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. Author manuscript; available in PMC: 2019 Oct 1.
Published in final edited form as: Med Care. 2018 Oct;56(10):847–854. doi: 10.1097/MLR.0000000000000972

Table 2.

Measuring the proportion change in between-HRR variation explained by resident characteristics, facility characteristics, and state and the strength of clustering within HRRs and state for initiating commonly used opioids or doses ≥50 mg OME/day (N=62,889 residents in 12,345 facilities within 298 hospital referral regions).1

Characteristics included in multilevel model2
Null model Resident Resident + Facility Resident + Facility + State
Initiating oxycodone
    PCV3 Referent 1.3% 7.5% 84.1%
    ICCHRR4 0.37 0.36 0.35 0.06
    ICCstate5 - - - 0.24
Initiating hydrocodone6
    PCV Referent −2.0% 0.2% 58.2%
    ICCHRR 0.16 0.17 0.16 0.07
    ICCstate - - - 0.09
Initiating tramadol6
    PCV Referent −3.8% −2.5% 59.1%
    ICCHRR 0.10 0.10 0.10 0.04
    ICCstate - - - 0.06
Initiating doses ≥50 mg OME/day
    PCV Referent 1.5% 9.4% 46.6%
    ICCHRR 0.06 0.07 0.06 0.03
    ICCstate - - - 0.03

Abbreviations: HRR, hospital referral region; ICC, Intraclass correlation coefficient; OME; oral morphine equivalent; PCV, proportional change in cluster variation

1

See Methods Appendix for further detail on multilevel model building.

2

Multilevel logistic models with a random intercept for hospital referral region were sequentially fitted using resident and facility characteristics as described in Supplementary Table 3. The final model was a cross-classified multilevel model including a second random intercept for state.

3

PCV described the proportional change in HRR variation explained by the multilevel model and was estimated as (variance of random intercept in null model – variance of random intercept in adjusted model) / variance of random intercept in null model.

4

ICCHRR estimates the correlation in the propensity to initiate the same opioid or dose between two individuals randomly selected from each HRR. The ICCHRR for the final model is an estimate of the correlation between two persons in the same HRR but different states.

5

ICCstate was estimated using a cross-classified logistic model and estimates the correlation in the propensity to initiate the same opioid or dose between two individuals in the same state but different HRRs.

6

Adding resident and facility characteristics to this model increased the variance. This can occur when there is negative correlation between the opioid initiated and resident/facility factors within HRRs.48