A mathematical model to predict endothelial cell density following penetrating keratoplasty with selective dropout from graft failure

Tonya D. Riddlesworth, Craig Kollman, Jonathan H. Lass, Sanjay V. Patel, R. Doyle Stulting, Beth Ann Benetz, Robin L. Gal, Roy W. Beck

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


METHODS. In a subset (n = 591) of Cornea Donor Study participants, postoperative ECD was determined by a central reading center. Various statistical models were considered to estimate the ECD trend longitudinally over 10 years of follow-up. A biexponential model with and without a logarithm transformation was fit using the Gauss-Newton nonlinear least squares algorithm. To account for correlated data, a log-polynomial model was fit using the restricted maximum likelihood method. A sensitivity analysis for the potential bias due to selective dropout was performed using Bayesian analysis techniques.

RESULTS. The three models using a logarithm transformation yield similar trends, whereas the model without the transform predicts higher ECD values. The adjustment for selective dropout turns out to be negligible. However, this is possibly due to the relatively low rate of graft failure in this cohort (19% at 10 years). Fuchs’ dystrophy and pseudophakic/aphakic corneal edema (PACE) patients had similar ECD decay curves, with the PACE group having slightly higher cell densities by 10 years.

CONCLUSIONS. Endothelial cell loss after PK can be modeled via a log-polynomial model, which accounts for the correlated data from repeated measures on the same subject. This model is not significantly affected by the selective dropout due to graft failure. Our findings warrant further study on how this may extend to ECD following endothelial keratoplasty.

PURPOSE. We constructed several mathematical models that predict endothelial cell density (ECD) for patients after penetrating keratoplasty (PK) for a moderate-risk condition (principally Fuchs’ dystrophy or pseudophakic/aphakic corneal edema).

Original languageEnglish (US)
Pages (from-to)8409-8415
Number of pages7
JournalInvestigative Ophthalmology and Visual Science
Issue number12
StatePublished - Dec 2014


  • Endothelial cell density
  • Mathematical model
  • Penetrating keratoplasty

ASJC Scopus subject areas

  • Ophthalmology
  • Sensory Systems
  • Cellular and Molecular Neuroscience


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