Assessing the properties of patient-specific treatment effect estimates from causal forest algorithms under essential heterogeneity

Table 2 Summary information for simulated populations

Simulation	A	B	C	D	E	F	G	H	I	J	K
	Proportion of true (TE_i) influencing expect treatment effect (ETE_i) – (K_i)^a	% of Treatment Choice Variation Explained by (TE_i)^b	Fully Observed Heterogeneity: % of Patients Overlapped^c	Partially Observed Heterogeneity: % of Patients Overlapped^d	Average True Absolute Treatment Effect (TE_i) Within Subset (Percentage of Patients)						Parametric Linear Probability Model Estimate (ATT)
					Full Population		Overlapped with Fully Observed Heterogeneity		Non-Overlapped with Fully Observed Heterogeneity
					Treated	Untreated	Treated	Untreated	Treated	Untreated
1	0	.0006	100	100	.250 (49.8)	.251 (50.2)	.250 (49.8)	.251 (50.2)			.249
2	.10	.18	100	100	.256 (49.8)	.246 (50.2)	.256 (49.8)	.246 (50.2)			.255
3	.20	1.4	100	100	.264 (50.0)	.237 (50.0)	.264 (50.0)	.237 (50.0)			.267
4	.30	5.3	100	100	.277 (50.1)	.224 (49.9)	.277 (50.1)	.224 (49.9)			.276
5	.40	11.9	100	100	.290 (50.1)	.212 (49.9)	.290 (50.1)	.212 (49.9)			.292
6	.50	20.1	100	100	.301 (50.2)	.200 (49.8)	.301 (50.2)	.200 (49.8)			.300
7	.60	27.8	97.0	100	.310 (50.2)	.191 (49.8)	.304 (48.7)	.196 (48.3)	.500 (1.5)	.001 (1.5)	.307
8	.70	34.5	90.7	100	.317 (50.3)	.184 (49.7)	.300 (45.5)	.200 (45.2)	.475 (4.8)	.025 (4.5)	.316
9	.80	39.8	84.5	100	.322 (50.2)	.179 (49.8)	.297 (42.3)	.203 (42.1)	.457 (7.9)	.044 (7.6)	.321
10	.90	44.3	78.3	100	.326 (50.2)	.175 (49.8)	.293 (39.2)	.207 (39.1)	.442 (11.0)	.059 (10.7)	.321
11	1.00	48.0	68.8	100	.329 (50.3)	.172 (49.7)	.285 (34.4)	.214 (34.4)	.423 (15.8)	.077 (15.3)	.329

^aThe proportion of patient-specific TE_i knowledge used by decision makers in simulation “j” in developing the expected treatment effect for patient “i” that is distinct from the population average treatment effect based on the equation ETE_i = K_j * (TE_i(X_1i,X_2i,X_3i,X_4i,X_5i,X_6i)—.25) + .25. The population average treatment effect is .25 in all simulations
^bThe percentage of treatment choice variation explained by TE_i using a linear probability model of treatment choice T_i on true TE_i using SAS PROC REG procedure with the SCORR1 option
^cPercentage of patients in sample with treatment propensity score greater than .05 and less than .95 when all six patient factors are fully specified in the propensity score equation
^dPercentage of patients in sample with treatment propensity score greater than .05 and less than .95 when only X_1i, X_2i, X_3i, X_4i factors are specified in the propensity score equation

ISSN: 1471-2288