Do Trauma Centers Save Lives?

A Statistical Solution

Daniel O. Scharfstein

Collaborators

• Brian Egleston

• Ciprian Crainiceanu

• Zhiqiang Tan

• Tom Louis

Issues

• Outcome Dependent Sampling• Missing Data• Confounding

– Direct Adjustment– Propensity Score Weighting

• Propensity Model Selection• Weight Trimming• Clustering

Population: (Y,X,T)

Counterfactual Population: Y(0),XCounterfactual Population: Y(1),X

Counterfactual Sample Counterfactual Sample

Sub-Sample

Sample

Big Picture

Population: (Y,X,T)

Sub-Sample

Sample

TC NTC

N 10970 4039

% Dying 8.0% 5.9%

TC NTC

N 3044 1999

% Dying 27.8% 11.9%

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.

Missing DataSocio-demographic Pre-Hospital Injury Severity Hospital 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%)

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.

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

Selection Bias

TC NTC

Age < 55 79% 53%

Male 73% 57%

Race

White, Non-Hispanic 56% 72%

Hispanic 18% 13%

Non-white, Non-Hispanic 26% 16%

Charlson

0 77% 58%

1 14% 17%

2 5% 10%

3 or more 5% 16%

TC NTC

Mechanism of Injury

Blunt - Motor Vehicle 53% 32%

Blunt - Fall 20% 53%

Blunt - Other 10% 10%

Penetrating - Firearm 12% 4%

Penetrating - Other 5% 2%

Pupils - Abnormal 9% 5%

GCS Motor Score

6 74% 90%

4-5 8% 4%

2-3 1% 1%

1 - Not Chemically Paralyzed 5% 3%

Chemically Paralyzed 12% 2%

Selection Bias

TC NTC

NISS

<16 24% 52%

16-24 16% 56%

25-34 29% 15%

>34 18% 9%

Max AIS

<=3 8% 73%

4 27% 20%

5-6 15% 7%

EMS Level/Intubation

ALS - Intubated 12% 3%

ALS - Not Intubated 69% 41%

BLS 11% 35%

Not Transported by EMS 8% 22%

Selection Bias

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)

Causal Estimand

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

Example (Hernan et al., 2000)

Direct Adjustment

Direct Adjustment

Direct Adjustment

Direct Adjustment

Direct Adjustment

Direct Adjustment

Population: (Y,X,T)

Counterfactual Population: Y(0),XCounterfactual Population: Y(1),X

Counterfactual Sample Counterfactual Sample

Sub-Sample

Sample

Propensity Score Weighting

Y(1) Counterfactual Population

Y(0) Counterfactual Population

Why does this work?

Propensity Model Selection

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

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.

Clustering

• Assumed a working independence correlation structure.

• Fixed up standard errors using the sandwich variance technique.

Results

TC NTC TC NTC

Age < 55 79% 53% 72% 73%

Male 73% 57% 69% 67%

Race

White, Non-Hispanic 56% 72% 60% 58%

Hispanic 18% 13% 16% 17%

Non-white, Non-Hispanic 26% 16% 24% 25%

Charlson

0 77% 58% 72% 73%

1 14% 17% 14% 13%

2 5% 10% 6% 6%

3 or more 5% 16% 8% 8%

CounterfactualPopulationsSample

TC NTC TC NTC

Mechanism of Injury

Blunt - Motor Vehicle 53% 32% 48% 50%

Blunt - Fall 20% 53% 28% 27%

Blunt - Other 10% 10% 10% 9%

Penetrating - Firearm 12% 4% 10% 10%

Penetrating - Other 5% 2% 4% 4%

Pupils - Abnormal 9% 5% 8% 9%

GCS Motor Score

6 74% 90% 78% 77%

4-5 8% 4% 7% 6%

2-3 1% 1% 1% 1%

1 - Not Chemically Paralyzed 5% 3% 4% 4%

Chemically Paralyzed 12% 2% 10% 11%

ResultsCounterfactualPopulationsSample

TC NTC TC NTC

NISS

<16 24% 52% 30% 30%

16-24 16% 56% 7% 7%

25-34 29% 15% 26% 24%

>34 18% 9% 16% 19%

Max AIS

<=3 8% 73% 61% 60%

4 27% 20% 26% 26%

5-6 15% 7% 13% 14%

EMS Level/Intubation

ALS - Intubated 12% 3% 10% 10%

ALS - Not Intubated 69% 41% 61% 61%

BLS 11% 35% 17% 17%

Not Transported by EMS 8% 22% 12% 12%

ResultsCounterfactualPopulationsSample

30 Days 90 Days 365 Days

Total NSCOT Population

% Dying in TC 7.6% 8.7% 10.4%

% Dying in NTC 10.0% 11.4% 13.8%

RR 0.76 (0.58,1.00) 0.77 (0.60,0.98) 0.75 (0.60,0.95)

Results

Case Fatality Ratios Adjusted for Differences in Casemix

0

5

10

15

InHospital

30 days 90 days 365 daysTCs

NTCs

Adjusted

Relative Risk:

.60.75

.95

30 Days 90 Days 365 Days

AGE<55

% Dying in TC 7.6% 8.7% 10.4%

% Dying in NTC 10.0% 11.4% 13.8%

RR 0.76 (0.58,1.00) 0.77 (0.60,0.98) 0.75 (0.60,0.95)

AGE>=55

% Dying in TC 1.5% 1.5% 1.8%

% Dying in NTC 1.1% 1.2% 2.9%

RR 1.39 (0.68,2.84) 1.33 (0.68,2.60) 0.63 (0.32,1.22)

Results

MAXAIS <=3

30 Days 90 Days 365 Days

AGE<55

% Dying in TC 6.0% 6.7% 7.4%

% Dying in NTC 9.4% 11.1% 13.2%

RR 0.64 (0.44,0.93) 0.60 (0.41,0.89) 0.56 (0.38,0.82)

AGE>=55

% Dying in TC 14.0% 17.2% 23.9%

% Dying in NTC 15.1% 23.0% 27.4%

RR 0.92 (0.54,1.57) 0.75 (0.51,1.11) 0.87 (0.58,1.32)

Results

MAXAIS = 4

30 Days 90 Days 365 Days

AGE<55

% Dying in TC 25.1% 26.1% 26.3%

% Dying in NTC 38.5% 38.5% 38.5%

RR 0.65 (0.45,0.94) 0.68 (0.47,0.98) 0.68 (0.47,0.99)

AGE>=55

% Dying in TC 44.6% 50.2% 51.5%

% Dying in NTC 61.6% 63.7% 63.7%

RR 0.72 (0.45,1.17) 0.79 (0.51,1.21) 0.81 (0.53,1.23)

Results

MAXAIS = 5,6

Relative Risks by Age and Severity

Age of Patient

Severity < 55 >=55

Moderate (AIS 3) 0.32

0.631.22 0.74

1.081.57

Serious (AIS 4) 0.38

0.560.82 0.58

0.871.32

Severe (AIS 5-6) 0.47

0.680.99 0.53

0.811.23

Potential Lives Saved Nationwide H-CUP Hospital Discharge Data

360,293 adults who meet NSCOT inclusion criteria

45% Treated in NTCs162,132

16,862 DeathsIf Treated in TCs

22,374 Deaths If Treated in NTCs

5,512 Each Year

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

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

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)