Table 4.

Results of simulation study, when omitting X₂ (“instrumental variable,” ie, related only to exposures) from all analysis. Bias (standard deviation, SD) and mean squared error (MSE) of estimates

	Generalised Propensity Score Analysis				Generalised Prognostic Score Analysis
	Subclassification		Full Matching		Effect Modifier Included				Effect Modifier (Wrongfully) Ignored
					Subclassification		Full Matching		Subclassification		Full Matching
	Bias	MSE	Bias	MSE	Bias	MSE	Bias	MSE	Bias	MSE	Bias	MSE
	(SD)	×1000	(SD)	×1000	(SD)	×1000	(SD)	×1000	(SD)	×1000	(SD)	×1000
ATEB,A	−0.008	0.5453	0.000	0.7973	−0.005	0.4742	−0.001	0.6139	−0.005	0.4701	−0.001	0.6341
	(0.022)		(0.028)		(0.021)		(0.025)		(0.021)		(0.025)
ATEC,A	−0.007	0.9263	−0.001	1.3437	−0.004	0.7590	0.002	1.2912	−0.001	0.7366	0.005	1.3531
	(0.030)		(0.037)		(0.027)		(0.036)		(0.027)		(0.036)
ATEB,C	−0.002	0.9305	0.000	1.5498	−0.001	0.7497	−0.003	1.5167	−0.004	0.7570	−0.006	1.5963
	(0.030)		(0.039)		(0.027)		(0.039)		(0.027)		(0.040)
ATTB,A	−0.022	0.9290	−0.009	0.8251	−0.009	0.4550	0.000	0.5000	−0.009	0.4478	0.000	0.5061
	(0.021)		(0.027)		(0.020)		(0.022)		(0.019)		(0.023)
ATTC,A	−0.001	0.8189	0.013	1.5119	−0.009	0.8570	−0.001	0.9676	−0.009	0.8344	0.000	0.9533
	(0.029)		(0.037)		(0.028)		(0.031)		(0.028)		(0.031)
ATTB,C *	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐	‐
ATRB,A	−0.006	0.8355	−0.001	1.4711	−0.004	0.6121	−0.002	1.0467	−0.004	0.6059	−0.002	1.0727
	(0.028)		(0.038)		(0.024)		(0.032)		(0.024)		(0.033)
ATRC,A	−0.005	1.5473	−0.004	2.5417	−0.002	0.9275	0.002	1.9736	0.003	0.9174	0.009	2.1754
	(0.039)		(0.050)		(0.030)		(0.044)		(0.030)		(0.046)
ATRB,C	−0.001	1.8331	0.002	3.4033	−0.002	1.0085	−0.004	2.6074	−0.007	1.0342	−0.011	2.8121
	(0.043)		(0.058)		(0.032)		(0.051)		(0.031)		(0.052)

^* Due to nontransitivity, ATT_B,C was not estimated.