Comparison of robustness to outliers between robust poisson models and log-binomial models when estimating relative risks for common binary outcomes: a simulation study

Table 1 Relative bias (%) in log scale (n = 1500)

RR	Prob (Y = 1)	Contamination rate	Association bet Z and Y: Linear		Association bet Z and Y: Linear		Association bet Z and Y: Non-Linear		Association bet Z and Y: Non-Linear
RR	Prob (Y = 1)	Contamination rate	Level of association bet Z and X, Z and Y: Moderate		Level of association bet Z and X, Z and Y: Strong		Level of association bet Z and X, Z and Y: Moderate		Level of association bet Z and X, Z and Y: Strong
			LB	RP	LB	RP	LB	RP	LB	RP
1.5	10%	0%	1.8	1.8	2.0	2.0	0.0	0.0	−0.6	−0.8
		2%	−17.8	−16.7	−16.0	−16.0	−30.0	−19.5	−28.5	−20.4
		5%	−43.4	−36.7	−41.8	−36.9	−51.7	−41.3	−49.1	−43.0
	25%	0%	−0.4	−0.4	0.4	0.3	0.5	0.5	−0.8	−0.8
		2%	−10.4	−10.9	−10.1	−11.4	−14.1	−11.8	−18.6	−16.2
		5%	−25.3	−24.4	−26.6	−27.3	−34.6	−28.2	−43.4	−36.2
	40%	0%	0.2	0.2	−0.7	−0.7	−0.0	−0.1	0.9	0.7
		2%	−7.5	−8.0	−9.8	−10.8	−11.0	−10.5	−14.9	−13.1
		5%	−19.2	−19.4	−23.4	−24.6	−26.9	−24.7	−36.9	−32.2
2.0	10%	0%	0.4	0.4	1.5	1.5	−0.2	−0.2	0.6	0.7
		2%	−18.9	−18.1	−17.1	−16.8	−26.3	−19.0	−25.0	−18.0
		5%	−42.0	−37.5	−40.2	−36.7	−47.9	−39.5	−47.4	−39.6
	25%	0%	0.5	0.5	0.3	0.3	0.3	0.3	0.9	0.8
		2%	−9.0	−9.2	−9.2	−9.9	−12.3	−10.4	−13.7	−11.7
		5%	−23.3	−22.2	−23.7	−23.6	−30.0	−24.7	−34.5	−28.5
	40%	0%	−0.1	−0.1	0.1	0.1	0.3	0.3	−0.3	−0.3
	40%	2%	−6.7	−7.0	−7.2	−7.8	−8.4	−8.0	−10.9	−10.2
		5%	−16.9	−16.6	−18.5	−19.0	−21.2	−19.5	−26.6	−24.5

Association between Z and X always linear.
LB: Log-Binomial Model.
RP: Robust Poisson.
Relative bias was defined as the average of the 1,000 estimated RR in log scale minus the log of the true RR divided by the log of the true RR.

ISSN: 1471-2288