Table 5.

Illustrated Example from Multinational Clinical Trial with 3 Outcomes Using GRACE Data (Random-Coefficient Model) ^a

Model	Package, Function, and Method of Estimation	Incremental Costs; Mean (SE), €	Incremental QALYs; Mean (SE)	Incremental Proportion with Severe Cough (SE)
Model G1: Bivariate mixed-effects regression with Costs ∼ normal QALYs ∼ normal Cough ∼ binomial (link = log)	Stata mixed, ml
	Stata mixed, reml
	Stata merlin, ml	154.34 (2.70)	0.0003 (0.0310)	−0.0202 (0.0138)
	Stata gsem, ml	154.34 (2.69)	0.0003 (0.0312)	−0.0202 (0.0140)
	R lme, ml via PQL	154.34 (2.71)	0.0003 (0.0311)	−0.0202 (0.0137)
	R lme, reml via PQL	135.87 (11.22)	0.0003 (0.0312)	−0.0202 (0.0137)
	WinBUGS MCMC	131.90 (14.59)	0.0004 (0.0007)	−0.0046 (0.0291)
Model G2: Bivariate mixed-effects regression with Costs ∼ gamma (link = log) QALYs ∼ normal Cough ∼ binomial (link = logit)	Stata mixed, ml via PQL
	Stata mixed, reml via PQL
	Stata merlin, ml	108.97 (14.36)	0.0003 (0.0311)	−0.0044 (0.0227)
	Stata gsem, ml	108.96 (14.36)	0.0003 (0.0311)	−0.0044 (0.0227)
	R lme, ml via PQL	108.96 (14.36)	0.0003 (0.0311)	−0.0044 (0.0227)
	R lme, reml via PQL	107.65 (14.41)	0.0003 (0.0311)	−0.0018 (0.0259)
	WinBUGS MCMC	113.00 (13.21)	0.0002 (0.0005)	−0.0073 (0.0267)
Model G3: Bivariate mixed-effects regression with Costs ∼ normal 1. QALYs ∼ gamma (link = log) Cough ∼ binomial (link = log)	Stata mixed, ml via PQL
	Stata mixed, reml via PQL
	Stata merlin, ml
	Stata gsem, ml
	R lme, ml via PQL	108 (1400)	0.0002 (0.062)	−0.0040 (0.02278)
	R lme, reml via PQL	108 (14.39)	0.0002 (0.062)	−0.0011 (0.02605)
	WinBUGS MCMC	107 (12.65)	−0.0001 (0.0047)	−0.0090 (0.0282)

ml, maximum likelihood/maximum quasi-likelihood; reml, restricted maximum likelihood/restricted maximum quasi-likelihood; MCMC, Markov Chain Monte Carlo simulation; SE, standard error.

^aEmpty cells indicate the model did not converge or the particular routine was currently unavailable.