1. Lipids Standardization and DAGs Enrique Schisterman, PhD Epidemiology Branch – DESPR – NICHD 1

2. Background  PCBs are lipophilic xenobiotics  Literature on exposure to PCBs is conflicting  Poses challenges for interpretation of potential health risks  Differences in laboratory practices may account for some of the equivocal findings 2

3. Background  Limited understanding of the true relations between:  Serum and adipose tissue concentrations of PCBs  Serum PCBs and serum lipids  Which in turn makes model specification difficult 3

4. Background  Investigators typically make assumptions about the relation between serum lipids and serum PCBs expressing PCB measurements as:  Wet-weight (PCB per unit serum)  Lipid-standardization value (PCB concentration per unit lipids)  Adjusted model (Lipids are separate term)  Two-stage analysis (Lipids are regressed on PCBs with residuals entered as individual risk factors) 4

5. Lipid Standardization  The various strategies for handling serum lipids imply different causal pathways  What is considered best practice in the lab may have an unintended impact on data analysis 5

6. Objectives  Describe 4 proposed approaches for handling serum lipids  Show the impact of different common statistical modeling approaches on risk estimates  Evaluate the bias under a range of plausible causal systems  Determine which model best reflects underlying causal assumptions 6

7. Proposed Approach 1  Unadjusted: Wet-weight values  PCBs per unit serum 7

8. Proposed Approach 2  Lipid Standardization  PCB concentration per unit of lipids 8

9. Proposed Approach 3  Adjusted  Lipids is a separate term  Lipids is a predictor/potential confounder 9

10. Proposed Approach 4  Two-stage model  Lipids are regressed on PCBs with residuals entered as individual risk factors 10

11. Proposed Approaches  Unadjusted: Wet-weight values  Lipid Standardized  Adjusted  Two-Stage 11

12. Simulation Study  To evaluate the impact of these approaches for handling serum lipids in models on risk estimates, Schisterman et al. simulated data from a log normal distribution to determine bias  They varied:  True underlying causal relations  Statistical model used for risk estimates  Relation between PCBs and serum lipids  Measurement error in serum lipids 12

13. DAG A: Simple cause & effect  PCB S causes Y, Lipids unrelated PCB S Y Lipids 13

14. DAG A: Simple cause & effect  PCB S causes Y, Lipids unrelated PCB S Y Lipids Modellogit(Y)=…% Bias UnadjustedPCB S -0.8 StandardizedPCB S / Lipids-75.9 AdjustedPCB S + Lipids-0.7 Two-stagePCB S + Residuals-0.7 14

15. DAG A: Simple cause & effect  PCB S causes Y, Lipids unrelated PCB S Y Lipids Modellogit(Y)=…% Bias UnadjustedPCB S -0.8 StandardizedPCB S / Lipids-75.9 AdjustedPCB S + Lipids-0.7 Two-stagePCB S + Residuals-0.7 15

16. DAG A: Extensions PCB S Y Lipids PCB S Y Lipids 1 PCB S Y Lipids PCB S Y Lipids A 23 ModelA123 Unadjusted-0.81.20.4-0.4 Standardized-75.9-51.3-79.8-85.0 Adjusted-0.71.80.8-0.1 Two-stage-0.71.80.5-0.3 16

17. DAG B: Confounding  U causes PCB S and Lipids, both cause Y PCB S Y LipidsU 17

18. DAG B: Confounding  U causes PCB S and Lipids, both cause Y PCB S Y LipidsU Modellogit(Y)=…% Bias UnadjustedPCB S 24.0 StandardizedPCB S / Lipids-128.8 AdjustedPCB S + Lipids0.1 Two-stagePCB S + Residuals27.2 18

19. DAG B: Extensions ModelB12 Unadjusted24.0-15.4-11.2 Standardized-128.8-351.3-128.3 Adjusted0.1-99.4-25.4 Two-stage27.21.1-8.7 PCB S Y Lipids PCB S Y Lipids 1 PCB S Y Lipids 2 A 19

20. DAG B: Extensions PCB S Y Lipids PCB S Y Lipids 1 PCB S Y Lipids 2 ModelB12 Unadjusted24.0-15.4-11.2 Standardized-128.8-351.3-128.3 Adjusted0.1-99.4-25.4 Two-stage27.21.1-8.7 A Overadjustment 20

21. DAG C: PCB S per Lipids as Ascending Proxy  PCB in adipose tissue causes PCB in serum per lipids, and causes Y PCB S /LipidsY PCB A 21

22. DAG C: PCB S per Lipids as Ascending Proxy  PCB in adipose tissue causes PCB in serum per lipids, and causes Y PCB S /LipidsY PCB A Modellogit(Y)=…% Bias UnadjustedPCB S -86.3 StandardizedPCB S / Lipids AdjustedPCB S + Lipids Two-stagePCB S + Residuals-85.9 22

23. Summary of Bias by DAG DAGTypeUnadjustedStandardizedAdjustedTwo-stage A Cause & Effect -0.8-75.9-0.7 A11.2-51.31.8 A20.4-79.80.80.5 A3-0.4-85-0.1-0.3 BConfounding24-1290.127.2 B1 Intermediate -15.4-351-99.41.1 B2-11.2-128-25.4-8.7 CPCB s /Lipids-86.3 -85.9 23

24. Summary  Evaluated 4 statistical models commonly used to assess the effects of PCBs (or other lipophilic environmental contaminants) on human health  Each model showed minimal bias for at least the causal truth for which it was ideally suited  Bias ranged from -351% to 24%  Standardized model produced large biases for most of the evaluated DAGs  The adjusted model produced small biases even for the DAG for which standardization is optimal 24

25. Limitations  Only considered DAGs with 2 to 4 factors  Including additional factors necessarily makes evaluation more complex and the trade-off between efficiency and robustness more important  Though in their simulation the adjusted model produced consistently unbiased estimates, there are situations where adjustment should be avoided  Collider  Common cause 25

26. Conclusion  Simulations demonstrate that statistical models that fail to uphold the underlying causal assumptions lead to biased results  This bias can have negative implications on the interpretation of effects of exposures on human health end points  Investigators must consider biology, biologic medium, laboratory measurement, and other underlying modeling assumptions when devising a statistical model 26

27. References  Schisterman EF, Whitcomb BW, Buck Louis GM, Louis TA. Lipid Adjustment in the Analysis of Environmental Contaminants and Human Health Risks. Environmental Health Perspectives 2005;113(7):853-7. 27