Table 3.

Parameter inputs for decision tree and Markov model. L+/−: functioning or non-functioning liver allograft. K +/−: functioning or non-functioning kidney, allograft (if initial transplant is SLK) or native (if initial transplant is liver). KD: Kidney disease. OPTN-: Kidney disease not meeting OPTN criteria for SLK. OPTN+: Kidney disease meeting OPTN criteria for SLK.

Parameter	Stratum	Base Model	Range	Distribution	Source	Technical Appendix
Probability of outcome at month 1 post-index transplant
Post-SLK transplant:
L+K−	OPTN−	0.012	0.003–0.026	beta (4,334)	SRTR cohort	A
	OPTN+	0.019	0.010–0.030	beta (13,687)
L−K+	OPTN−	0.003	0.000–0.011	beta (1,337)	SRTR cohort	A
	OPTN+	0.013	0.006–0.022	beta (9,691)
Death	OPTN−	0.024	0.010–0.042	beta (8,330)	SRTR cohort	A
	OPTN+	0.020	0.011–0.032	beta (14,686)
Post-liver transplant:
L+K−	No KD	0.003	0.001–0.005	beta (11,3289)	9	A
	OPTN−	0.006	0.005–0.007	beta (215,34185)
	OPTN+	0.033	0.019–0.046	beta (23,680)
L−K+	No KD	0.022	0.020–0.023	beta (722,32933)	SRTR cohort	A
	OPTN−	0.018	0.016–0.020	beta (306,16758)
	OPTN+	0.013	0.009–0.019	beta (25,1866)
Death	No KD	0.023	0.021–0.024	beta (759,32896)	SRTR cohort	A
	OPTN−	0.036	0.033–0.038	beta (609,16455)
	OPTN+	0.044	0.036–0.054	beta (84,1807)
Transition probabilities per cycle, month 1 and beyond post-index transplant
Post-SLK transplant:
Death (L+K+ → death)	time-dependent, see Table A5			non-parametric	SRTR cohort	A
Liver graft fails (L+K+ → L−K+L+K− → L−K−)	time-dependent, see Table A5			non-parametric	SRTR cohort	A
Kidney graft fails (L+K+ → L+K−)	time-dependent, see Table A5			non-parametric	SRTR cohort	A
Post-liver transplant:
Death (L+K+ → death)	time-dependent, see Table B5			non-parametric	SRTR cohort	A
Liver graft fails (L+K+ → L−K+L+K− → L−K−)	time-dependent, see Table A5			non-parametric	SRTR cohort	A
Native kidneys fail (L+K+ → L+K−)	time-dependent, see Table A5			non-parametric	9	A
Post-both transplants:
Death on dialysis (L+K− → death)	all	death rate without dialysis × hazard ratio (3.32)	hazard ratio: 2.96–3.71	hazard ratio: log-normal (1.200,0.058)	10	A
Liver graft failure on dialysis (L+K− → L−K−)	all	liver failure rate without dialysis × hazard ratio (1.49)	hazard ratio: 1.10–2.04	hazard ratio: log-normal (0.3988,0.1573)	11	A
Death after second transplant (kidney)	all	death rate without second transplant × time-dependent hazard ratio	time-dependent, see Figure B2	non-parametric	12	B
Kidney graft failure after second transplant (kidney)	time-dependent, see Table B2			non-parametric	12	B
Kidney wait-list information
Proportion of patients who have matching living donors	all	0.059	0.049–0.069	beta (132,2105)	12	B
Adjustment for liver / SLK re-transplantation
Hazard ratio for death (compared to first transplant)	all	1.7	1.56–1.84	log-normal (0.531,0.042)	13	A
Probability of receiving SLK pre-OPTN (based on 2013 data)
	No KD	0.000	0	none	2013 SRTR cohort
	OPTN−	0.022	0.015–0.030	beta (34,1510)
	OPTN+	0.326	0.272–0.382	beta (91,188)
Utility weights
Post-liver transplant:
No kidney failure	all	0.747	0.720–0.774	beta (742,251)	14	D
With kidney failure	all	0.573	0.523–0.624	beta (210,156)	14,15	D

^aGamma distribution is described here by a shape parameter, α, and an inverse scale parameter, β.