Table 3 Simulation results from PLSI PH model and Cox PH model
Variable | True rank | True coefficient | PLSI PH rank | PLSI PH estimate | PLSI PH 95% CI | PLSI PH Proportion of contribution (%) | Cox PH rank | Cox PH original estimate | Cox PH original 95% CI | Cox PH normed estimate | Cox PH normed 95% CI |
|---|---|---|---|---|---|---|---|---|---|---|---|
Identity link function | |||||||||||
 Environmental factors | |||||||||||
  a-Tocopherol | 1 | 0.560 | 1 | 0.546 | (0.437, 0.656) | 29.9 | 1 | 0.558 | (0.428, 0.688) | 0.546 | (0.446, 0.646) |
  g-tocopherol | 2 | 0.490 | 2 | 0.500 | (0.427, 0.572) | 25.0 | 2 | 0.511 | (0.417, 0.605) | 0.500 | (0.428, 0.571) |
  Retinyl-palmitate | 3 | 0.420 | 3 | 0.408 | (0.297, 0.520) | 16.7 | 3 | 0.418 | (0.310, 0.526) | 0.409 | (0.301, 0.516) |
  Retinol | 7 | 0.140 | 7 | 0.122 | (0.029, 0.216) | 1.5 | 7 | 0.125 | (0.029, 0.221) | 0.122 | (0.034, 0.210) |
  3,3,4,4,5-pncb | 8 | 0.070 | 8 | 0.059 | (−0.039, 0.158) | 0.4 | 8 | 0.061 | (− 0.040, 0.161) | 0.059 | (− 0.033, 0.151) |
  PCB194 | 6 | −0.210 | 6 | −0.207 | (− 0.346, − 0.068) | 4.3 | 6 | − 0.212 | (− 0.351, − 0.074) | − 0.208 | (− 0.329, − 0.087) |
  2.3.4.6.7.8.hxcdf | 5 | − 0.280 | 5 | − 0.270 | (− 0.356, − 0.183) | 7.3 | 5 | − 0.275 | (− 0.367, − 0.183) | − 0.269 | (− 0.354, − 0.185) |
  trans.b.carotene | 4 | − 0.350 | 4 | − 0.388 | (− 0.467, − 0.310) | 15.1 | 4 | − 0.397 | (− 0.493, − 0.302) | −0.389 | (− 0.465, − 0.313) |
 Covariates | |||||||||||
  Age |  | 0.005 |  | 0.009 | (0.001, 0.017) |  |  | 0.009 | (0.002, 0.016) |  |  |
  Sex (female) |  | −0.076 |  | −0.039 | (− 0.216, 0.138) |  |  | −0.039 | (− 0.217, 0.138) |  |  |
 Race/Ethnicity | |||||||||||
  Non-Hispanic white |  | Ref |  | Ref |  |  |  | Ref |  |  |  |
  Non-Hispanic black |  | −0.138 |  | −0.135 | (− 0.367, 0.097) |  |  | −0.135 | (− 0.361, 0.091) |  |  |
  Mexican American |  | 0.175 |  | 0.114 | (−0.116, 0.344) |  |  | 0.114 | (−0.107, 0.335) |  |  |
  Other race |  | 0.409 |  | 0.528 | (0.118, 0.937) |  |  | 0.528 | (0.077, 0.978) |  |  |
  Other Hispanic |  | 0.355 |  | 0.477 | (−0.021, 0.975) |  |  | 0.477 | (0.018, 0.936) |  |  |
Quadratic link function | |||||||||||
 Environmental factors | |||||||||||
  a-Tocopherol | 1 | 0.560 | 1 | 0.526 | (0.403, 0.648) | 27.6 | 1 | 0.289 | (0.124, 0.455) | 0.861 | (0.621, 1.101) |
  g-tocopherol | 2 | 0.490 | 2 | 0.513 | (0.296, 0.730) | 26.3 | 3 | 0.098 | (−0.011, 0.207) | 0.292 | (−0.024, 0.607) |
  Retinyl-palmitate | 3 | 0.420 | 3 | 0.445 | (0.231, 0.659) | 19.8 | 6 | 0.037 | (−0.088, 0.161) | 0.109 | (−0.253, 0.470) |
  Retinol | 7 | 0.140 | 7 | 0.161 | (0.041, 0.281) | 2.6 | 4 | −0.041 | (− 0.154, 0.072) | − 0.122 | (− 0.465, 0.222) |
  3,3,4,4,5-pncb | 8 | 0.070 | 8 | 0.061 | (−0.023, 0.146) | 0.4 | 8 | 0.013 | (−0.102, 0.128) | 0.040 | (− 0.305, 0.384) |
  PCB194 | 6 | −0.210 | 6 | −0.208 | (−0.322, − 0.093) | 4.3 | 7 | 0.020 | (−0.132, 0.172) | 0.059 | (− 0.338, 0.457) |
  2.3.4.6.7.8.hxcdf | 5 | − 0.280 | 5 | −0.252 | (− 0.392, − 0.113) | 6.4 | 5 | − 0.039 | (− 0.138, 0.061) | − 0.115 | (− 0.445, 0.215) |
  trans.b.carotene | 4 | − 0.350 | 4 | − 0.355 | (− 0.477, − 0.234) | 12.6 | 2 | − 0.120 | (− 0.228, − 0.012) | −0.358 | (− 0.637, − 0.079) |
 Covariates | |||||||||||
  Age |  | 0.005 |  | 0.003 | (−0.002, 0.008) |  |  | −0.005 | (−0.012, 0.003) |  |  |
  Sex (female) |  | − 0.076 |  | −0.081 | (−0.269, 0.108) |  |  | −0.103 | (−0.297, 0.092) |  |  |
 Ethnicity | |||||||||||
  Non-Hispanic white |  | Ref |  | Ref |  |  |  | Ref |  |  |  |
  Non-Hispanic black |  | −0.138 |  | 0.044 | (− 0.211, 0.299) |  |  | 0.083 | (−0.154, 0.320) |  |  |
  Mexican American |  | 0.175 |  | 0.100 | (−0.152, 0.352) |  |  | 0.125 | (−0.118, 0.369) |  |  |
  Other race |  | 0.409 |  | 0.186 | (−0.438, 0.811) |  |  | −0.189 | (−0.722, 0.345) |  |  |
  Other Hispanic |  | 0.355 |  | 0.096 | (−0.567, 0.759) |  |  | −0.096 | (− 0.634, 0.442) |  |  |