BMC Medical Research Methodology

Table 4 Results of the association parameter α obtained from joint model and TVCM fitted to data generated considering the sample size n∈(35,75,150,300,600) and different probability distributions (scenarios 3:6 of Table 1) for the random effect b_i0 with variance Σ₁₁=1.44, α=0.3 and σ_ε=0.3 with CV =9.4%

From: Joint model robustness compared with the time-varying covariate Cox model to evaluate the association between a longitudinal marker and a time-to-event endpoint

		Joint model					TVCM(1x/week)
Distribution	n	Est	ESE	ASE	%Bias	CP	Est	ESE	ASE	%Bias	CP
	35	0.315	0.191	0.179	5.0	95	0.287	0.182	0.176	-4.3	95
	75	0.308	0.123	0.116	2.7	94	0.286	0.117	0.114	-4.7	95
Normal	150	0.306	0.085	0.081	2.0	94	0.285	0.081	0.079	-5.0	94
	300	0.302	0.057	0.056	0.7	95	0.282	0.055	0.055	-6.0	94
	600	0.304	0.040	0.040	1.3	95	0.284	0.038	0.039	-5.3	93
	35	0.323	0.054	0.051	7.7	95	0.315	0.066	0.062	5.0	96
	75	0.309	0.033	0.033	3.0	95	0.303	0.038	0.038	1.0	95
Bimodal	150	0.305	0.023	0.023	1.7	95	0.301	0.025	0.025	0.3	96
	300	0.302	0.016	0.016	0.7	96	0.299	0.017	0.018	-0.3	96
	600	0.302	0.011	0.011	0.7	96	0.299	0.012	0.012	-0.3	95
	35	0.366	0.256	0.211	22	93	0.309	0.215	0.195	3.0	95
	75	0.334	0.134	0.125	11	94	0.297	0.121	0.118	-1.0	96
Chisquare	150	0.316	0.088	0.083	5.3	94	0.287	0.079	0.079	-4.3	95
	300	0.318	0.059	0.057	6.0	94	0.289	0.054	0.054	-3.7	95
	600	0.309	0.040	0.039	3.0	95	0.283	0.036	0.037	-5.7	94
	35	0.352	0.232	0.200	17	93	0.305	0.197	0.187	1.7	96
	75	0.327	0.135	0.122	9.0	93	0.291	0.120	0.116	-3.0	96
Gamma	150	0.316	0.079	0.081	5.3	96	0.287	0.073	0.077	-4.3	96
	300	0.316	0.061	0.056	5.3	94	0.289	0.056	0.054	-3.7	94
	600	0.311	0.041	0.039	3.7	94	0.286	0.037	0.037	-4.7	95

Mean of the maximum likelihood estimates (Est), empirical Monte Carlo standard error (ESE), asymptotic standard error (ASE), percentage bias (%Bias) and 95% coverage probabilities (CP) are shown

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