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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

slide2
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?