Comparison of a time-varying covariate model and a joint model of time-to-event outcomes in the presence of measurement error and interval censoring: application to kidney transplantation

Campbell, Kristen R.; Juarez-Colunga, Elizabeth; Grunwald, Gary K.; Cooper, James; Davis, Scott; Gralla, Jane

doi:10.1186/s12874-019-0773-1

Table 4 Results from the simulation study

From: Comparison of a time-varying covariate model and a joint model of time-to-event outcomes in the presence of measurement error and interval censoring: application to kidney transplantation

		No Measurement Error			Low Measurement Error			High Measurement Error
	Variable	True Value	M2	M4	True Value	M2	M4	True Value	M2	M4
Lighter interval censoring	b ₁	-0.03	-0.02 (0.00)		-0.03	-0.03 (0.005)		-0.03	-0.03 (0.005)
	b ₀	7.00	6.92 (0.001)		7.00	7.02 (0.05)		7.00	6.99 (0.07)
	\(\sigma ^{2}_{e}\)	0	0.00 (0.00)		1.00	1.00 (0.01)		8.00	8.01 (0.09)
	ρ	-0.005	-0.01 (0.001)		-0.005	-0.005 (0.06)		-0.005	-0.001 (0.08)
	\(\sigma ^{2}_{0}\)	1.75	1.76 (0.003)		1.75	1.76 (0.15)		1.75	1.75 (0.16)
	\(\sigma ^{2}_{1}\)	0.004	0.004 (0.00)		0.004	0.004 (0.000)		0.004	0.004 (0.001)
	β₀, γ₀	-2.00	-2.10 (0.006)	0.63 (0.009)	-2.00	-2.14 (0.26)	0.21 (0.39)	-2.00	-2.14 (0.27)	-0.82 (0.31)
	β₁ (HLA)	0.25	0.26 (0.002)	0.24 (0.002)	0.25	0.26 (0.07)	0.24 (0.07)	0.25	0.26 (0.07)	0.23 (0.07)
	α	0.50	0.54 (0.00)	0.41 (0.00)	0.50	0.53 (0.04)	0.47 (0.04)	0.50	0.54 (0.04)	0.47 (0.04)
	λ₀, η	-0.50	-0.52 (0.002)	-0.33 (0.001)	-0.50	-0.53 (0.07)	-0.32 (0.05)	-0.50	-0.54 (0.08)	-0.18 (0.04)
Heavier interval censoring	b ₁	-0.03	-0.02 (0.00)		-0.03	-0.03 (0.004)		-0.03	-0.03 (0.005)
	b ₀	7.00	6.93 (0.00)		7.00	7.00 (0.05)		7.00	7.00 (0.08)
	\(\sigma ^{2}_{e}\)	0	0.00 (0.00)		1.00	1.00 (0.01)		8.00	8.01 (0.09)
	ρ	-0.005	-0.01 (0.001)		-0.005	-0.005 (0.06)		-0.005	-0.001 (0.08)
	\(\sigma ^{2}_{0}\)	1.75	1.76 (0.003)		1.75	1.76 (0.15)		1.75	1.75 (0.16)
	\(\sigma ^{2}_{1}\)	0.004	0.004 (0.00)		0.004	0.004 (0.000)		0.004	0.004 (0.001)
	β₀, γ₀	-2.00	-3.99 (0.01)	-0.80 (0.01)	-2.00	-4.00 (0.49)	-1.61 (0.56)	-2.00	-4.20 (0.55)	-2.24 (0.49)
	β₁ (HLA)	0.25	0.28 (0.002)	0.24 (0.002)	0.25	0.27 (0.09)	0.23 (0.08)	0.25	0.28 (0.09)	0.23 (0.08)
	α	0.50	1.08 (0.002)	0.69 (0.002)	0.50	1.09 (0.11)	0.87 (0.10)	0.50	1.15 (0.13)	0.89 (0.09)
	λ₀, η	-0.50	-0.56 (0.002)	-0.26 (0.001)	-0.50	-0.59 (0.10)	-0.25 (0.06)	-0.50	-0.64 (0.12)	-0.18 (0.05)

Data were simulated from the joint model with shared random intercepts, M2, and used to fit M2 and M4 by MCMC. Six simulations were performed with varying amounts of measurement error (none (\(\sigma _{e}^{2}=0\)), low (\(\sigma _{e}^{2}=1\)), and high (\(\sigma _{e}^{2}=8\))) and varying amounts of interval censoring (lighter (as in our data) and heavier (3 year intervals)). Unlike in Table 3, none of these estimates are converted into hazard ratios, because the interest here is comparing the results from the simulation to the true values. The numbers presented are mean (standard deviation) of the estimates from the 200 datasets for each simulation condition

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