1. Do Trauma Centers Save Lives? A Statistical Solution Daniel O. Scharfstein

2. Collaborators Brian Egleston Ciprian Crainiceanu Zhiqiang Tan Tom Louis

3. Issues Outcome Dependent Sampling Missing Data Confounding –Direct Adjustment –Propensity Score Weighting Propensity Model Selection Weight Trimming Clustering

4. Population: (Y,X,T) Counterfactual Population: Y(0),XCounterfactual Population: Y(1),X Counterfactual Sample Sub-Sample Sample Big Picture

5. Population: (Y,X,T) Sub-Sample Sample

7. TCNTC N109704039 % Dying8.0%5.9%

9. TCNTC N30441999 % Dying27.8%11.9%

11. Sample Weights Reciprocal of the conditional probability of being included in the sub-sample given –ISS –AIS –Age –Dead/Alive at Sample Ascertainment –Dead/Alive at 3 Months post injury Weights depend on outcome - they can’t be ignored.

13. Missing Data Socio-demographicPre-Hospital Injury SeverityHospital Injury Severity Age (0%)SBP/Shock (38.1%)AIS (0%) Gender (0%)GCS Motor (30.0%)NISS (0%) Race (0%)Paralytics (8.6%)Lowest SRR (0%) Insurance (1.2%)Intubation (6.0%)APS (0%) EMS Level/ Mode of Transport (19.0%) SBP/Shock (1.0%) Outcome MOI (2.0%)Pupils (5.7%) Death (0%)GCS Motor (2.4%) Midline Shift (1.8%) Co-morbidities Open Skull Fracture (0%) Obesity (4.6%)Flail Chest (0%) Coagulopathy (4.6%)Heart Rate (0.9%) Charlson (4.6%)Paralysis (1.1%) Long Bone Fracture/Amputation (0%)

14. Multiple Imputation For proper MI, we fill in the missing data by randomly drawing from the posterior predictive distribution of the missing data given the observed data. To reflect the uncertainty in these imputed values, we create multiple imputed datasets. An estimate (and variance) of the effect of trauma center is computed for each completed data. The results are combined to obtain an overall estimate. The overall variance is the sum of the within imputation variance and the between imputation variance.

15. Multiple Imputation To draw from the posterior predictive distribution, a model for the joint distribution of the variables and a prior distribution on the model parameters must be specified. Joe Schafer’s software UM’s ISR software - IVEWARE –Specifies a sequence of full conditionals, which is not, generally, compatible with a joint distribution. WINBUGS - Crainiceanu and Egleston –Specifies a sequence of conditional models, which is compatible with a joint distribution

16. Selection Bias TCNTC Age < 5579%53% Male73%57% Race White, Non-Hispanic56%72% Hispanic18%13% Non-white, Non-Hispanic26%16% Charlson 077%58% 114%17% 25%10% 3 or more5%16%

17. TCNTC Mechanism of Injury Blunt - Motor Vehicle53%32% Blunt - Fall20%53% Blunt - Other10% Penetrating - Firearm12%4% Penetrating - Other5%2% Pupils - Abnormal9%5% GCS Motor Score 674%90% 4-58%4% 2-31% 1 - Not Chemically Paralyzed5%3% Chemically Paralyzed12%2% Selection Bias

18. TCNTC NISS <1624%52% 16-2416%56% 25-3429%15% >3418%9% Max AIS <=38%73% 427%20% 5-615%7% EMS Level/Intubation ALS - Intubated12%3% ALS - Not Intubated69%41% BLS11%35% Not Transported by EMS8%22% Selection Bias

19. Notation T denotes treatment received (0/1) X denotes measured covariates Y(1) denotes the outcome a subject would have under trauma care. Y(0) denotes the outcome a subject would have under non-trauma care. Only one of these is observed, namely Y=Y(T), the outcome of the subject under the care actually received. Observed Data: (Y,T,X)

20. Causal Estimand

21. Selection Bias We worked with scientific experts to define all possible “pre-treatment” variables which are associated with treatment and mortality. We had extensive discussions about unmeasured confounders. Within levels of the measured variables, we assumed that treatment was randomized. T is independent of {Y(0),Y(1)} given X

22. Example (Hernan et al., 2000)

23. Direct Adjustment

29. Population: (Y,X,T) Counterfactual Population: Y(0),XCounterfactual Population: Y(1),X Counterfactual Sample Sub-Sample Sample

30. Propensity Score Weighting

32. Y(1) Counterfactual Population

33. Y(0) Counterfactual Population

34. Why does this work?

35. Propensity Model Selection Select a propensity score model such that the distribution of X is comparable in the two counterfactual populations (Tan, 2004).

36. Weight Trimming The propensity score weighted estimator can be sensitive to individuals with large PS weights. When the weights are highly skewed, the variance of the estimator can be large. We trim the weights to minimize MSE.

38. Clustering Assumed a working independence correlation structure. Fixed up standard errors using the sandwich variance technique.

39. Results TCNTCTCNTC Age < 5579%53%72%73% Male73%57%69%67% Race White, Non-Hispanic56%72%60%58% Hispanic18%13%16%17% Non-white, Non-Hispanic26%16%24%25% Charlson 077%58%72%73% 114%17%14%13% 25%10%6% 3 or more5%16%8% Counterfactual Populations Sample

40. TCNTCTCNTC Mechanism of Injury Blunt - Motor Vehicle53%32%48%50% Blunt - Fall20%53%28%27% Blunt - Other10% 9% Penetrating - Firearm12%4%10% Penetrating - Other5%2%4% Pupils - Abnormal9%5%8%9% GCS Motor Score 674%90%78%77% 4-58%4%7%6% 2-31% 1 - Not Chemically Paralyzed5%3%4% Chemically Paralyzed12%2%10%11% Results Counterfactual Populations Sample

41. TCNTCTCNTC NISS <1624%52%30% 16-2416%56%7% 25-3429%15%26%24% >3418%9%16%19% Max AIS <=38%73%61%60% 427%20%26% 5-615%7%13%14% EMS Level/Intubation ALS - Intubated12%3%10% ALS - Not Intubated69%41%61% BLS11%35%17% Not Transported by EMS8%22%12% Results Counterfactual Populations Sample

42. 30 Days90 Days365 Days Total NSCOT Population % Dying in TC7.6%8.7%10.4% % Dying in NTC10.0%11.4%13.8% RR0.76 (0.58,1.00)0.77 (0.60,0.98)0.75 (0.60,0.95) Results

43. Case Fatality Ratios Adjusted for Differences in Casemix 0 5 10 15 In Hospital 30 days 90 days365 days TCs NTCs Adjusted Relative Risk:.60.75.95

44. 30 Days90 Days365 Days AGE<55 % Dying in TC7.6%8.7%10.4% % Dying in NTC10.0%11.4%13.8% RR0.76 (0.58,1.00)0.77 (0.60,0.98)0.75 (0.60,0.95) AGE>=55 % Dying in TC1.5% 1.8% % Dying in NTC1.1%1.2%2.9% RR1.39 (0.68,2.84)1.33 (0.68,2.60)0.63 (0.32,1.22) Results MAXAIS <=3

45. 30 Days90 Days365 Days AGE<55 % Dying in TC6.0%6.7%7.4% % Dying in NTC9.4%11.1%13.2% RR0.64 (0.44,0.93)0.60 (0.41,0.89)0.56 (0.38,0.82) AGE>=55 % Dying in TC14.0%17.2%23.9% % Dying in NTC15.1%23.0%27.4% RR0.92 (0.54,1.57)0.75 (0.51,1.11)0.87 (0.58,1.32) Results MAXAIS = 4

46. 30 Days90 Days365 Days AGE<55 % Dying in TC25.1%26.1%26.3% % Dying in NTC38.5% RR0.65 (0.45,0.94)0.68 (0.47,0.98)0.68 (0.47,0.99) AGE>=55 % Dying in TC44.6%50.2%51.5% % Dying in NTC61.6%63.7% RR0.72 (0.45,1.17)0.79 (0.51,1.21)0.81 (0.53,1.23) Results MAXAIS = 5,6

47. Relative Risks by Age and Severity Age of Patient Severity< 55>=55 Moderate (AIS 3) 0.32 0.63 1.220.74 1.08 1.57 Serious (AIS 4) 0.38 0.56 0.820.58 0.87 1.32 Severe (AIS 5-6) 0.47 0.68 0.990.53 0.81 1.23

48. Potential Lives Saved Nationwide H-CUP Hospital Discharge Data 360,293 adults who meet NSCOT inclusion criteria 45% Treated in NTCs 162,132 16,862 Deaths If Treated in TCs 22,374 Deaths If Treated in NTCs 5,512 Each Year

49. Conservative Estimate Study non-trauma centers were limited to those treating at least 25 major trauma patients each year; most non-trauma centers are smaller 17 of the study non-trauma centers had a designated trauma team and 8 had a trauma director

50. Conclusions... to date The results demonstrate the benefits of trauma center care and argue strongly for continued efforts at regionalization At the same time, they highlight the difficulty in improving outcomes for the geriatric trauma patient

51. Biostatistician’s Dream More efficient estimation (Tan,Wang) Functional outcomes in the presence of death (Egleston) Sensitivity Analysis (Egleston) Instrumental variable analysis (Cohen, Louis, Crainiceanu) Imputation (Crainiceanu, Egleston)