Table.

Black-white stroke incidence rate difference (IRD) results from the REGARDS cohort and from simulation scenarios (2,000 simulated samples)

	Age 45–54 years			Age 55–64 years			Age 65–74 years			Age 75–84 years			Age 85–94 years
	IRDa (SEb)	% biasc	RMSEd	IRDa (SEb)	% biasc	RMSEd	IRDa (SEb)	% biasc	RMSEd	IRDa (SEb)	% biasc	RMSEd	IRDa (SEb)	% biasc	RMSEd
REGARDSe	19.8 (5.4)	-	-	11.6 (3.9)	-	-	13.1 (6.2)	-	-	−2.7 (13.1)	-	-	−44.9 (42.7)	-	-
Truth in simulations	20.0	-	-	20.0	-	-	20.0	-	-	20.0	-	-	20.0	-	-
Scenario Af	21.6 (1.9)	8%	2.5	21.2 (3.1)	6%	3.3	20.3 (5.1)	1%	5.1	19.8 (10.1)	−1%	10.1	20.5 (25.5)	3%	25.5
Scenario Bg	18.8 (1.8)	−6%	2.1	16.6 (2.8)	−17%	4.4	12.5 (4.8)	−37%	8.9	8.3 (9.3)	−59%	15.0	9.6 (24.4)	−52%	26.5
Scenario Ch	18.3 (1.9)	−9%	2.5	14.1 (2.8)	−29%	6.5	5.0 (4.6)	−75%	15.7	−13.8 (8.9)	−169%	35.0	−43.0 (22.7)	−315%	66.9

See eTable 4 for average incidence rate estimates for blacks and whites in each scenario.

^aIRD = stroke incidence rate difference per 10,000 person-years for blacks versus whites in each age band. For REGARDS, the IRD is the observed age-specific IRD in REGARDS. For truth in simulations, the causal IRD=20/10,000 person-years. For simulation scenario results, the IRD is the average of the observed age-specific IRD across 2,000 simulated samples for each simulation scenario.

^bSE = standard error. For REGARDS, the SE is the SE for REGARDS age-specific IRD estimates. For simulations, the SE is the empirical SE, calculated as the standard deviation of observed age-specific IRDs across the 2,000 simulated samples for each simulation scenario. The SEs (for REGARDS) and empirical SEs (simulations), increase across age bands because the number of people remaining alive and at risk for stroke declines with age (see proportion of birth cohort alive at each age in eTable 2).

^c% bias in the simulation estimates is defined as deviation from the truth, $100\ast ({\overline{\widehat{\text{IRD}}}}_{\text{observed}}-{\text{IRD}}_{\text{causal}})/{\text{IRD}}_{\text{causal}}$.

^dRMSE = root mean square error for simulations is defined as the square root of the mean squared deviation of the observed IRD from the causal IRD. The RMSE is influenced by both the bias and the variance of the observed IRD. Thus, the decrease in sample size across age bands contributes to the increase in RMSE across age bands.

^ePersonal communication with Dr. George Howard, PI of REGARDS Study, December 2016.

^fScenario A: U increases stroke risk, but has no direct effect on mortality risk.

^gScenario B: U increases stroke risk and mortality risk.

^hScenario C: U increases stroke risk for both blacks and whites, but only directly affects mortality for blacks.