1 / 47

Are You Looking for the Right Interactions?

Are You Looking for the Right Interactions?. A presentation given 2/28/2012 in the Biostatistics in Psychiatry seminar series at Columbia University by Sharon Schwartz Department of Epidemiology Mailman School of Public Health Columbia University. Interaction is Model Dependent.

freya
Download Presentation

Are You Looking for the Right Interactions?

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Are You Looking for the Right Interactions? A presentation given 2/28/2012 in the Biostatistics in Psychiatry seminar series at Columbia University by Sharon Schwartz Department of Epidemiology Mailman School of Public Health Columbia University

  2. Interaction is Model Dependent The Problem

  3. Forms or word? What You See Depends on How you Look at It Musician or Woman? Vases or Faces?

  4. MOTIVATING EXAMPLE Do Intimacy problems interact with stressful life events to cause depression? Tennent and Bebbington NO Brown and Harris YES

  5. Interaction (aka, Effect Modification) The effect of an exposure differs in the presence or absence of another variable (X)

  6. MOTIVATING EXAMPLE Do Intimacy problems interact with stressful life events to cause depression? Risk of disease in each cell is displayed It depends on how you look at it

  7. MOTIVATING EXAMPLE Is the effect of stressful life events different in the presence vs. absence of Intimacy Problems? YES RD = 32 - 3 = 29 RD = 10 - 1 = 9 NO RR = 32/3 = 10 RR = 10/1 = 10

  8. So who is right – Brown & Harris or Tennet & Bebbington? Is the effect of stressful life events different in the presence vs. absence of Intimacy Problems? YES RD = 32 - 3 = 29 RD = 10 - 1 = 9 NO RR = 32/3 = 10 RR = 10/1 = 10

  9. What is the Causal Question?: Are there some individuals who became depressed because they experienced both stressful life events and intimacy problems

  10. Causal Question in Counterfactual Terms Are there some individuals who experienced stressful life and intimacy problems who became depressed, who would not have become depressed had they not experienced both stressful life events and intimacy problems?

  11. Hypothesized Causes of Depression Stressful Life Events T J Intimacy Problems The exposure has an effect when it is in the presence of its causal partners (here intimacy problems)

  12. Hypothesized Causes of Depression Intimacy Problems Stressful Life Events T J Intimacy Problems P Stressful Life Events R Genetic Variant

  13. EFFECT MODIFICATION, INTERACTION AND SYNERGY: WHAT DO WE REALLY WANT TO KNOW?

  14. Synergy: Who are the Exposure’sCausal Partners?

  15. WHAT DO WE MEAN BY INTERACTION ? CONCEPTUALLY: CAUSAL PARTNERS IN THE SAME CAUSAL PIE IMPLICATIONS FOR DISEASE RISK: RISK OF DISEASE FROM CAUSAL PARTNERS WHEN THEY CO-OCCUR IS GREATER THAN WOULD BE EXPECTED BASED ON THEIR INDEPENDENT EFFECTS ALONE

  16. BEGIN FROM YOUR CAUSAL MODEL ROTHMAN’S CAUSAL MODEL SINGLE CAUSE OF INTEREST

  17. CAUSES OF DISEASES AND THE RELATIONSHIP TO “TYPES” EXPOSURE OF INTEREST: X CAUSES OF DISEASE OF INTEREST NOT X C D E X A

  18. C D CAUSES OF DISEASES AND THE RELATIONSHIP TO “TYPES” EXPOSURE OF INTEREST: X CAUSES OF DISEASE OF INTEREST NOT X C D E A X “TYPES” OF PEOPLE REGARDING DISEASE OF INTEREST GIVEN THAT EXPOSURE OF INTEREST IS X NOT A, C&D, OR E A E IMMUNE SUSCEPTIBLE DOOMED PROTECTIVE

  19. INTEREST IN EXPOSURE X: WHAT CAN WE KNOW ABOUT CAUSATION? TYPE PROPORTION DISEASE EXPERIENCE DISEASE EXPERIENCE IF EXPOSED IF UNEXPOSED D+ D+ 1: DOOMED P1 P2 --- 2: A CAUSAL D+ --- D+ P3 3: A PROTECTIVE P4 --- --- 4: IMMUNE P1&P2 RISK IF EXPOSED = RISK IF UNEXPOSED = RISK DIFFERENCE = RISK RATIO = P1 & P3 P2 - P3 P1 & P2/ P1 & P3

  20. BOTTOM LINE OF CAUSAL INFERENCE WITH SINGLE RISK FACTOR (ASSUMING EXCHANGEABILITY) NOTE: SINCE THIS IS A STUDY WE USED AN UNEXPOSED AS A COUNTERFACTUAL FOR THE EXPOSED - ERGO Q’S NOW ENTER MORE TYPE 2’S THAN 3’S RR = P1 & P2/ Q1 & Q3 >1 THERE ARE MORE PEOPLE FOR WHOM THE EXPOSURE IS CAUSAL THAN PEOPLE FOR WHOM THE EXPOSURE IS PROTECTIVE MORE TYPE 3’S THAN 2’S RR = P1& P2/Q1+Q3 < 1 THERE ARE MORE PEOPLE FOR WHOM THE EXPOSURE IS PROTECTIVE THAN PEOPLE FOR WHOM THE EXPOSURE IS CAUSAL TYPE 2’S = TYPE 3’S OR NO TYPE 2’S OR 3’S RR = P1 & P2/Q1 & Q3 = 1 EITHER THE EXPOSURE HAS NO EFFECT OR THERE ARE EQUAL NUMBERS OF PEOPLE FOR WHOM IT IS CAUSAL AND FOR WHOM IT IS PROTECTIVE

  21. Using this Causal Model:How do we know if There is Synergy Out There?

  22. IF WE ASSUME ALL ACTIVE EFFECTS ARE CAUSAL AND NONE ARE PROTECTIVE, THEN THERE ARE 6 POSSIBLE OUTCOMES FROM THE COMBINATION OF ANY TWO RISK FACTORS OF INTEREST DARROCH, ROTHMAN, GREENLAND USE THIS ASSUMPTION IN DEVELOPING THEIR MODEL

  23. ASSESSING INTERACTION BETWEEN VARIABLES X AND Z DISEASE EXPERIENCE IF EXPOSED TO: X&Z NEITHER CAUSE TYPE TYPE X Z X A A D+ ---- D+ --- 6 - X susceptible B --- D+ D+ --- 4 - Z susceptible Z B 1 - doomed CD CD D+ D+ D+ D+ 16 - immune --- --- --- --- NONE A X OR Z A D+ D+ D+ --- 2- parallelism B B X --- --- D+ --- 8 - synergy E E Z D=100% D=100% D=100% D =100%

  24. WHAT IS SYNERGY? (TYPE 8) WHEN TWO RISK FACTORS ARE PARTNERS IN THE SAME SUFFICIENT CAUSE BOTH ARE NECESSARY FOR THE COMPLETION OF THE CAUSAL PIE X Z HERE X&Z ARE SYNERGISTIC FOR INDIVIDUALS WITH E E

  25. WHAT IS PARALLELISM? (TYPE 2) WHEN INDIVIDUALS HAVE COMPONENTS TO COMPLETE TWO DIFFERENT PIES EACH WITH A RISK FACTOR UNDER STUDY X A Z B HERE X&Z ARE PARALLEL FOR INDIVIDUALS WITH A & B

  26. Exposures of interest = X,Z X Z John is exposed to X, Z John’s perfect proxies are Nhoj X, Z - A B T0 T1 T2 T End Effect of X Effect of Z John A = 1 B = 1 D Nhoj X D A = 1 B = 1 A = 1 B = 1 Nhoj Z D Nhoj - A = 1 B = 1 -- Did John get the disease? What is the causal effect of x? What is the causal effect of z? What caused John’s disease?

  27. Inevitable Parallelism Will occur with a probability of A*B X Z A B

  28. “Functional Equivalence” Parallelism Z X A A

  29. ASSESSING INTERACTION BETWEEN VARIABLES X AND Z DISEASE EXPERIENCE IF EXPOSED TO: X&Z NEITHER CAUSE TYPE TYPE X Z X A A D+ ---- D+ --- 6 - X susceptible B --- D+ D+ --- Z B 4 - Z susceptible CD 1 - doomed CD D+ D+ D+ D+ 16 - immune --- --- --- --- NONE A X OR Z A 2- parallelism D+ D+ D+ --- B B X E --- --- D+ --- 8 - synergy E Z 100% 100% 100% 100%

  30. KNOWN: PROPORTION OF PEOPLE WITH DISEASE IN EACH EXPOSURE CATEGORY UNKNOWN: PROPORTION OF “TYPES” OF PEOPLE IN EACH EXPOSURE CATEGORY PARTIAL SOLUTION: RELATIONSHIP BETWEEN THE KNOWN AND UNKNOWN

  31. ASSESSING INTERACTION BETWEEN VARIABLES X AND Z DISEASE EXPERIENCE IF EXPOSED TO: X&Z NEITHER CAUSE TYPE TYPE X Z X A A 6 - X susceptible D+ ---- D+ --- B --- D+ D+ --- 4 - Z susceptible Z B CD 1 - doomed CD D+ D+ D+ D+ 16 - immune --- --- --- --- NONE A X OR Z A 2- parallelism D+ D+ D+ --- B B X E 8 - synergy --- --- D+ --- E Z 100% 100% 100% 100%

  32. PROPORTION DISEASE AMONG X ONLY: PROPORTION DISEASE AMONG Z ONLY: PROPORTION DISEASE AMONG X&Z: PROPORTION DISEASE (I.E., DISEASE RISK) AMONG UNEXPOSED: KNOWN: PROPORTION OF PEOPLE WITH DISEASE IN EACH EXPOSURE CATEGORY UNKNOWN: PROPORTION OF “TYPES” OF PEOPLE IN EACH EXPOSURE CATEGORY PARTIAL SOLUTION: RELATIONSHIP BETWEEN THE KNOWN AND UNKNOWN DOOMED + X SUSCEPTIBLE + PARALLE L DOOMED + Z SUSCEPTIBLE + PARALLEL DOOMED + Z SUSCEPTIBLE + X SUSCEPTIBLE + PARALLEL & SYNERGISTIC DOOMED

  33. - R(XZ) R(X) R(XZ)= R(X) = R(Z) = R = DARROCH’S TABLE RISKS IN TERMS OF OBSERVED PROPORTIONS PROPORTION DISEASE AMONG THOSE EXPOSED TO X & Z PROPORTION DISEASE AMONG THOSE EXPOSED TO X ONLY PROPORTION DISEASE AMONG THOESE EXPOSED TO Z ONLY PROPORTION DISEASE AMONG UNEXPOSED TO X AND Z RISKS IN TERMS OF UNOBSERVABLE TYPES R(XZ) = RX = RZ = DOOMED, SUS X, SUS Z, PARALLEL, SYNERGISTIC DOOMED, SUS X, PARALLEL DOOMED, SUS Z, PARALLEL DOOMED R = - DOOMED, SUS X, SUS Z, PARALLEL, SYNERGISTIC = DOOMED, SUS X, PARALLEL SUS Z + SYNERGISTIC R(XZ) - R

  34. R(XZ)= R(X) = R(Z) = R = DARROCH’S TABLE RISKS IN TERMS OF OBSERVED PROPORTIONS PROPORTION DISEASE AMONG THOSE EXPOSED TO X & Z PROPORTION DISEASE AMONG THOSE EXPOSED TO X ONLY PROPORTION DISEASE AMONG THOESE EXPOSED TO Z ONLY PROPORTION DISEASE AMONG UNEXPOSED TO X AND Z RISKS IN TERMS OF UNOBSERVABLE TYPES R(XZ) = RX = RZ = DOOMED, SUS X, SUS Z, PARALLEL, SYNERGISTIC DOOMED, SUS X, PARALLEL DOOMED, SUS Z, PARALLEL DOOMED R = SUS Z SYNERGISM R(XZ) - R(X)

  35. - R(X) R R(XZ)= R(X) = R(Z) = R = DARROCH’S TABLE RISKS IN TERMS OF OBSERVED PROPORTIONS PROPORTION DISEASE AMONG THOSE EXPOSED TO X & Z PROPORTION DISEASE AMONG THOSE EXPOSED TO X ONLY PROPORTION DISEASE AMONG THOESE EXPOSED TO Z ONLY PROPORTION DISEASE AMONG UNEXPOSED TO X AND Z RISKS IN TERMS OF UNOBSERVABLE TYPES R(XZ) = RX = RZ = DOOMED, SUS X, SUS Z, PARALLEL, SYNERGISTIC DOOMED, SUS X, PARALLEL DOOMED, SUS Z, PARALLEL DOOMED R = - DOOMED, SUS X, PARALLEL = DOOMED SUS X + PARALLEL R(XZ) - R

  36. R(XZ)= R(X) = R(Z) = R = DARROCH’S TABLE RISKS IN TERMS OF OBSERVED PROPORTIONS PROPORTION DISEASE AMONG THOSE EXPOSED TO X & Z PROPORTION DISEASE AMONG THOSE EXPOSED TO X ONLY PROPORTION DISEASE AMONG THOESE EXPOSED TO Z ONLY PROPORTION DISEASE AMONG UNEXPOSED TO X AND Z RISKS IN TERMS OF UNOBSERVABLE TYPES R(XZ) = RX = RZ = DOOMED, SUS X, SUS Z, PARALLEL, SYNERGISTIC DOOMED, SUS X, PARALLEL DOOMED, SUS Z, PARALLEL DOOMED R = SYNERGISM R(XZ) - R(X) SUS Z R(X) - R SUS X PARALLEL

  37. - R(XZ) RZ R(XZ)= R(X) = R(Z) = R = DARROCH’S TABLE RISKS IN TERMS OF OBSERVED PROPORTIONS PROPORTION DISEASE AMONG THOSE EXPOSED TO X & Z PROPORTION DISEASE AMONG THOSE EXPOSED TO X ONLY PROPORTION DISEASE AMONG THOESE EXPOSED TO Z ONLY PROPORTION DISEASE AMONG UNEXPOSED TO X AND Z RISKS IN TERMS OF UNOBSERVABLE TYPES R(XZ) = RX = RZ = DOOMED, SUS X, SUS Z, PARALLEL, SYNERGISTIC DOOMED, SUS X, PARALLEL DOOMED, SUS Z, PARALLEL DOOMED R = - DOOMED, SUS X, SUS Z, PARALLEL, SYNERGISTIC = DOOMED, SUS Z, PARALLEL SUS X + SYNERGISTIC R(XZ) - R

  38. R(XZ)= R(X) = R(Z) = R = DARROCH’S TABLE RISKS IN TERMS OF OBSERVED PROPORTIONS PROPORTION DISEASE AMONG THOSE EXPOSED TO X & Z PROPORTION DISEASE AMONG THOSE EXPOSED TO X ONLY PROPORTION DISEASE AMONG THOESE EXPOSED TO Z ONLY PROPORTION DISEASE AMONG UNEXPOSED TO X AND Z RISKS IN TERMS OF UNOBSERVABLE TYPES R(XZ) = RX = RZ = DOOMED, SUS X, SUS Z, PARALLEL, SYNERGISTIC DOOMED, SUS X, PARALLEL DOOMED, SUS Z, PARALLEL DOOMED R = SYNERGISM SUS Z R(XZ) - R(X) R(X) - R SUS X PARALLEL R(XZ) - R R(XZ) - R(Z)

  39. - R(Z) R R(XZ)= R(X) = R(Z) = R = DARROCH’S TABLE RISKS IN TERMS OF OBSERVED PROPORTIONS PROPORTION DISEASE AMONG THOSE EXPOSED TO X & Z PROPORTION DISEASE AMONG THOSE EXPOSED TO X ONLY PROPORTION DISEASE AMONG THOESE EXPOSED TO Z ONLY PROPORTION DISEASE AMONG UNEXPOSED TO X AND Z RISKS IN TERMS OF UNOBSERVABLE TYPES R(XZ) = RX = RZ = DOOMED, SUS X, SUS Z, PARALLEL, SYNERGISTIC DOOMED, SUS X, PARALLEL DOOMED, SUS Z, PARALLEL DOOMED R = - DOOMED, SUSZ, PARALLEL = DOOMED SUS Z + PARALLEL R(XZ) - R

  40. R(XZ)= R(X) = R(Z) = R = DARROCH’S TABLE RISKS IN TERMS OF OBSERVED PROPORTIONS PROPORTION DISEASE AMONG THOSE EXPOSED TO X & Z PROPORTION DISEASE AMONG THOSE EXPOSED TO X ONLY PROPORTION DISEASE AMONG THOESE EXPOSED TO Z ONLY PROPORTION DISEASE AMONG UNEXPOSED TO X AND Z RISKS IN TERMS OF UNOBSERVABLE TYPES R(XZ) = RX = RZ = DOOMED, SUS X, SUS Z, PARALLEL, SYNERGISTIC DOOMED, SUS X, PARALLEL DOOMED, SUS Z, PARALLEL DOOMED R = SYNERGISM SUS Z R(XZ) - R(X) R(X) - R SUS X PARALLEL R(XZ) - R R(XZ) - R(Z) R(Z) - R

  41. R(XZ)= R(X) = R(Z) = R = DARROCH’S TABLE RISKS IN TERMS OF OBSERVED PROPORTIONS PROPORTION DISEASE AMONG THOSE EXPOSED TO X & Z PROPORTION DISEASE AMONG THOSE EXPOSED TO X ONLY PROPORTION DISEASE AMONG THOESE EXPOSED TO Z ONLY PROPORTION DISEASE AMONG UNEXPOSED TO X AND Z RISKS IN TERMS OF UNOBSERVABLE TYPES R(XZ) = RX = RZ = DOOMED, SUS X, SUS Z, PARALLEL, SYNERGISTIC DOOMED, SUS X, PARALLEL DOOMED, SUS Z, PARALLEL DOOMED R = SYNERGISM SUS Z R(XZ) - R(X) R(X) - R SUS X PARALLEL R(XZ) - R R(XZ) - R(Z) R(Z) - R [SYNERGISM + SUS Z] - [SUS Z + PARALLEL] = [R(XZ) - R(X)] - [R(Z) - R]= [SYNERGISM - PARALLEL] = R(XZ) - R(X) - R(Z) + R

  42. DARROCH’S TABLE: example R(XZ) = DOOMED, SUS X, SUS Z, PARALLEL, SYNERGISTIC RX = DOOMED, SUS X, PARALLEL RZ = DOOMED, SUS Z, PARALLEL R = DOOMED SYNERGISM SUS Z R(XZ) - R(X) R(X) - R SUS X PARALLEL R(XZ) - R R(XZ) - R(Z) R(Z) - R R(XZ) = 20.7R R(X) = 7.2R R(Z) = 5.1R [SYNERGISM + SUS Z] - [SUS Z + PARALLEL] = [R(XZ) - R(X)] - [R(Z) - R] = [SYNERGISM - PARALLEL] = R(XZ) - R(X) - R(Z) + R 20.7 - 7.2 - 5.1 + 1 = 9.4 INTERPRETATION: THERE ARE MORE SYNERGISTIC THAN PARALLEL TYPES IN THIS SAMPLE

  43. BOTTOM LINE CAUSAL INFERENCE RE: INTERACTION (DARROCH MODEL) IF THERE IS EVIDENCE OF POSITIVE ADDITIVE INTERACTION IN YOUR DATA: SYNERGISM EXISTS THERE ARE MORE PEOPLE FOR WHOM THE EXPOSURES WORK SYNERGISTICALLY THAN IN A PARALLEL MANNER IF THERE IS NO ADDITIVE INTERACTION IN YOUR DATA: THERE MAY BE NO SYNERGISM THE PROPORTION OF PEOPLE FOR WHOM THE EXPOSURES WORK SYNERGISTICALLY MAY BE THE SAME AS THE PROPORTION FOR WHOM THE EXPOSURES WORK IN A PARALLEL MANNER IF THERE IS EVIDENCE OF NEGATIVE ADDITIVE INTERACTION IN YOUR DATA PARALLELISM EXISTS THERE ARE MORE PEOPLE FOR WHOM THE EXPOSURES WORK IN A PARALLEL MANNER THAN FOR WHOM THE EXPOSURES WORK SYNERGISTICALLY

  44. Synergy Assessment in Practice Interaction Contrast R11-R10-R01+R00 Interaction Contrast Ratio [IC/R00: (aka RERI: Relative Excess Risk due to Interaction)] RR11-RR10-RR01 + 1 Attributable Proportion due to interaction RR11-RR10-RR01 +1 / RR11 Synergy index RR11-1/(RR10-1) ( RR01-1)

  45. SO WHO IS RIGHT? Do Intimacy problems interact with stressful life events to cause depression? Tennent and Bebbington Brown and Harris

  46. So who is right? Brown and Harris Interaction Contrast = R11-R10-R01+R00 = SYNERGY - PARALLEL 32-10-3 +1 = 20

  47. CONCLUSION CAUSAL INTERACTION IS BEST REPRESENTED BY ADDITIVITY WITH A TWIST

More Related