Appendix Table 3.

Example Data for 10,000 Individuals in 2 Populations (High-Risk and Low-Risk) for a Scenario in Which the Unmeasured Covariate U Is a Cause of the Outcome Y Only^a

Unmeasured Variable and Covariateb	High-Risk Population				Low-Risk Population
	A = 0		A = 1		A = 0		A = 1
	Y = 1	Y = 0	Y = 1	Y = 0	Y = 1	Y = 0	Y = 1	Y = 0
U = 0
L = 1	260	1,473	37	211	402	2,276	57	326
L = 0	318	1,799	210	1,192	491	2,781	325	1,842
U = 1
L = 1	780	638	112	91	260	213	37	31
L = 0	953	779	631	516	317	260	210	172

^a The causal graph for this scenario is depicted in Appendix Figure 3. In the example data, the true causal effects of treatment A, and measured covariate L on the outcome Y are null.

^bA is an indicator for treatment (1 if treated, 0 otherwise), L is an indicator for a measured covariate (such as CD4 count), Y is an indicator for mortality, and U is an indicator for an unmeasured covariate, such as underlying immune function.