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References Adjusting for selection bias in case control studie S.Geneletti, S.Richardson, N.Best Department of Epidemiology and Public Health, Imperial College 24/07/2008 References OUTLINE 1. Examples 2. Hypospadias Study 3. What is a DAG? 4.

  1. References Adjusting for selection bias in case control studie S.Geneletti, S.Richardson, N.Best Department of Epidemiology and Public Health, Imperial College 24/07/2008

  2. References OUTLINE 1. Examples 2. Hypospadias Study 3. What is a DAG? 4. Conditional Independence 5. SB in terms of DAGs 6. Odds ratios 7. Idea 8. Bias Breaking model 9. Hypospadias results 10. Simulations 11. Final Comments

  3. References SELECTION BIAS Basic problem • Selection bias comes about when there is differential selection of cases and controls • and a variable that is associated to the exposure under investigation is implicated in the selection process • Case control studies are particularly prone to this problem • This is because in order to make valid comparisons the populations of cases and controls must come from the same target population • It is a problem of internal validity • We tackle the problem using DAGs, Conditional independence and extra data

  4. References SELECTION BIAS Basic problem • Selection bias comes about when there is differential selection of cases and controls • and a variable that is associated to the exposure under investigation is implicated in the selection process • Case control studies are particularly prone to this problem • This is because in order to make valid comparisons the populations of cases and controls must come from the same target population • It is a problem of internal validity • We tackle the problem using DAGs, Conditional independence and extra data

  5. References SELECTION BIAS Basic problem • Selection bias comes about when there is differential selection of cases and controls • and a variable that is associated to the exposure under investigation is implicated in the selection process • Case control studies are particularly prone to this problem • This is because in order to make valid comparisons the populations of cases and controls must come from the same target population • It is a problem of internal validity • We tackle the problem using DAGs, Conditional independence and extra data

  6. References SELECTION BIAS Basic problem • Selection bias comes about when there is differential selection of cases and controls • and a variable that is associated to the exposure under investigation is implicated in the selection process • Case control studies are particularly prone to this problem • This is because in order to make valid comparisons the populations of cases and controls must come from the same target population • It is a problem of internal validity • We tackle the problem using DAGs, Conditional independence and extra data

  7. References SELECTION BIAS Basic problem • Selection bias comes about when there is differential selection of cases and controls • and a variable that is associated to the exposure under investigation is implicated in the selection process • Case control studies are particularly prone to this problem • This is because in order to make valid comparisons the populations of cases and controls must come from the same target population • It is a problem of internal validity • We tackle the problem using DAGs, Conditional independence and extra data

  8. References SELECTION BIAS Basic problem • Selection bias comes about when there is differential selection of cases and controls • and a variable that is associated to the exposure under investigation is implicated in the selection process • Case control studies are particularly prone to this problem • This is because in order to make valid comparisons the populations of cases and controls must come from the same target population • It is a problem of internal validity • We tackle the problem using DAGs, Conditional independence and extra data

  9. References HYPOSPADIAS CASE CONTROL STUDY Story • Hypospadias is a congenital malformation of newborn boys • Is it associated to gestational age or smoking? [4, 5] • Concern that controls have a higher SES than cases - selection bias? • SES measured using the Carstairs score (C-score) - an area (ward) level index of deprivation ([6])

  10. References HYPOSPADIAS CASE CONTROL STUDY Story • Hypospadias is a congenital malformation of newborn boys • Is it associated to gestational age or smoking? [4, 5] • Concern that controls have a higher SES than cases - selection bias? • SES measured using the Carstairs score (C-score) - an area (ward) level index of deprivation ([6])

  11. References HYPOSPADIAS CASE CONTROL STUDY Story • Hypospadias is a congenital malformation of newborn boys • Is it associated to gestational age or smoking? [4, 5] • Concern that controls have a higher SES than cases - selection bias? • SES measured using the Carstairs score (C-score) - an area (ward) level index of deprivation ([6])

  12. References HYPOSPADIAS CASE CONTROL STUDY Story • Hypospadias is a congenital malformation of newborn boys • Is it associated to gestational age or smoking? [4, 5] • Concern that controls have a higher SES than cases - selection bias? • SES measured using the Carstairs score (C-score) - an area (ward) level index of deprivation ([6])

  13. References HYPOSPADIAS CASE CONTROL STUDY Data collection • Ward (and hence C-score) and exposure measure of people who participated - full participants (indexed by f) • Ward (and hence C-score) of people who were asked to participate but declined - partial participants (indexed by p) • For partial pariticipants we don’t have exposure measure • Finally, C-score of people who lived in the region the study was conducted from census

  14. References HYPOSPADIAS CASE CONTROL STUDY Data collection • Ward (and hence C-score) and exposure measure of people who participated - full participants (indexed by f) • Ward (and hence C-score) of people who were asked to participate but declined - partial participants (indexed by p) • For partial pariticipants we don’t have exposure measure • Finally, C-score of people who lived in the region the study was conducted from census

  15. References HYPOSPADIAS CASE CONTROL STUDY Data collection • Ward (and hence C-score) and exposure measure of people who participated - full participants (indexed by f) • Ward (and hence C-score) of people who were asked to participate but declined - partial participants (indexed by p) • For partial pariticipants we don’t have exposure measure • Finally, C-score of people who lived in the region the study was conducted from census

  16. References HYPOSPADIAS CASE CONTROL STUDY Data collection • Ward (and hence C-score) and exposure measure of people who participated - full participants (indexed by f) • Ward (and hence C-score) of people who were asked to participate but declined - partial participants (indexed by p) • For partial pariticipants we don’t have exposure measure • Finally, C-score of people who lived in the region the study was conducted from census

  17. References BOXPLOT Is there also case selection bias? partial participant cases (pcs) have low SES (high Carstairs)

  18. References WHAT IS A DAG? DAGs are directed acyclic graphs • All arrows have direction • No cycles A → B → A • DAGs are used to encode conditional independence statements • A ⊥ ⊥ C | B [1] means p ( A , C | B ) = p ( A | B ) p ( C | B ) • Arrows are not causal unless extra assumptions made - time ordering, intervention A B C A B C A B C

  19. References WHAT IS A DAG? DAGs are directed acyclic graphs • All arrows have direction • No cycles A → B → A • DAGs are used to encode conditional independence statements • A ⊥ ⊥ C | B [1] means p ( A , C | B ) = p ( A | B ) p ( C | B ) • Arrows are not causal unless extra assumptions made - time ordering, intervention A B C A B C A B C

  20. References WHAT IS A DAG? DAGs are directed acyclic graphs • All arrows have direction • No cycles A → B → A • DAGs are used to encode conditional independence statements • A ⊥ ⊥ C | B [1] means p ( A , C | B ) = p ( A | B ) p ( C | B ) • Arrows are not causal unless extra assumptions made - time ordering, intervention A B C A B C A B C

  21. References WHAT IS A DAG? DAGs are directed acyclic graphs • All arrows have direction • No cycles A → B → A • DAGs are used to encode conditional independence statements • A ⊥ ⊥ C | B [1] means p ( A , C | B ) = p ( A | B ) p ( C | B ) • Arrows are not causal unless extra assumptions made - time ordering, intervention A B C A B C A B C

  22. References WHAT IS A DAG? DAGs are directed acyclic graphs • All arrows have direction • No cycles A → B → A • DAGs are used to encode conditional independence statements • A ⊥ ⊥ C | B [1] means p ( A , C | B ) = p ( A | B ) p ( C | B ) • Arrows are not causal unless extra assumptions made - time ordering, intervention A B C A B C A B C

  23. References WHAT IS A DAG? DAGs are directed acyclic graphs • All arrows have direction • No cycles A → B → A • DAGs are used to encode conditional independence statements • A ⊥ ⊥ C | B [1] means p ( A , C | B ) = p ( A | B ) p ( C | B ) • Arrows are not causal unless extra assumptions made - time ordering, intervention A B C A B C A B C

  24. References SIMPLE EXAMPLE - INHERITANCE M F 1. Male and female are independent M ⊥ ⊥ F

  25. References SIMPLE EXAMPLE - INHERITANCE M F C 1. Male and female are independent M ⊥ ⊥ F 2. Then they meet and have a child

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