Utility in Treating Kidney Failure in End-Stage Liver Disease with Simultaneous Liver- Kidney Transplantation
Supplemental Materials
Appendix 1, SDC: Details methods on flexible parametric modelling, competing risk model, and multiple imputation.
Appendix 2, SDC: Analysis for Cohort #1 compared to primary analysis.
Appendix 3, SDC: Analysis for Cohort #2 compared to primary analysis.
Appendix 4, SDC: Multiple imputation results compared to primary analysis.
Appendix 5, SDC: Calculation of life years from transplantation.
Appendix 1, SDC: Details methods on flexible parametric modelling.
Primary Outcome: Allograft Survival
We used flexible parametric models to estimate the mean allograft lifespan in the first 10 years post-transplant, i.e. the area under the curve for the allograft survival censored at 10 years1. This model was chosen because the proportional hazard assumption of the Cox model was not met for the main exposure of interest: transplant type (SLK vs. Ki/SKP). Flexible parametric models fit a Weibull model with cubic splines1 and make fewer assumptions than the usual parametric accelerated failure time models. Transplant type was included as a time-varying covariate.
Flexible models were presented on the cumulative hazard scale. There were three parts to the model: the baseline hazard,the time-varying effect of transplant type, and the log hazard ratios for the covariates. The baseline hazard and transplant type were fitted with cubic splines. The number of knots determined the number of parameters needed to fit the splines in the model.
Optimal fit and choice of knots was determined by comparing the Akaike information criterion (AIC) and Bayesian information criterion (BIC) for multiple models, with a range of 1 to 10 knots tested. The covariates included donor KDRI, donor group (kidney versus kidney-pancreas), donor sex, kidney cold ischemia time, delayed graft function, and recipient age, sex, race,
diabetes status, prior kidney transplant status, dialysis status, and insurance status. We used Stata stpm2 user-written command to fit flexible models.
We predicted the absolute difference in 10-year restricted mean survival time (RMST) by transplant type. The RMST gives an estimate of the average event-free survival time for
comparison between the SLK and Ki/SKP transplants. The means are restricted by the censoring that occurs at the end of the 10-year observation period and are evaluated as the area under the survival curve2. The interpretation of this parameter is thus the expected allograft lifespan in the first 10-years post-transplant. In Stata, the predicted RMST and confidence interval was
requested as a post estimation command to the stmp2 command.
The adjusted RMSTs and survival curves shown are based on population-averaged estimates.
Population-averaged estimates are preferred because they show the counterfactual comparison of what would have happened to the allografts had they all been allocated to Ki/SPK transplant candidates versus what would have happened to the allografts had they all been allocated to SLK transplant patients under the assumed model. To compute these estimates, survival times were predicted from the model assuming each patient received a Ki/SPK transplant, then repeated assuming each patient received a SLK transplant. The predicted outcomes were combined to estimate the population-averaged estimates for each transplant group.
Secondary Outcomes: Death and Allograft Failure
Since patients are at risk of either death or kidney allograft failure and an early death could prevent some chance of graft failure, these events are considered competing events. We
modelled two cause-specific hazards, the hazard of death and the hazard of allograft failure, separately, using a modification of the flexible parametric models3. We modeled predicted cumulative incidence plots on patients 20, 40, and 60 years old who were dialysis-dependent at the time of transplant, holding constant all other covariates previously listed.
Imputation of Missing Data
To examine bias and precision in our complete case analysis due to missing data we repeated the estimates of RMST for Figures 2 and 4 using multiple imputation with chained equations MICE4. All data were assumed to be missing at random conditional on the following covariates in our imputation model: KDPI, delayed graft function, dialysis, PRA, HLA mismatch,
education, donor race, donor height, transplant group, donor age, donor gender, donor weight, donor hepatitis C seropositivity, donor death due to CVA, donation after cardiac death, kidney cold ischemia time, recipient age, recipient gender, recipient race, recipient payment source, primary kidney diagnosis, liver allocation era and Nelson-Aalen estimator5 of the cumulative hazard of allograft failure and patient death. For Figure 4, the imputations were stratified by transplant type so that the imputation model was consistent with the analysis model. We specified a burn-in period of 100 iterations for each of the 5 imputed datasets.
PRA, HLA, and college education had the most missing data; 52%, 10%, and 16%
respectively were missing during the MELD era. These variables were not included in the main analysis of the manuscript but were included in the analysis models for the imputed results.
College education of the recipient was found to be significantly associated with allograft loss.
The donor-paired design was not considered in the analysis models for the imputed data. A ratio of the standard errors with and without robust adjustment for the pairing was .97 (close to 1). This implied that the design effect of the donor-paired design was very small.
Reference:
1. Lambert PC, Patrick R. Further development of flexible parametric models for survival analysis. The Stata Journal. 2009;9(2):265-290.
2. Royston P. Tools to simulate realistic censored survival-time distributions. The Stata Journal. 2012;12(4):639-654.
3. Hinchliffe SR, Lambert PC. Flexible parametric modelling of cause-specific hazards to estimate cumulative incidence functions. BMC Med Res Methodol. 2013;13:13.
4. White IR, Royston P, Wood AM. Multiple imputation using chained equations: Issues and guidance for practice. Stat Med. 2011;30(4):377-399.
5. White IR, Royston P. Imputing missing covariate values for the Cox model. Stat Med.
2009;28(15):1982-1998.
Appendix 2, SDC: Sensitivity analysis of Cohort #1 (excluding 84 SLK recipients on dialysis at the time of transplant but missing dialysis duration) and comparison to results of the primary analysis.
Table S1. Survival analysis follow up data and adjusted 10-year expected allograft lifespan, in primary analysis cohort and cohort #1.
Primary Analysis Cohort #1
SLK Ki/SPK SLK Ki/SPK
Number at risk at year 0, 2, 4,
6, 8 and 10
Pre-MELD Era
0: 407 2: 284 4: 253 6: 224 8: 195 10: 181
0: 407 2: 348 4: 312 6: 283 8: 230 10: 205
0: 378 2: 260 4: 229 6: 202 8: 175 10: 164
0: 378 2: 323 4: 289 6: 261 8: 211 10: 188 MELD Era 0: 2658
2: 1710 4: 1203 6: 837 8: 497 10: 217
0: 2658 2: 1898 4: 1330 6: 895 8: 509 10: 213
0: 2603 2: 1675 4: 1177 6: 816 8: 485 10: 208
0: 2603 2: 1858 4: 1296 6: 868 8: 491 10: 200 Adjusted 10-
year expected allograft lifespan (years)
Pre-MELD Era
5.96 (5.49-6.44)
7.21 (6.83-7.58)
5.75 (5.22-6.28)
7.23 (6.82-7.64)
MELD Era 6.53
(6.32-6.74)
7.64 (7.46-7.82)
6.57 (6.35-6.79)
7.64 (7.45-7.82)
Figure S1. Time-to-all-cause kidney allograft loss by transplant type, restricted to Cohort #1.
Appendix 3, SDC: Sensitivity analysis of Cohort #2 (SLK recipients on dialysis for 90 or more days at the time of transplant) and comparison to results of the primary analysis.
Table S2. Survival analysis follow up data and adjusted 10-year expected allograft lifespan, in primary analysis cohort and cohort #2.
Primary Analysis Cohort #2
SLK Ki/SPK SLK Ki/SPK
Number at risk at year 0, 2, 4,
6, 8 and 10
Pre-MELD Era
0: 407 2: 284 4: 253 6: 224 8: 195 10: 181
0: 407 2: 348 4: 312 6: 283 8: 230 10: 205
0: 133 2: 98 4: 91 6: 82 8: 77 10: 68
0: 133 2: 107 4: 97 6: 88 8: 77 10: 63 MELD Era 0: 2658
2: 1710 4: 1203 6: 837 8: 497 10: 217
0: 2658 2: 1898 4: 1330 6: 895 8: 509 10: 213
0: 1180 2: 736 4: 509 6: 331 8: 196 10: 88
0: 1180 2: 872 4: 605 6: 391 8: 210 10: 92 Adjusted 10-
year expected allograft lifespan (years)
Pre-MELD Era
5.96 (5.49-6.44)
7.21 (6.83-7.58)
6.48 (5.77-7.19)
6.96 (6.27-7.66)
MELD Era 6.53
(6.32-6.74)
7.64 (7.46-7.82)
6.31 (6.04-6.59)
7.57 (7.31-7.83)
Figure S2. Time-to-all-cause kidney allograft loss by transplant type, restricted to Cohort #2.
Appendix 4, SDC: Results of multiple imputation on the primary outcomes reportedly in the analysis.
Primary Analysis With imputation, but without adjustment for pairing
SLK Ki/SPK SLK Ki/SPK
Adjusted 10-year expected allograft lifespan (years)
6.53 (6.32-6.74)
7.64 (7.46-7.82)
6.56 (6.35-6.77)
7.60 (7.41-7.77)
Difference in adjusted 10-year expected allograft lifespans (years), SLK – Ki/SPK
Primary Analysis With Imputation 3 covariates added**
assuming independent observations
Not stratified -1.13 (-1.41, -0.85) -1.07 (-1.35, -0.80)
Meld=0 -1.71 (-2.26, -1.17) -1.64 (-2.13, -1.14)
Meld=1 -0.99 (-1.28, -0.71) -0.93 (-1.22, -0.64)
SLK* meld interaction P=0.02 P=0.01
KDPI=1 -0.69 (-1.07, -0.31) -0.67 (-1.04, -0.29)
KDPI=2 -1.31 (-1.64, -0.99) -1.25 (-1.57, -0.93)
SLK*KDPI=2 interaction
P=.04 P=0.06
KDPI=3 -1.41 (-2.22, -0.60) -1.19 (-2.00, -0.38)
SLK*KDPI=3 interaction P=0.49 P=0.81
Organ Type = Ki -1.25 (-1.55, -0.95) -1.17 (-1.48, -0.87) Organ Type = SPK -0.62 (-1.11, -0.12) -0.63 (-1.10, -0.16)
SLK*Organ type P=0.09 P= 0.15
Donor gender = male -1.15 (-1.46, -0.83) -1.11 (-1.43,-0.79) Donor gender = female -1.10 (-1.48, -0.72) -0.99 (-1.37,-0.62)
SLK*gender interaction P= 0.58 P=0.38
** Additional covariates: PRA, HLA, and college education.
Appendix 5, SDC: Calculation of life years from transplantation (LYFT).
Cohort was limited to the MELD era only.
LYFT from simultaneous pancreas-kidney transplantation Recipient
Age
LYFTa (year) Nb Weightc Weighted LYFT (year)d
Median 25%ile 75%ile Median 25%ile 75%ile
34 11.61 10.99 12.38 140 0.25 2.88 2.72 3.07
35-49 9.13 8.34 10.07 306 0.54 4.94 4.52 5.45
50-64 7.05 6.56 7.55 117 0.21 1.46 1.36 1.56
SUM 563 1.00 9.30 8.60 10.08
LYFT from kidney transplantation Recipient
Age
LYFTa (year) Nb Weightc Weighted LYFT (year)d
Median 25%ile 75%ile Median 25%ile 75%ile
Recipient with diabetes
34 6.98 6.56 7.55 18 0.0079 0.055 0.052 0.060
35-49 5.30 4.97 5.83 158 0.070 0.37 0.35 0.41
50-64 4.03 3.77 4.44 403 0.18 0.72 0.67 0.79
65 3.36 3.05 3.44 157 0.069 0.23 0.21 0.24
Recipient without diabetes
34 8.79 8.28 9.40 276 0.12 1.07 1.01 1.14
35-49 7.32 6.69 7.95 538 0.24 1.74 1.59 1.89
50-64 5.84 5.43 6.22 516 0.23 1.33 1.24 1.42
65 4.63 4.37 5.03 200 0.089 0.41 0.39 0.45
SUM 2266 1.00 5.92 5.50 6.39
a LYFT: See Wolfe RA, McCullough KP, Schaubel DE et al.. Calculating life years from transplant (LYFT) for kidney and kidney-pancreas candidates. Am J Transplant 2008; 8:997- 1011.
b N: Number of patients in each age category in our study cohort with the transplant type.
c Weight: Calculated as N / sum.
d Weighted LYFT: Calculated as weight * LYFT.