Skip to main content
. Author manuscript; available in PMC: 2020 Sep 1.
Published in final edited form as: Epidemiology. 2019 Sep;30(5):768–779. doi: 10.1097/EDE.0000000000001053

Table 2.

Performance comparisons for each causal scenario A, B and B’, for covariate-adjusted standardization using our urine pooling protocols vs. naïve standardization after equal-volume pooling for 1000 simulated studies of 500 cases and 500 controls each.

Beta Pool
size
Naïve Standardization Covariate-adjusted standardization using our
pooling protocols


95% CI
coverage
Bias (SE) 95% CI
coverage
Mean 95%
CI width
Power Bias (SE)
Scenario A
0 1a 0.95 −0.003 (0.003) 0.95 0.42 0.05 −0.003 (0.003)
0 2 0.96 0.000 (0.003) 0.95 0.42 0.05 0.003 (0.004)
0 5 0.95 −0.006 (0.003) 0.96 0.43 0.04 −0.008 (0.004)
0 10 0.95 −0.002 (0.003) 0.95 0.43 0.05 0.006 (0.004)
0.26 1a 0.95 0.003 (0.004) 0.95 0.44 0.97 0.003 (0.004)
0.26 2 0.93 −0.037 (0.003) 0.96 0.44 0.97 0.003 (0.004)
0.26 5 0.92 −0.036 (0.004) 0.95 0.46 0.96 0.008 (0.004)
0.26 10 0.93 −0.029 (0.004) 0.96 0.50 0.97 0.016 (0.004)
0.69 1a 0.95 0.008 (0.004) 0.95 0.50 1.00 0.008 (0.004)
0.69 2 0.81 −0.113 (0.004) 0.95 0.54 1.00 0.013 (0.004)
0.69 5 0.86 −0.102 (0.005) 0.96 0.66 1.00 0.031 (0.005)
0.69 10 0.88 −0.068 (0.007) 0.96 0.92 1.00 0.077 (0.008)
Scenario B
0 1a 0.95 0.001 (0.004) 0.95 0.44 0.06 0.001 (0.004)
0 2 0.95 −0.008 (0.003) 0.96 0.45 0.04 0.003 (0.004)
0 5 0.95 0.004 (0.004) 0.96 0.49 0.04 0.003 (0.004)
0 10 0.95 0.003 (0.004) 0.95 0.58 0.06 −0.010 (0.005)
0.26 1a 0.95 0.005 (0.004) 0.95 0.45 0.96 0.005 (0.004)
0.26 2 0.93 −0.047 (0.003) 0.95 0.47 0.96 0.005 (0.004)
0.26 5 0.93 −0.028 (0.004) 0.94 0.53 0.91 0.010 (0.005)
0.26 10 0.92 −0.016 (0.005) 0.96 0.65 0.84 0.031 (0.005)
0.69 1a 0.94 0.009 (0.004) 0.94 0.51 1.00 0.009 (0.004)
0.69 2 0.83 −0.123 (0.004) 0.97 0.56 1.00 0.013 (0.004)
0.69 5 0.87 −0.089 (0.006) 0.96 0.74 1.00 0.046 (0.006)
0.69 10 0.92 −0.021 (0.009) 0.96 1.15 1.00 0.118 (0.011)
Scenario B’
0 1a 0.95 −0.003 (0.003) 0.95 0.42 0.05 −0.003 (0.003)
0 2 0.95 0.000 (0.003) 0.95 0.42 0.05 0.003 (0.003)
0 5 0.95 −0.007 (0.003) 0.95 0.43 0.06 −0.002 (0.004)
0 10 0.95 0.002 (0.003) 0.96 0.43 0.04 0.000 (0.004)
0.26 1a 0.95 0.004 (0.004) 0.95 0.44 0.97 0.004 (0.004)
0.26 2 0.77 −0.110 (0.003) 0.95 0.44 0.97 0.009 (0.004)
0.26 5 0.8 −0.101 (0.003) 0.95 0.46 0.97 0.012 (0.004)
0.26 10 0.81 −0.087 (0.004) 0.95 0.50 0.96 0.017 (0.004)
0.69 1a 0.95 0.001 (0.004) 0.95 0.50 1.00 0.001 (0.004)
0.69 2 0.2 −0.311 (0.003) 0.96 0.54 1.00 0.010 (0.004)
0.69 5 0.39 −0.284 (0.004) 0.96 0.65 1.00 0.011 (0.005)
0.69 10 0.57 −0.256 (0.006) 0.96 0.92 1.00 0.071 (0.008)
a

Pool size of 1 means no pooling; analysis used individual observations. In each “pool size 1” row, entries are the same for both naïve standardization and for our proposed methods and are repeated only for convenience.