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Exploring finite-sample bias in propensity score weights

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ENAR 2018

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Exploring finite-sample bias in propensity score weights

  1. 1. E N A R 2 0 1 8 Exploring finite-sample bias in propensity score weights LUCY D’AGOSTINO MCGOWAN & ROBERT GREEVY, JR.
  2. 2. E N A R 2 0 1 8 Overview Finite sample bias Unmeasured confounding – the problem Unmeasured confounding – a solution 1 2 3
  3. 3. E N A R 2 0 1 8 treatmentcontrol
  4. 4. E N A R 2 0 1 8 trtcontrol
  5. 5. E N A R 2 0 1 8 trtcontrol 151 ATE
  6. 6. E N A R 2 0 1 8 treatmentcontrol 1 ATM
  7. 7. E N A R 2 0 1 8 treatmentcontrol ATO
  8. 8. E N A R 2 0 1 8 ATE ATM AT0
  9. 9. E N A R 2 0 1 8 ATE ATM AT0
  10. 10. E N A R 2 0 1 8 ATE ATM AT0
  11. 11. E N A R 2 0 1 8 Finite-sample bias
  12. 12. E N A R 2 0 1 8
  13. 13. E N A R 2 0 1 8 Freedman & Berk Simulation
  14. 14. E N A R 2 0 1 8 yz x1 x2
  15. 15. E N A R 2 0 1 8 yz x1 x2 1 0.25 10.75 2 1
  16. 16. E N A R 2 0 1 8 yz x1 x2 1 0.25 10.75 2 1
  17. 17. E N A R 2 0 1 8 yz x1 x2 1 0.25 10.75 2 1
  18. 18. E N A R 2 0 1 8 yz x1 x2 1 0.25 10.75 2 1
  19. 19. E N A R 2 0 1 8 z x1 x2 Propensity score model
  20. 20. E N A R 2 0 1 8 yz x1 x2 Outcome model
  21. 21. E N A R 2 0 1 8 treatmentctrl
  22. 22. E N A R 2 0 1 8 n = 1000
  23. 23. E N A R 2 0 1 8
  24. 24. E N A R 2 0 1 8 Standard errors
  25. 25. E N A R 2 0 1 8 yz x1 x2 Outcome model
  26. 26. E N A R 2 0 1 8
  27. 27. E N A R 2 0 1 8
  28. 28. E N A R 2 0 1 8 Recap • Replicated the finite-sample bias seen by Freedman and Berk using the ATE weights • ATM and ATO weights had improved finite-sample properties • The variance for the ATO and ATM is preferable to that of the ATE
  29. 29. E N A R 2 0 1 8 Unmeasured confounding the problem
  30. 30. E N A R 2 0 1 8
  31. 31. E N A R 2 0 1 8 z x1 x2 Propensity score model
  32. 32. E N A R 2 0 1 8 yz x1 x2 Outcome model
  33. 33. E N A R 2 0 1 8 ATE
  34. 34. E N A R 2 0 1 8 ATO
  35. 35. E N A R 2 0 1 8 Unmeasured confounding a solution
  36. 36. E N A R 2 0 1 8 E-value E − value = 𝐿𝐵 𝑜𝑏𝑠 + 𝐿𝐵 𝑜𝑏𝑠 × (𝐿𝐵 𝑜𝑏𝑠 − 1) VanderWeele and Ding (2017)
  37. 37. E N A R 2 0 1 8 Adjusted E-value E − value 𝑎𝑑𝑗 = 𝐿𝐵 𝑜𝑏𝑠 𝐿𝐵 𝑎𝑑𝑗 + 𝐿𝐵 𝑜𝑏𝑠 𝐿𝐵 𝑎𝑑𝑗 × 𝐿𝐵 𝑜𝑏𝑠 𝐿𝐵 𝑎𝑑𝑗 − 1
  38. 38. E N A R 2 0 1 8 Adjusted E-value E − value 𝑎𝑑𝑗 = 𝐿𝐵 𝑜𝑏𝑠 𝐿𝐵 𝑎𝑑𝑗 + 𝐿𝐵 𝑜𝑏𝑠 𝐿𝐵 𝑎𝑑𝑗 × 𝐿𝐵 𝑜𝑏𝑠 𝐿𝐵 𝑎𝑑𝑗 − 1
  39. 39. E N A R 2 0 1 8 Right Heart Catheterization Data Connors et al (1996)
  40. 40. E N A R 2 0 1 8 Right Heart Catheterization data • We chose 20 covariates for demonstration purposes • demographics • comorbidities • physiological measurements • diagnosis categories • APACHE score • SUPPORT (probability of surviving 2 months) • DNR status on day 1 Connors et al (1996)
  41. 41. E N A R 2 0 1 8 Right Heart Catheterization data •Fit a propensity score model •Use ATO weights •Fit weighted cox model for 30 day survival
  42. 42. E N A R 2 0 1 8
  43. 43. E N A R 2 0 1 8
  44. 44. E N A R 2 0 1 8
  45. 45. E N A R 2 0 1 8 @LucyStats http://bit.ly/LucyStatsENAR2018 lucymcgowan.com Thank you!

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