TRANSPLANT CENSORING AND THE NATURAL HISTORY OF MELD VIA EM ESTIMATION

Purpose: To obtain natural history estimates for disease progression on the U.S. liver transplant wait list

Method: The U.S. liver transplant wait list is prioritized by MELD, a combination of laboratory values positively correlated with 90-day mortality.  The U.S. Scientific Registry for Transplant Recipients publishes 30-day MELD transition data appropriate for Markov modeling.  However, this data cannot be regarded as natural history, as transplant interrupts MELD transitions.  Moreover, the data shows some MELDs more likely to improve than worsen, odd because listed candidates should on average expect worsening MELDs.  We hypothesize this is due to censoring by transplant, and fit a statistical model that allows this using the EM algorithm.

Results: The fitted model confirms transplant censoring (Figure 1) and produces estimates of the natural history of MELD without transplant that differ from naïve estimates in important ways (Figure 2).  Transplant censoring also implies that policy changes that increase transplant rates would improve untransplanted progression, and the fitted model provides an estimate of this effect (Figure 3).

Conclusion: Estimating transplant censoring is potentially important. A policy change that increases transplant rates would increase censoring of worsening MELD transitions, resulting in an improvement in untransplanted progression.  In this case it would not be accurate to use naive estimates of untransplanted progression.  Similarly, if we are modeling a specific region of the U.S. where transplant rates are higher (lower) than the national level, then untransplanted progression would be better (worse) than the national estimates, and naïve national estimates would be misleading.  By accounting for transplant censoring, our natural history estimates avoid these pitfalls.