Table 3.

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 = 4.0 for associations between Z₁ and event J = 1and 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	−0.002	−0.002	0.3	0.3	0.110	0.109	0.013	0.013	95.0	95.1
IPEW estimatorc	−0.621		−0.001	0.000	0.1	0.1	0.110	0.108	0.010	0.010	96.4	96.5
RD, d conditional riskc	−0.191		0.000	0.000	−0.2	−0.2	0.030	0.030	0.001	0.001	96.2	96.6
Subdistribution log(HR)e
Covariate adjusted	−0.768	−0.704	−0.005	0.208	0.6	−29.6	0.111	0.109	0.013	0.056	95.1	51.7
IPEW estimatorc	−0.704		−0.002	−0.035	0.3	5.0	0.110	0.108	0.011	0.012	96.2	94.9
RD,d CIFc	−0.200		0.000	−0.009	0.0	4.7	0.030	0.030	0.001	0.001	96.1	94.6

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.