Time dependent hazard ratio estimation using instrumental variables without conditioning on an omitted covariate

Table 2 Parameters are constant within a dataset but vary between datasets

Element	Value Set
log Odds Ratio U vs X: α_UX	(−log(10), log(10))
log Odds Ratio W vs X: α_WX	(log(2), log(50)
ρ: correlation of copula	0.50, 0.99
Copula family	Gaussian, Clayton, Gumbel
Stepwise log Hazard Ratio Period 1 β₁	[−ln(3),−ln(3)+log(6)/24,…, ln(3)]
Stepwise log Hazard Ratio Period 2 β₂	[−ln(3),−ln(3)+log(6)/24,…, ln(3)]
log-linear HR intercept	\([ -1, -0.8,\dots,1]\)
log-linear HR slope over time	\([ -0.5, -0.4,\dots, 0.5]\)
Sample size of each dataset	1000
Censoring frequency	0.50
Number of events	500

Before each dataset is constructed the parameters above are randomly drawn with equal probability from the value set

ISSN: 1471-2288