Combining Data Sources to Produce

Nationally Representative Estimates of

Hospital Encounter Characteristics

Jay Breidt

2023 FCSM Research and Policy Conference

Hyattsville, Maryland

Joint work with Dean Resnick, NORC; Geoffrey

Jackson and Donielle White, NCHS
Background, I

• National Hospital Care Survey (NHCS)

• conducted by the National Center for Health Statistics (NCHS)

• stratified simple random sample of non-federal and

noninstitutional hospitals with six or more staffed inpatient

beds

• subject to hospital-level nonresponse

• responding hospitals, A, provide (essentially) complete

encounter data for all patients for 2020

• Invaluable research resource for patterns of health care

delivery and utilization in the United States

• patient demographics, diagnoses/procedures, length of stay

• linkable to external data sources including National Death

Index and Centers for Medicare & Medicaid Services data

• 2020 data includes critically important hospital records for the

first year of COVID patients

2/17
Background, II

• Focus here on A = responding NHCS inpatient hospitals

• provide (essentially) complete encounter data for all patients

for 2020

• Combine A with other data sources in order to produce

nationally representative estimates

• Proprietary commercial database, B

• nonprobability “sample” of participating hospitals

• good coverage of hospital population by various measures

(e.g., geographic dispersion)

• participating hospitals provide (essentially) complete encounter

data for 2020

• Hospital population info from Healthcare Cost and Utilization

Project National Inpatient Sample (HCUP-NIS), C

• essentially a census of hospitals, though a sample of patients

within hospitals

3/17
Challenges and opportunities

• Massive data at the encounter level

• number of hospitals in A ∪ B is hundreds out of thousands of

US hospitals

• number of encounters in A ∪ B is tens of millions

• No linkages!

• deidentified hospitals in B

• data use agreement precludes linking hospitals in A and B

• no hospital identifiers in C, hence cannot link to A or B

4/17
Estimation goals: produce nationally-representative estimates

Goal Data Controls Weights Release

1 Both national summaries hospital national

A ∪ B (using HCUP-NIS) level estimates

2.1 Only Goal 1 estimates encounter restricted-use

A (+ nat’l summaries) level data file

2.2 Subsample Goal 1 estimates encounter public-use

of A (+ nat’l summaries) level data file

5/17
Goal 1: Combined, weighted dataset for national estimates

• A is a probability sample

• known inclusion probabilities, but not all hospitals respond

• potential differential nonresponse

• use information available for respondents and population to

model propensity to respond

• B is not a probability sample

• potential differential participation

• use information available for participants and population to

model propensity to participate

• Caution: no way to know how response and participation

propensities might interact

• Use modeled propensities to construct hospital-level weights

6/17
Modeling hospital response propensities for NHCS

• S ⊂ U is stratified NHCS sample, with known inclusion

probabilities πh > 0

• stratification is determined by bed size, type of hospital, and

rural/urban designation

• Define Ah = 1 if hospital h responds to NHCS and Ah = 0

otherwise and define A = {h ∈ S ⊂ U : Ah = 1}

• Pseudo-log-likelihood criterion is

X

h∈U

1{h∈S}

πh

Ah log 

ρh

1 − ρh



+

X

h∈C

log (1 − ρh)

• Assume logistic model for ρh

• Because covariates are entirely categorical, can fit using

standard logistic regression software

7/17
Modeling hospital participation propensities for proprietary

• Define Bh = 1 if h ∈ U participates in proprietary and Bh = 0

otherwise and define B = {h ∈ U : Bh = 1}

• Define the participation propensity, γh = P [Bh = 1] and

assume a logistic model

• The log-likelihood for estimation of parameters in γh is

X

h∈B

log 

γh

1 − γh



+

X

h∈C

log (1 − γh).

• Since xh is entirely categorical, we can again use standard

logistic regression software to maximize the log-likelihood

8/17
Goal 1 hospital-level weights, I

• Once both propensity models are fitted, we construct

hospital-level weights:

w

A

h =

1

πhρbh

, h ∈ A; w

B

h =

1

γbh

, h ∈ B

• (constant within cells because covariates are categorical)

• We combine the data with a separate dual-frame

estimator, by first choosing λ ∈ (0, 1) and then

computing national estimates as

X

h∈A∪B

w

AB

h

X

i∈Hh

yhi = λ

X

h∈A

w

A

h

X

i∈Hh

yhi +(1−λ)

X

h∈B

w

B

h

X

i∈Hh

yhi

where yhi is a measurement for encounter record i in hospital

h and Hh is the entire set of encounter records

• we choose λ = nA/(nA + nB )

9/17
Variance estimation for Goal 1

• Variance of the separate estimator:

λ

2Var 

Tb

A



+ (1 − λ)

2Var 

Tb

B



+ 2λ(1 − λ)Cov Tb

A,TbB



,

where sampling covariance term cannot be determined

• best case: NHCS respondents are unlikely to be participants,

and vice-versa

• worst case: NHCS respondents and participants are likely to be

the same

• Stratified delete-a-group jackknife variance estimator, with

B serving as its own stratum

• treats A and B as independent: λ

2VbA + (1 − λ)2VbB

• accounts for uncertainty due to estimation of propensity

models

10/17
Goal 2 encounter-level weights, I

• Given the combined national estimates, need to reweight only

the NHCS data to construct

• Goal 2.1: weighted restricted-use data set that reproduces key

national estimates

• Goal 2.2: subsample of Goal 2.1 data set to be released as

public use file

• Key considerations:

• no proprietary microdata will be released

• proprietary data only appear in the national estimates that are

used as controls for the new weights

• achieving controls requires weights that vary across encounter

records within hospitals

• try to minimize variation of weights within hospitals

11/17
Goal 2 encounter-level weights, II

• Vector of key national estimates,

Tez =

X

h∈A∪B

X

i∈Hh

w

AB

h

zhi

• zhi includes coarsened diagnosis codes, discharge status, length

of stay, age group, sex, newborn status

• Goal 2 is to find encounter-level weights {w

A

hi}h∈A that vary

as little as possible within hospitals while satisfying

Tez =

X

h∈A∪B

X

i∈Hh

w

AB

h

zhi =

X

h∈A

X

i∈Hh

w

A

hizhi

• This is a (large) survey calibration problem

12/17
Goal 2 encounter-level weights, III

• Generalized regression (GREG) version of this calibration is

obtained via

T

∗

y =

X

h∈A

w

A

h

X

i∈Hh



yhi − z

⊤

hiβb

N



+ Te⊤

z βb

N

where

βb

N =





X

h∈A

X

i∈Hh

w

A

h

zhiz

⊤

hi





−1

X

h∈A

X

i∈Hh

w

A

h

zhi yhi

13/17
Goal 2 encounter-level weights, IV

• GREG version of these weights is (for h ∈ A)

w

A

hi = w

A

h







1 + 

Tez − Tb

Az

⊤





X

h∈A

X

i∈Hh

w

A

h

zhiz

⊤

hi





−1

zhi







• The GREG weights are calibrated to the combined estimates:

T

∗

z =

X

h∈A

X

i∈Hh

w

A

hiz

⊤

hi = Tez

• We use a closely-related raking approach

14/17
Goal 2 variance estimation, I

• GREG can be written

T

∗

y = Tb

Ay +



Tez − Tb

Az

⊤

βN +



Tez − Tb

Az

⊤ 

βb

N − βN



≃

n

Tb

Ay − (1 − λ)Tb⊤

AzβN

o

+ (1 − λ)Tb⊤

BzβN

• λ = 1: estimator ignores proprietary sample B

• λ = 0: like ordinary GREG, with model-based predictions for B

instead of U

• λ ∈ (0, 1): uses a shrunken version of the model-based

predictions

• Variance estimation: first term is A-only, second term is

B-only

15/17
Goal 2 variance estimation, II

• Focusing on “sampling” error only,

Var T

∗

y



≃ Var Tb

A,y−(1−λ)z ⊤βN



+(1 − λ)

2β⊤

NVar 

Tb

Bz



βN

+2(1 − λ)Cov Tb

A,y−(1−λ)z ⊤βN

,Tb⊤

Bz



βN

• covariance term may be small

• first two terms could be estimated directly, but would require

cumbersome computations for each y

• Stratified delete-a-group jackknife for A only

• use earlier A ∪ B jackknife weights to compute replicate

control totals

• calibrate each set of A-only replicate weights to the replicate

controls

16/17
Summary

• Principled weighting methodology for combining probability

and nonprobability data, accounting for sampling design and

differential propensities

• Calibration strategy for producing microdata set using only

the probability data source

• Replication-based variance estimation at all levels

• Questions or comments welcomed:

breidt-jay@norc.org

• Thank you!

17/17