Table 1.

Simulation results, estimands for event of type J = 1, true cause-specific HR_J=2 = 2.0, true association between Z₁ and A OR= 2.0, true association between Z₂ and A OR=2.0, true cause-specific HR = 2.0 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	−0.692	−0.692	−0.006	−0.005	0.8	0.8	0.128	0.126	0.019	0.019	96.7	96.3
IPEW estimatorc	−0.679		−0.004	−0.004	0.6	0.6	0.128	0.126	0.022	0.051	97.1	97.1
RD, d conditional riskc	−0.168		−0.000	−0.000	0.1	0.2	0.031	0.030	0.001	0.001	96.9	96.8
Subdistribution log(HR)e
Covariate adjusted	−0.746	−0.733	−0.007	0.109	1.0	−14.8	0.128	0.126	0.015	0.027	96.1	87.5
IPEW estimatorc	−0.733		−0.005	−0.016	0.7	2.2	0.128	0.126	0.015	0.015	96.6	96.9
RD,d CIFc	−0.170		−0.001	−0.003	0.3	1.8	0.029	0.020	0.001	0.000	96.4	96.6

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 = 200.

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