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. 2015 Jul 24;124(2):220–227. doi: 10.1289/ehp.1509693

Table 4.

Results from simulation studies comparing seven methods for serum lipid level adjustment when assessing the relationship between a serum biomarker and disease risk under different causal scenarios (Figure 2) and true effect sizes (true ORs = 2.0, 1.3, 1.0, 0.77, or 0.5).

Analysis method Scenario D Scenario E Scenario F
Bias (SE)a CI coverage Bias (SE)a CI coverage Bias (SE)a CI coverage
True OR = 2.0, true β for ETz = 0.650 (D and E) or 0.838 (F)
1. Unadjusted –0.15 (0.003) 0.63 –0.04 (0.004) 0.92 0.03 (0.006) 0.94
2. Standardizedb 0.01 (0.003) 0.95* 0.01 (0.003) 0.94* 0.01 (0.005) 0.94*
3. Covariate-adjusted standardization (CAS)b,c 0.01 (0.003) 0.94* 0.11 (0.004) 0.86 0.29 (0.006) 0.72
4. Covariate adjustment (CA)b 0.17 (0.004) 0.78 0.19 (0.004) 0.73 0.33 (0.007) 0.68
5. 2-stage modelb –0.12 (0.003) 0.73 –0.13 (0.004) 0.77 –0.02 (0.006) 0.92
6. Standardization plus CAb 0.01 (0.003) 0.94* 0.01 (0.003) 0.94* 0.01 (0.005) 0.94*
7. CAS plus CAb,c 0.01 (0.003) 0.94* 0.11 (0.004) 0.86 0.29 (0.006) 0.72
True OR = 1.3, true β for ETz = 0.245 (D and E) or 0.316 (F)
1. Unadjusted –0.05 (0.002) 0.90 –0.01 (0.002) 0.95* 0.01 (0.003) 0.96*
2. Standardizedb 0.00 (0.002) 0.94* 0.00 (0.002) 0.94* 0.00 (0.003) 0.96*
3. CASb,c 0.00 (0.002) 0.95* 0.04 (0.002) 0.93 0.09 (0.004) 0.89
4. CAb 0.06 (0.003) 0.91 0.06 (0.003) 0.88 0.10 (0.004) 0.88
5. 2-stage modelb –0.05 (0.002) 0.90 –0.05 (0.002) 0.91 –0.02 (0.003) 0.94*
6. Standardization plus CAb 0.00 (0.002) 0.95* 0.00 (0.002) 0.94* 0.00 (0.003) 0.96*
7. CAS plus CAb,c 0.00 (0.002) 0.95* 0.04 (0.002) 0.93 0.09 (0.004) 0.89
True OR = 1.0, true β for ETz = 0.0
1. Unadjusted 0.01 (0.002) 0.96* 0.01 (0.002) 0.96* 0.00 (0.003) 0.96*
2. Standardizedb 0.00 (0.002) 0.95* 0.00 (0.002) 0.95* 0.00 (0.003) 0.96*
3. CASb,c 0.00 (0.002) 0.95* 0.00 (0.002) 0.96* 0.00 (0.003) 0.97
4. CAb 0.00 (0.003) 0.95* 0.00 (0.003) 0.95* 0.00 (0.003) 0.97
5. 2-stage modelb 0.01 (0.002) 0.96* 0.01 (0.002) 0.96 0.01 (0.003) 0.96*
6. Standardization plus CAb 0.00 (0.002) 0.95* 0.00 (0.002) 0.95* 0.00 (0.003) 0.96*
7. CAS plus CAb,c 0.00 (0.002) 0.95* 0.00 (0.002) 0.95* 0.00 (0.003) 0.97
True OR = 0.77, true β for ETz = –0.245 (D and E) or –0.316 (F)
1. Unadjusted 0.06 (0.002) 0.85 0.02 (0.002) 0.95* 0.00 (0.003) 0.96*
2. Standardizedb 0.00 (0.002) 0.95* 0.00 (0.002) 0.95* 0.00 (0.003) 0.95*
3. CASb,c 0.00 (0.002) 0.95* –0.03 (0.002) 0.93 –0.07 (0.003) 0.91
4. CAb –0.06 (0.003) 0.90 –0.06 (0.003) 0.89 –0.08 (0.003) 0.90
5. 2-stage modelb 0.06 (0.002) 0.86 0.07 (0.002) 0.87 0.05 (0.003) 0.92
6. Standardization plus CAb 0.00 (0.002) 0.95* 0.00 (0.002) 0.95* 0.00 (0.003) 0.95*
7. CAS plus CAb,c 0.00 (0.002) 0.95* –0.03 (0.002) 0.93 –0.08 (0.003) 0.91
True OR = 0.5, true β for ETz = –0.650 (D and E) or –0.838 (F)
1. Unadjusted 0.17 (0.003) 0.55 0.06 (0.004) 0.90 0.01 (0.005) 0.94*
2. Standardizedb 0.00 (0.003) 0.94* –0.01 (0.003) 0.93 0.00 (0.004) 0.95*
3. CASb,c 0.00 (0.003) 0.95* –0.09 (0.004) 0.89 –0.22 (0.006) 0.78
4. CAb –0.16 (0.004) 0.79 –0.17 (0.004) 0.77 –0.26 (0.006) 0.74
5. 2-stage modelb 0.14 (0.003) 0.69 0.15 (0.004) 0.72 0.09 (0.005) 0.89
6. Standardization plus CAb 0.00 (0.003) 0.94* –0.01 (0.003) 0.93 –0.01 (0.004) 0.95*
7. CAS plus CAb,c 0.00 (0.003) 0.94* –0.09 (0.004) 0.89 –0.23 (0.006) 0.77
Abbreviations: ETz, target-tissue exposure z-score; EPz, proxy exposure z-score; SE, standard error; CI, confidence interval. Each simulation was repeated 1,000 times. Samples included 500 observations when the true OR = 2.0 or 0.5 and 1,000 observations otherwise. aBias is equal to the mean observed beta coefficient for βPz, which is either the serum exposure z-score (Methods 1, 4, 5) or the z-score for the serum exposure to lipid level ratio (Methods 2, 3, 6), minus the true beta coefficient for ETz. The standard deviation of the bias estimate is the square root of the average variance of βPz divided by the square root of the number of simulations. bE and F are adjusted for X. cSerum lipid levels are predicted using X. *CI coverage is consistent with 0.95 (0.95 ± 0.0135). Note that CI coverage values are rounded, and only those values that are consistent with 95% have been marked with an asterisk.