February 19,H.S.,1,Selection Bias Concepts,Hein Stigum Presentation, data and programs at: http:/folk.uio.no/heins/talks,Questions,Given measured appropriate variables: Can you adjust for confounding? Yes Can you adjust for selection bias? Depends on the definition,February 19,H.S.,2,Contents,Background Define bias Selection bias as effect modification (old concept) as collider stratification bias (new concept) DAG structure Examples Size and direction of bias,February 19,H.S.,3,Bias definition,Bias Frequency: expected risk true risk Effect: association causal effect,February 19,H.S.,4,Selection bias concepts,Concept,Effect responders Effect non responders Differential response bias Differential loss to follow up Healthy worker bias Berksons bias (case control),DAG structure,Effect modification Collider stratification bias,February 19,H.S.,5,Selection bias as effect modification,February 19,H.S.,6,Selection bias: Risk,Selection of responders The prevalence is different among the responders compared to the full population the responders compared to the non responders,February 19,H.S.,7,R1,R0,Rp,Non responders,Responders,Population,Rp is the weighted mean of R0 and R1,Effect modification,Selection of responders The effect of E on D is different among the responders compared to the full population the responders compared to the non responders,February 19,H.S.,8,RR1,RR0,RRp,Non responders,Responders,Population,Problems,Is not a bias, RR0 and RR1 are the true effects Is effect modification by selection variable S Leads to the conclusion that: Biolocical effects are protected from bias The bias can not be adjusted for RRp is the average of RR0 and RR1,February 19,H.S.,9,E,D,S,“DAG” structure:,Not true for collider stratification bias,Selection bias as collider stratification bias,February 19,H.S.,10,Example with paths,Study Milk on bone density Exclude Calcium supplements,February 19,H.S.,11,Lessons learned: Biological effect not protected May adjust for selection bias,Structure: Collider stratification,Examples,Differential response Survey: Alcohol and CHD Differential loss to follow up Randomized trial: drug and disease Healthy worker effect Cross-section: Melt hall dust and lung disease,February 19,H.S.,12,Note: no confounding,Selection bias structure,February 19,H.S.,13,Paths,1. Causal,2. Confounding An open non-causal path without colliders,3. Selection bias A non-causal path that is open due to conditioning on a collider,BCVs?,Collider stratification bias,Selection bias = Collider stratification bias Selection bias, Path definition A non causal path that is open due to conditioning on a collider,February 19,H.S.,15,Selection bias examples,February 19,H.S.,16,Folic acid and cardiac malformation,Selection: Study only live born Bias?,February 19,H.S.,17,Yes, ECD is open,Selection: Non grieving parents volonteer Bias?,Yes, ECD is (partially) open,Education and unfaithfulness,Study the effect among couples in a relationship (not divorced)?,Feb-19,H.S.,18,Selection bias,Size and Direction of bias,February 19,H.S.,19,Example 1, full table,Proportion responding in 1,1 group,True and biased RRs,(Adjusted) RRs,Example 2,Pattern: Only D influence response,Result: RR (and RD) biased, OR unbiased ODS, Case-Control,Example 3,Pattern: Both E and D influence response,Result: Surprise: responders are unbiased Theory: bias in at least one stratum,Example 4,Pattern: Both E and D influence response,Result: Surprise: both strata biased upwards True RR is not a weighted average,Example 5,Pattern: Both E and D influence response,Result: Same DAG, different results The DAG does not fully determine the selection!,Summing up,Selection bias as “effect modification”: Is not a bias, should not be called selection bias Has properties different from proper selection bias Selection bias as “collider stratification”: Structure defined in DAG, Distinct from confounding Consistent with Differential response bias Differential loss to follow up Healthy worker bias Berksons bias (case control),February 19,H.S.,25,February 19,H.S.,26,Litterature,Hernan and Robins, Causal Inference,