Table 6.

Simulation results, estimands for event of type J = 1, true cause-specific HR_J=2 = 4.0, true association between Z₁ and A OR = 4.0, true association between Z₂ and A OR = 4.0, true cause-specific HR = 4.0 for associations between Z₁ and event J = 1 and between Z₂ and event J = 2

	Truth		Avg. Bias		Avg. Pct. Bias		Avg. Std. Error		MSEa		95% Coverage
	Conditional on…b		Controlling for…		Controlling for…		Controlling for…		Controlling for…		Controlling for…
Parameter	Z1 & Z2	Z1 only	Z1 & Z2	Z1 only	Z1 & Z2	Z1 only	Z1 & Z2	Z1 only	Z1 & Z2	Z1 only	Z1 & Z2	Z1 only
Cause-specific log(HR)
Covariate adjusted	−0.695	−0.695	−0.001	−0.002	0.2	0.3	0.122	0.119	0.016	0.015	94.1	93.8
IPEW estimatorc	−0.625		0.001	0.010	−0.2	−1.6	0.127	0.118	0.014	0.013	96.4	96.4
RD, d conditional riskc	−0.192		0.001	0.003	−0.7	−1.7	0.038	0.035	0.001	0.001	95.9	96.1
Subdistribution log(HR)e
Covariate adjusted	−0.962	−0.890	−0.005	0.395	0.5	−44.3	0.125	0.119	0.017	0.170	94.1	10.1
IPEW estimatorc	−0.891		−0.001	−0.098	0.1	11.0	0.126	0.117	0.014	0.022	96.7	88.9
RD,d CIFc	−0.242		0.001	−0.023	−0.3	9.5	0.032	0.029	0.001	0.001	96.8	89.3

Abbreviations: Avg., average; CIF, cumulative incidence function; HR, hazard ratio; IPEW, inverse probability of exposure weighted; MSE, mean squared error; OR, odds ratio; Pct., percent; RD, risk difference

^aMean Squared Error. $\mathit{MSE}(\widehat{\mathrm{\theta }})={[\mathit{Bias}(\widehat{\theta },\theta )]}^2+\mathit{Var}(\theta )$ where Var (θ) is the Monte Carlo variance

^bTruth varies according to variables included in the model for the HR because it is a non-collapsible measure.

^cTruth is marginal (not conditional on any covariates)

^dDifference in cumulative incidence functions or conditional risk functions estimated at t = 50

^eBecause cause-specific hazards were simulated to be proportional, subdistribution hazards are not proportional. Truth here is a time-averaged subdistribution hazard ratio.