0.128

0.281

All

1.830

0.041

0.190

3) No β₂ and β₃

Bias

Vaccine

0.002

All

–0.034

0.009

Variance

Vaccine

0.063

All

0.246

0.030

4) Add X(T)

Bias

Vaccine

–0.005

0.007

–0.032

All

–0.007

–0.003

0.005

–0.036

Variance

Vaccine

0.129

0.302

1.682

All

1.774

0.125

0.290

0.396

β_{1}, β_{2}, β_{3}

together

Bias

Vaccine

–0.020

0.012

–0.108

Few Events

All

–0.014

–0.022

0.015

–0.111

Variance

Vaccine

0.479

1.081

6.523

All

6.510

0.458

1.055

1.518

β_{1}, β_{2}, β_{3}

together

Bias

Vaccine

–0.002

0.002

–0.013

Placebo Vx

All

–0.009

–0.002

0.003

–0.023

Variance

Vaccine

0.157

0.296

0.461

All

1.434

0.157

0.296

0.430

7) No β₃

Bias

Vaccine

0.001

–0.0003

All

–0.012

0.005

–0.003

Variance

Vaccine

0.042

0.161

All

1.423

0.036

0.152

8) No β₂ and β₃

Bias

Vaccine

0.0002

All

–0.012

0.002

Variance

Vaccine

0.029

All

0.240

0.025

Design	Scenario	Feature	Data	β₀	β₁	β₂	β₃
Reference			All	–0.002	1.3e–4	–9e–5	–0.037
		Variance	Vaccine		0.161	0.331	1.707
			All	1.825	0.158	0.326	0.453
	2) No β₃	Bias	Vaccine		0.009	–0.009
			All	–0.005	0.014	–0.014
		Variance	Vaccine		0.128	0.281
			All	1.830	0.041	0.190
	3) No β₂ and β₃	Bias	Vaccine		0.002
			All	–0.034	0.009
		Variance	Vaccine		0.063
			All	0.246	0.030
	4) Add X(T)	Bias	Vaccine		–0.005	0.007	–0.032
			All	–0.007	–0.003	0.005	–0.036
		Variance	Vaccine		0.129	0.302	1.682
			All	1.774	0.125	0.290	0.396
B.	5) $β_{1}, β_{2}, β_{3}$ together	Bias	Vaccine		–0.020	0.012	–0.108
Few Events			All	–0.014	–0.022	0.015	–0.111
		Variance	Vaccine		0.479	1.081	6.523
			All	6.510	0.458	1.055	1.518
C.	6) $β_{1}, β_{2}, β_{3}$ together	Bias	Vaccine		–0.002	0.002	–0.013
Placebo Vx			All	–0.009	–0.002	0.003	–0.023
		Variance	Vaccine		0.157	0.296	0.461
			All	1.434	0.157	0.296	0.430
	7) No β₃	Bias	Vaccine		0.001	–0.0003
			All	–0.012	0.005	–0.003
		Variance	Vaccine		0.042	0.161
			All	1.423	0.036	0.152
	8) No β₂ and β₃	Bias	Vaccine		0.0002
			All	–0.012	0.002
		Variance	Vaccine		0.029
			All	0.240	0.025

Table 1

Open in new tab

Monte Carlo bias and variance for the WIPL estimates under different scenarios. The first 4 scenarios belong to Design A and have an average of 1778 (94) placebo (vaccine) cases. Scenario 5 belongs to Design B and has an average of 242 (27) placebo (vaccine) cases. Scenarios 6-8 belong to Design C and has 1254, 94, 25 on placebo original, vaccine, and CPV vaccine arms. All scenarios include $β_{1}, β_{2}, β_{3}$ in cox model and do not use X(T) value from cases in model fitting unless otherwise noted.

Design	Scenario	Feature	Data	β₀	β₁	β₂	β₃
A.	1) $β_{1}, β_{2}, β_{3}$ together	Bias	Vaccine		5e–4	–1e–5	–0.031
Reference			All	–0.002	1.3e–4	–9e–5	–0.037
		Variance	Vaccine		0.161	0.331	1.707
			All	1.825	0.158	0.326	0.453
	2) No β₃	Bias	Vaccine		0.009	–0.009
			All	–0.005	0.014	–0.014
		Variance	Vaccine		0.128	0.281
			All	1.830	0.041	0.190
	3) No β₂ and β₃	Bias	Vaccine		0.002
			All	–0.034	0.009
		Variance	Vaccine		0.063
			All	0.246	0.030
	4) Add X(T)	Bias	Vaccine		–0.005	0.007	–0.032
			All	–0.007	–0.003	0.005	–0.036
		Variance	Vaccine		0.129	0.302	1.682
			All	1.774	0.125	0.290	0.396
B.	5) $β_{1}, β_{2}, β_{3}$ together	Bias	Vaccine		–0.020	0.012	–0.108
Few Events			All	–0.014	–0.022	0.015	–0.111
		Variance	Vaccine		0.479	1.081	6.523
			All	6.510	0.458	1.055	1.518
C.	6) $β_{1}, β_{2}, β_{3}$ together	Bias	Vaccine		–0.002	0.002	–0.013
Placebo Vx			All	–0.009	–0.002	0.003	–0.023
		Variance	Vaccine		0.157	0.296	0.461
			All	1.434	0.157	0.296	0.430
	7) No β₃	Bias	Vaccine		0.001	–0.0003
			All	–0.012	0.005	–0.003
		Variance	Vaccine		0.042	0.161
			All	1.423	0.036	0.152
	8) No β₂ and β₃	Bias	Vaccine		0.0002
			All	–0.012	0.002
		Variance	Vaccine		0.029
			All	0.240	0.025

Design	Scenario	Feature	Data	β₀	β₁	β₂	β₃
A.	1) $β_{1}, β_{2}, β_{3}$ together	Bias	Vaccine		5e–4	–1e–5	–0.031
Reference			All	–0.002	1.3e–4	–9e–5	–0.037
		Variance	Vaccine		0.161	0.331	1.707
			All	1.825	0.158	0.326	0.453
	2) No β₃	Bias	Vaccine		0.009	–0.009
			All	–0.005	0.014	–0.014
		Variance	Vaccine		0.128	0.281
			All	1.830	0.041	0.190
	3) No β₂ and β₃	Bias	Vaccine		0.002
			All	–0.034	0.009
		Variance	Vaccine		0.063
			All	0.246	0.030
	4) Add X(T)	Bias	Vaccine		–0.005	0.007	–0.032
			All	–0.007	–0.003	0.005	–0.036
		Variance	Vaccine		0.129	0.302	1.682
			All	1.774	0.125	0.290	0.396
B.	5) $β_{1}, β_{2}, β_{3}$ together	Bias	Vaccine		–0.020	0.012	–0.108
Few Events			All	–0.014	–0.022	0.015	–0.111
		Variance	Vaccine		0.479	1.081	6.523
			All	6.510	0.458	1.055	1.518
C.	6) $β_{1}, β_{2}, β_{3}$ together	Bias	Vaccine		–0.002	0.002	–0.013
Placebo Vx			All	–0.009	–0.002	0.003	–0.023
		Variance	Vaccine		0.157	0.296	0.461
			All	1.434	0.157	0.296	0.430
	7) No β₃	Bias	Vaccine		0.001	–0.0003
			All	–0.012	0.005	–0.003
		Variance	Vaccine		0.042	0.161
			All	1.423	0.036	0.152
	8) No β₂ and β₃	Bias	Vaccine		0.0002
			All	–0.012	0.002
		Variance	Vaccine		0.029
			All	0.240	0.025

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