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The Natural History of MELD. Gordon Hazen INFORMS Healthcare June 21, 2011. MELD. The U.S. liver transplant wait list is prioritized by MELD. MELD = M odel for E nd-Stage L iver D isease A combination of laboratory values positively correlated with 90-day mortality Cox Regression:

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The natural history of meld

The Natural History of MELD

Gordon Hazen

INFORMS Healthcare June 21, 2011


MELD

  • The U.S. liver transplant wait list is prioritized by MELD.

    • MELD = Model for End-Stage Liver Disease

    • A combination of laboratory values positively correlated with 90-day mortality

    • Cox Regression:

      • MELD = 3.78[Ln serum bilirubin (mg/dL)] + 11.2[Ln INR] + 9.57[Ln serum creatinine (mg/dL)] + 6.43

    • Truncated to the range 6 – 40

  • Instituted by UNOS in 2002


A meld progression curiosity
A MELD Progression Curiosity

  • UNOS MELD Data 2007


A meld progression curiosity1
A MELD Progression Curiosity

  • Transition probabilities

  • Question: If not transplanted, does a patient tend to get better, or worse?


A meld progression curiosity2
A MELD Progression Curiosity

  • For MELDs 21-30, and 15-20, the tendency is to improve if not transplanted:

  • Possible explanation: Transplant tends to censor worsening MELDs more than it censors improving MELDs.

  • Implication: We do not know the natural history of MELD progression.


Overview
Overview

  • Why this matters

  • So what can be done about this?

    • Natural history model

    • EM estimation

  • Results

    • Natural history

    • Naïve versus natural history

  • Summary


Why this matters regional da modeling
Why this matters: Regional DA modeling

  • Transplant rates differ across regions

  • Therefore, decision analyses should be done separately by region

    • Use regional transplant probabilities

    • Use national MELD progression probabilities


Why this matters regional da modeling1
Why this matters: Regional DA modeling

  • The naïve approach:

  • Keep (naïve) estimates of untransplanted MELD progression


Why this matters regional da modeling2
Why this matters: Regional DA modeling

  • If region has low transplant rates, then

    • Fewer bad MELD transitions are censored; so

    • Untransplanted MELD progression should be worse than the national average

  • If region has high transplant rates, then

    • More bad MELD transitions are censored

    • Untransplanted MELD progression should be better than the national average

  • The (naïve) national estimates of untransplanted MELD progression do not reflect these changes.


Why this matters da policy modeling
Why this matters: DA policy modeling

  • If a policy change lowers transplant rates, then

    • Fewer bad MELD transitions are censored; so

    • Untransplanted MELD progression should be worse than before

  • If a policy change raises transplant rates, then

    • More bad MELD transitions are censored

    • Untransplanted MELD progression should be better than before

  • The (naïve) national estimates of untransplanted MELD progression do not reflect these changes.


So what can be done
So what can be done?

  • Estimate natural history of MELD progression

    • pxy = transition prob from MELD category x to category y in the absence of any transplants

  • Estimate region-specific transplant probs

    • trxy = prob in region r of transplant given MELD transition from category x to category y

  • The complete-data likelihood


So what can be done1
So what can be done?

  • We see therefore that Lc is the product of

    • (a) transition data: the product over x of independent multinomial observations

      ((#Tx)+xy+ (NoTx)+xy; all y)

      with category probabilities (pxy; all y) and total observation count (#Tx)+x+ + (#NoTx)+x+ ; and

    • (b) transplant data: the product over r and x of independent multinomial observations

      ((#Tx)rxy, (#NoTx)rxy; all y)

      with category probabilities (τrxy,1τrxy; all y) and total observation count (#Tx)rx++(#NoTx)rx+.


So what can be done2
So what can be done?

  • Would like to form the maximum likelihood estimates

  • But how to do this if we cannot observe (#Tx)rxy= # in region r who went from x to y and were transplanted?

  • We do observe (#Tx)rx+. So if we knew pxy and trxy, we could calculate the expected value of the unobserved (#Tx)rxy:


So what can be done3
So what can be done?

  • This is a missing data problem, for which the E-M algorithm is known to be a useful tool.

  • The E-M algorithm:

  • The E-M algorithm is known to converge to at least a local MLE.


Results natural history
Results: Natural history

  • The E-M estimates of pxy(natural history)

  • Bold denotes a number larger than the corresponding naïve untransplanted progression probability.

  • Red denotes a number smaller than the corresponding naïve untransplanted progression probability.


Results na ve vs e m natural history
Results: Naïve vs. E-M Natural history

  • MELD improvements for MELDs 21-30 and 15-20 are nearly eliminated.


D meld na ve vs e m natural history
DMELD: Naïve vs. E-M natural history

  • Using the following MELD assignments

  • the expected monthly change in MELD is:



Untransplanted progression
Untransplanted Progression

  • Note: Untransplanted progression = naïve progression  Natural history progression (the point of this talk)


Results projected impact of d transplant rate on na ve untransplanted meld progression
Results: Projected impact of Dtransplant rate on (naïve) untransplanted MELD progression

  • What happens if we scale up/down the transplant probabilities trxy? Do we see the predicted change in naïve progression?

  • For Region 7:


News flash 12 month data
News Flash: 12-month data

  • MELD improvements for MELDs 21-30 and 15-20

  • January 2007 only:


News flash 12 month data1
News Flash: 12-month data

  • MELD improvements for MELDs 21-30 and 15-20

  • 12-month data 2007:


Summary
Summary

  • E-M estimation can be used to capture natural history of MELD.

  • E-M estimates confirm that transplanting censors worsening MELD progression more than it does improving MELD progression.

  • The difference is not large on a monthly basis but can compound to make a difference.

  • MELD 21-30 natural history estimates still indicate a tendency to improve – is something else going on?


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