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Interval Regression Results for TCDF Including Fish and Game Dioxin Congener Intake
and Air Concentration Estimates
Heidi Reichert, MA Brenda Gillespie, PhD
The University of Michigan, Ann Arbor, MI, USASchool of Public Health
Institute for Social ResearchCollege of Engineering
Center for Statistical Consultation & Research
Scientific Advisory Board MeetingDecember 14, 2009
University of Michigan Dioxin Exposure Study December 14, 2009Slide 2
Study Team and Funding
• School of Public HealthDavid Garabrant, MD, MPH Alfred Franzblau, MDOlivier Jolliet, PhDLynn Zwica, MSKristine Knutson, MPH Elizabeth Hedgeman, MS, MPHQixuan Chen, PhDBiling Hong, MAShih-Yuan Lee, MSChiung-Wen Chang, MSXiaohui Jiang, MSXiaobo Zhong, MSMeghan Milbrath, MPHYvan Wenger, MSSharyn VantineWei Hao, MA
• LimnoTechTim Towey, MSNoémi Barabas, PhD
• Center for Statistical Consultation and Research
Brenda W. Gillespie, PhD Heidi Reichert, MADanielle GwinnScott Swan, MSCamelia Sima, MS
• College of EngineeringPeter Adriaens, PhD, PE Avery Demond, PhD, PEShu-Chi Chang, PhD Hoa Trinh, MS
• Institute for Social ResearchJames Lepkowski, PhD, MPHBarbara Lohr Ward, MBA Kathy LadronkaKristen Olson, PhDJennifer Sinibaldi, MS
This study was funded by The Dow Chemical Co. through an unrestricted grant to the University of Michigan. The University has complete independence to design, carry out and report all aspects of the study.
University of Michigan Dioxin Exposure Study December 14, 2009Slide 3
Background
• Regression modeling of congener concentrations in UMDES has used the SAS software for ordinary linear regression with adjustment for the sampling design (survey weights, stratification, and clustering).
• These models have used data with values below the limit of detection (LOD) replaced by LOD/sqrt(2).
• Interval regression models assume that values below LOD are left-censored, and incorporate the censoring into the model estimates.
University of Michigan Dioxin Exposure Study December 14, 2009Slide 4
Background – Software constraints
• Comparison of linear regression using LOD/sqrt(2) versus left-censored regression showed similar results when the % <LOD was small (e.g., <20%) (Gillespie et al., poster at Dioxin 2006 - Oslo).
• For TCDF (~68% below LOD), we used Statasoftware, which performs left-censored regression with survey design adjustment.
• SAS software for left-censored regression models does not allow adjustment for the survey design.
University of Michigan Dioxin Exposure Study December 14, 2009Slide 5
OLS vs. left-censored regression
• OLS = Ordinary Least Squares:– Estimates of β minimize Σi (Yi - Xβ)2
– Values below LOD are replaced by LOD/√2• Left-censored regression is based on the
likelihood function:– L(β,σ) = Πi∈{>LOD} f(yi | xi) Πi∈{<LOD} F(yi |xi)– If Y|X is normally distributed, then
log(L) ~ c1 + c2 Σ i∈{>LOD} (Yi - Xβ)2
+ c3 Σ i∈{<LOD} log Φ( Yi - Xβ)– If all >LOD, OLS = left-censored regression
University of Michigan Dioxin Exposure Study December 14, 2009Slide 6
Same as for the other short half-life congeners
Response variable: Log10(blood)
Predictor variables: Only recent (after 1980) exposure variables included (TCDF half-life: 2.1 yrs)
Forward stepwise selection was applied to identify factors that predict the serum dioxin levels.
Modeling strategy for TCDF with fish, game, air concentrations
Step 1: force in demographics and soil HP1 and SC0-6.Step 2: force in age, gender. Allow variables selected in step 1 to enter.Step 3: test interaction terms and combinations of variables of primary interest.Step 4: simplify model by deleting variables with wrong sign.Step 5: regression diagnostics.
University of Michigan Dioxin Exposure Study December 14, 2009Slide 7
Linear Regression models – new variables created.Fish and game congener intake, air concentration, log10(soil concentration)
Dioxin congener intake from fish from contaminated area (all species, TR/SR/SB)Fish_tr_sagrb_2378_TCDF
Dioxin congener intake from all other fish (sport caught elsewhere, store bought, restaurant)Fish_else_2378_TCDF
Dioxin congener intake from game from contaminated area (all species, TR/SR/SB)gmeat_tr_sagrb_2378_TCDF
Dioxin congener intake from all other game (sport caught elsewhere)gmeat_else_2378_TCDF
Air dioxin concentration in three time periods 1940-59, 1960-83, after 1984AC_40-59 AC_60_83 AC_after84
For 3 soil variables: HP1, SC, SoilMax log10(Soil variables) were created s_2378_TCDF_sqr2_SC lg_s_2378_TCDF_sqr2_SC
University of Michigan Dioxin Exposure Study December 14, 2009Slide 8
Linear Regression models for TCDF- final model, stable variables only
Factor 10^β PvalueDemoAge at interview - 50 yrs 1.010 0.198Gender, 1 for Female; 0 for Male 0.801 0.272Fish ConsumptionNum. of yrs ate any fish after 1980 1.040 0.011
Of 946 subjects, 645 were below LOD, 301 had observed values.
University of Michigan Dioxin Exposure Study December 14, 2009Slide 9
Linear Regression models for TCDF: final model plus 1
AIC, Adjusted R2 not readily available for interval regression models in the survey setting. Predictors evaluated based on p-values.
• Soil max was significant but unstable (due to one influential observation).• Fish from TR/SR/SB was marginally significant.• All remaining variables were not significant, or had negative slope.
Estimate = β, so when β is <0, 10β is less than 1 (inverse association)
Parm Estimate Pvalues_2378_tcdf_sqr2_hp1 8.3E-05 0.466s_2378_tcdf_sqr2_sc -4.2E-05 0.863s_2378_tcdf_sqr2_max 2.0E-05 0.000lg_s_2378_tcdf_sqr2_hp1 0.040 0.491lg_s_2378_tcdf_sqr2_sc -0.170 0.022lg_s_2378_tcdf_sqr2_max 0.033 0.536d_2378_tcdf_sqr2 -0.001 0.725d_2378_tcdf_sqr2_load -0.001 0.288lg_d_2378_tcdf_sqr2 0.041 0.688lg_d_2378_tcdf_sqr2_load -0.007 0.918ac_after84 -0.578 0.211lg_ac_after84 -0.024 0.652fish_tr_sagrb_2378_tcdf 0.001 0.061fish_else_2378_tcdf 0.002 0.434gmeat_else_2378_tcdf 0.036 0.889gmeat_tr_sagrb_2378_tcdf 0.042 0.380
University of Michigan Dioxin Exposure Study December 14, 2009Slide 10
parm avest p avest p avest p avest p avest p avest p avest pac_after84 -0.490113 0.282449lg_ac_after84 -0.025217 0.643732s_2378_tcdf_sqr2_hp1 8.94E-05 0.444734s_2378_tcdf_sqr2_sc -3.64E-05 0.890647s_2378_tcdf_sqr2_max 1.98E-05 2.50E-11 1.98E-05 2.50E-11 2.02E-05 1.05E-11 2.05E-05 8.32E-11lg_s_2378_tcdf_sqr2_hp1 0.043783 0.452399lg_s_2378_tcdf_sqr2_sclg_s_2378_tcdf_sqr2_maxd_2378_tcdf_sqr2d_2378_tcdf_sqr2_loadlg_d_2378_tcdf_sqr2lg_d_2378_tcdf_sqr2_loadfish_tr_sagrb_2378_tcdffish_else_2378_tcdfgmeat_tr_sagrb_2378_tcdfgmeat_else_2378_tcdf_Ieggd_tr_c_1 0.384705 0.102504 0.384705 0.102504 0.378679 0.100888 0.387658 0.089562 0.382253 0.104078 0.381043 0.104782 0.368604 0.119041_Ieggd_tr_c_2 -1.501473 3.20E-09 -1.501473 3.20E-09 -1.4328 3.37E-08 -1.471529 1.55E-08 -1.502623 3.07E-09 -1.497885 3.23E-09 -1.53525 2.94E-09_Ihnt_tr_80_1 0.733308 8.63E-08 0.733308 8.63E-08 0.736662 4.72E-08 0.753579 2.51E-08 0.738215 2.91E-08 0.741597 2.85E-08 0.713674 3.71E-09_Ihnt_tr_80_2 -0.121465 0.527115 -0.121465 0.527115 -0.130183 0.491333 -0.118745 0.533838 -0.124488 0.516626 -0.12549 0.512272 -0.123734 0.521793_cons -1.205916 1.58E-08 -1.205916 1.58E-08 -1.182229 5.78E-08 -1.181215 7.68E-08 -1.202955 1.26E-08 -1.202438 1.24E-08 -1.206952 1.03E-08age_center 0.004208 0.197033 0.004208 0.197033 0.004294 0.187238 0.004359 0.177486 0.004245 0.192702 0.00426 0.192125 0.004065 0.18867age_sq_centerbf_total_lifetimebmi_centeregg_dairy_sag_rb_d 0.419507 0.012961 0.419507 0.012961 0.41627 0.012104 0.436572 0.011413 0.419315 0.012669 0.417781 0.012833 0.418769 0.011016f4_after80_yrs 0.016754 0.013889 0.016754 0.013889 0.016716 0.014021 0.016697 0.013359 0.016741 0.013906 0.016797 0.013702 0.016842 0.013059female -0.087224 0.331903 -0.087224 0.331903 -0.090571 0.320192 -0.090706 0.325878 -0.091461 0.306242 -0.091615 0.305661 -0.090407 0.30314packyrs_Ihnt_tr_80_d
Step 6 Step 7 Step 8Step 5Step 3 (no change)Step2 Step 4
Linear Regression models for 2378-TCDF: forcing variables of interest into the model.
•Exploration of AC and soil variables Slide 1 of 2
University of Michigan Dioxin Exposure Study December 14, 2009Slide 11
parm avest p avest p avest p avest p avest p avest p avest pac_after84 -0.490113 0.282449lg_ac_after84 -0.025217 0.643732s_2378_tcdf_sqr2_hp1 8.94E-05 0.444734s_2378_tcdf_sqr2_sc -3.64E-05 0.890647s_2378_tcdf_sqr2_max 1.98E-05 2.50E-11 1.98E-05 2.50E-11 2.02E-05 1.05E-11 2.05E-05 8.32E-11lg_s_2378_tcdf_sqr2_hp1 0.043783 0.452399lg_s_2378_tcdf_sqr2_sclg_s_2378_tcdf_sqr2_maxd_2378_tcdf_sqr2d_2378_tcdf_sqr2_loadlg_d_2378_tcdf_sqr2lg_d_2378_tcdf_sqr2_loadfish_tr_sagrb_2378_tcdffish_else_2378_tcdfgmeat_tr_sagrb_2378_tcdfgmeat_else_2378_tcdf_Ieggd_tr_c_1 0.384705 0.102504 0.384705 0.102504 0.378679 0.100888 0.387658 0.089562 0.382253 0.104078 0.381043 0.104782 0.368604 0.119041_Ieggd_tr_c_2 -1.501473 3.20E-09 -1.501473 3.20E-09 -1.4328 3.37E-08 -1.471529 1.55E-08 -1.502623 3.07E-09 -1.497885 3.23E-09 -1.53525 2.94E-09_Ihnt_tr_80_1 0.733308 8.63E-08 0.733308 8.63E-08 0.736662 4.72E-08 0.753579 2.51E-08 0.738215 2.91E-08 0.741597 2.85E-08 0.713674 3.71E-09_Ihnt_tr_80_2 -0.121465 0.527115 -0.121465 0.527115 -0.130183 0.491333 -0.118745 0.533838 -0.124488 0.516626 -0.12549 0.512272 -0.123734 0.521793_cons -1.205916 1.58E-08 -1.205916 1.58E-08 -1.182229 5.78E-08 -1.181215 7.68E-08 -1.202955 1.26E-08 -1.202438 1.24E-08 -1.206952 1.03E-08age_center 0.004208 0.197033 0.004208 0.197033 0.004294 0.187238 0.004359 0.177486 0.004245 0.192702 0.00426 0.192125 0.004065 0.18867age_sq_centerbf_total_lifetimebmi_centeregg_dairy_sag_rb_d 0.419507 0.012961 0.419507 0.012961 0.41627 0.012104 0.436572 0.011413 0.419315 0.012669 0.417781 0.012833 0.418769 0.011016f4_after80_yrs 0.016754 0.013889 0.016754 0.013889 0.016716 0.014021 0.016697 0.013359 0.016741 0.013906 0.016797 0.013702 0.016842 0.013059female -0.087224 0.331903 -0.087224 0.331903 -0.090571 0.320192 -0.090706 0.325878 -0.091461 0.306242 -0.091615 0.305661 -0.090407 0.30314packyrs_Ihnt_tr_80_d
Step 6 Step 7 Step 8Step 5Step 3 (no change)Step2 Step 4
Linear Regression models for 2378-TCDF: forcing variables of interest into the model.
•Exploration of AC and soil variables Slide 1 of 2
Starting model
Force AC, log AC, and other soil variables in
one by one. None significant.Soil max is
significant and positive.
University of Michigan Dioxin Exposure Study December 14, 2009Slide 12
parm avest p avest p avest p avest p avest p avest p avest pac_after84lg_ac_after84s_2378_tcdf_sqr2_hp1s_2378_tcdf_sqr2_scs_2378_tcdf_sqr2_max 1.98E-05 2.50E-11lg_s_2378_tcdf_sqr2_hp1lg_s_2378_tcdf_sqr2_sc -0.159493 0.029633lg_s_2378_tcdf_sqr2_max 0.0344 0.511246d_2378_tcdf_sqr2 -0.001729 0.546608d_2378_tcdf_sqr2_load -0.001259 0.195907lg_d_2378_tcdf_sqr2 0.035195 0.730357lg_d_2378_tcdf_sqr2_load -0.007898 0.904977fish_tr_sagrb_2378_tcdffish_else_2378_tcdfgmeat_tr_sagrb_2378_tcdfgmeat_else_2378_tcdf_Ieggd_tr_c_1 0.384705 0.102504 0.46354 0.032488 0.370229 0.121397 0.414185 0.052162 0.418409 0.047184 0.377108 0.119254 0.379178 0.105189_Ieggd_tr_c_2 -1.501473 3.20E-09 -1.654194 1.04E-07 -1.526214 2.65E-09 -1.494783 3.58E-09 -1.490719 4.07E-09 -1.500959 2.97E-09 -1.495838 3.51E-09_Ihnt_tr_80_1 0.733308 8.63E-08 0.740147 8.74E-08 0.702083 2.57E-09 0.764459 8.28E-09 0.860687 3.95E-07 0.708474 7.67E-08 0.751133 1.69E-06_Ihnt_tr_80_2 -0.121465 0.527115 -0.041526 0.844615 -0.123998 0.522851 -0.124784 0.512128 -0.119665 0.526005 -0.126783 0.514032 -0.123653 0.515944_cons -1.205916 1.58E-08 -1.282565 4.34E-05 -1.208727 1.28E-08 -1.19669 1.90E-08 -1.195313 1.79E-08 -1.209063 2.10E-08 -1.200679 2.13E-08age_center 0.004208 0.197033 -0.004519 0.235279 0.004102 0.186263 0.004277 0.189387 0.004228 0.194566 0.004152 0.192699 0.004228 0.199252age_sq_centerbf_total_lifetimebmi_centeregg_dairy_sag_rb_d 0.419507 0.012961 0.388187 0.006066 0.421914 0.011033 0.415064 0.013614 0.414017 0.014743 0.415216 0.013343 0.418885 0.013488f4_after80_yrs 0.016754 0.013889 0.021024 0.047148 0.016774 0.013375 0.016787 0.01392 0.016763 0.01459 0.016855 0.013282 0.016796 0.013912female -0.087224 0.331903 -0.115888 0.300284 -0.090038 0.307864 -0.091597 0.307834 -0.088426 0.332258 -0.09141 0.301556 -0.091798 0.30563
Step12 Step13 Step14Step11Step9Step2 Step10
Linear Regression models for 2378-TCDF: forcing variables of interest into model.
Exploration of AC and soil variables Slide 2 of 2
University of Michigan Dioxin Exposure Study December 14, 2009Slide 13
parm avest p avest p avest p avest p avest p avest p avest pac_after84lg_ac_after84s_2378_tcdf_sqr2_hp1s_2378_tcdf_sqr2_scs_2378_tcdf_sqr2_max 1.98E-05 2.50E-11lg_s_2378_tcdf_sqr2_hp1lg_s_2378_tcdf_sqr2_sc -0.159493 0.029633lg_s_2378_tcdf_sqr2_max 0.0344 0.511246d_2378_tcdf_sqr2 -0.001729 0.546608d_2378_tcdf_sqr2_load -0.001259 0.195907lg_d_2378_tcdf_sqr2 0.035195 0.730357lg_d_2378_tcdf_sqr2_load -0.007898 0.904977fish_tr_sagrb_2378_tcdffish_else_2378_tcdfgmeat_tr_sagrb_2378_tcdfgmeat_else_2378_tcdf_Ieggd_tr_c_1 0.384705 0.102504 0.46354 0.032488 0.370229 0.121397 0.414185 0.052162 0.418409 0.047184 0.377108 0.119254 0.379178 0.105189_Ieggd_tr_c_2 -1.501473 3.20E-09 -1.654194 1.04E-07 -1.526214 2.65E-09 -1.494783 3.58E-09 -1.490719 4.07E-09 -1.500959 2.97E-09 -1.495838 3.51E-09_Ihnt_tr_80_1 0.733308 8.63E-08 0.740147 8.74E-08 0.702083 2.57E-09 0.764459 8.28E-09 0.860687 3.95E-07 0.708474 7.67E-08 0.751133 1.69E-06_Ihnt_tr_80_2 -0.121465 0.527115 -0.041526 0.844615 -0.123998 0.522851 -0.124784 0.512128 -0.119665 0.526005 -0.126783 0.514032 -0.123653 0.515944_cons -1.205916 1.58E-08 -1.282565 4.34E-05 -1.208727 1.28E-08 -1.19669 1.90E-08 -1.195313 1.79E-08 -1.209063 2.10E-08 -1.200679 2.13E-08age_center 0.004208 0.197033 -0.004519 0.235279 0.004102 0.186263 0.004277 0.189387 0.004228 0.194566 0.004152 0.192699 0.004228 0.199252age_sq_centerbf_total_lifetimebmi_centeregg_dairy_sag_rb_d 0.419507 0.012961 0.388187 0.006066 0.421914 0.011033 0.415064 0.013614 0.414017 0.014743 0.415216 0.013343 0.418885 0.013488f4_after80_yrs 0.016754 0.013889 0.021024 0.047148 0.016774 0.013375 0.016787 0.01392 0.016763 0.01459 0.016855 0.013282 0.016796 0.013912female -0.087224 0.331903 -0.115888 0.300284 -0.090038 0.307864 -0.091597 0.307834 -0.088426 0.332258 -0.09141 0.301556 -0.091798 0.30563
Step12 Step13 Step14Step11Step9Step2 Step10
Linear Regression models for 2378-TCDF: forcing variables of interest into model.
Exploration of AC and soil variables Slide 2 of 2
Log soil, dust and log dust entered.
No changes.
University of Michigan Dioxin Exposure Study December 14, 2009Slide 14
Conclusions
Number of years eating any fish after 1980 is positively associated with serum TCDF.
Fish intake from TR/SR/SB is marginally associated with TCDF (p=.062).
Fish intake from elsewhere and game meat consumption were not found to be associated with TCDF. Neither were dust or air concentration.
Soil max was significant due to one influential observation, whose removal rendered the variable insignificant. No other soil variables were found to have a significant, positive relationship with TCDF.
University of Michigan Dioxin Exposure Study December 14, 2009Slide 15
END