Table 2.

Simulation results, estimands for event of type J = 1, true cause-specific HR_J=2 = 2.0, true association between Z₁ and A OR = 4.0, true association between Z₂ and A OR = 4.0, 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	−0.008	−0.007	1.1	1.1	0.138	0.129	0.017	0.016	95.4	95.7
IPEW estimatorc	−0.679		−0.008	−0.006	1.2	0.9	0.139	0.129	0.018	0.015	96.0	96.2
RD, d conditional riskc	−0.168		−0.001	−0.001	0.8	0.6	0.033	0.031	0.001	0.001	95.7	96.1
Subdistribution log(HR)e
Covariate adjusted	−0.746	−0.733	−0.010	0.214	1.3	−19.2	0.136	0.129	0.018	0.062	95.6	61.1
IPEW estimatorc	−0.733		−0.009	−0.028	1.3	3.9	0.139	0.129	0.018	0.016	96.1	95.9
RD,d CIFc	−0.171		−0.001	−0.006	0.9	3.5	0.031	0.029	0.001	0.001	95.7	95.7

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.