A model for calculating the long-term estimated post-transplant survival of deceased donor liver transplant patients

Abstract

Background: The estimated long-term survival (EPTS) score is used for kidney allocation. A comparable prognostic tool to accurately quantify EPTS benefit in deceased donor liver transplant (DDLT) candidates is nonexistent.

Methods: Using the Scientific Registry of Transplant Recipients (SRTR) database, we developed, calibrated, and validated a nonlinear regression equation to calculate liver-EPTS (L-EPTS) for 5- and 10-year outcomes in adult DDLT recipients. The population was randomly split (70:30) into two discovery (N = 26,372 and N = 46,329) and validation cohorts (N = 11,288 and N = 19,859) for 5- and 10-year post-transplant outcomes, respectively. Discovery cohorts were used for variable selection, Cox proportional hazard regression modeling, and nonlinear curve fitting. Eight clinical variables were selected to construct the L-EPTS formula, and a five-tiered ranking system was created.

Findings: Tier thresholds were defined and the L-EPTS model was calibrated (R² = 0.96 [5-year] and 0.99 [10-year]). Patients' median survival probabilities in the discovery cohorts for 5- and 10-year outcomes ranged from 27.94% to 89.22% and 16.27% to 87.97%, respectively. The L-EPTS model was validated via calculation of receiver operating characteristic (ROC) curves using validation cohorts. Area under the ROC curve was 82.4% (5-year) and 86.5% (10-year).

Interpretation: L-EPTS has high applicability and clinical utility because it uses easily obtained pre-transplant patients characteristics to accurately discriminate between those who are likely to receive a prolonged survival benefit and those who are not. It is important to evaluate medical urgency alongside survival benefit and placement efficiency when considering the allocation of a scarce resource.

Funding: There are no funding sources related to this project.

Keywords: Liver; Long-term; Model; Prognostic; Survival; Transplant.

Fig. 1

Correlation heatmap for all independent variables evaluated in the EPTS model. Pearson's correlation coefficients were calculated for the data matrix containing the twelve independent variables evaluated in the discovery cohort (N = 46,338) for all 10-year outcomes to give a measure of collinearity. Blue indicates a positive correlation, and red indicates a negative correlation. The color saturation and circle area increase as the correlation coefficients increase in magnitude.

Fig. 2

Calibration of the five-tiered ranking system. The estimated median survival probability (EMSP) was calculated for all patients in the discovery cohorts (N = 26,372 and N = 46,329) and is provided as a function of mean survival years per tier for all 5-year (a) and 10-year (b) predictions. We defined the five-tiered thresholds by selecting the maximum correlation between the median survival probability and the mean years survived at 10-years post-transplant. The following tier thresholds were assigned: 5 (EMSP > 0.85), 4 (EMSP > 0.75 and ≤0.85), 3 (EMSP > 0.65 and ≤ 0.75), 2 (EMSP > 0.5 and ≤0.65), and 1 (EMSP ≤ 0.5). The goodness-of-fit (R²) was calculated using linear regression and reported at 0.96 and 0.99 for 5- and 10-years post-transplant.

Fig. 3

ROC and AUC of the validation cohorts. Logistic regression was performed on the validation cohorts (N = 11,288 and N = 19,859) using the generalized linear model for all (a) 5- and (b) 10-year post-transplant predictions. The area under the receiver operating characteristic curve or AUC was reported at 0.824 and 0.865 for all 5- and 10-year predictions.