Comparing statistical methods in assessing the prognostic effect of biomarker variability on time-to-event clinical outcomes

Table 2 Average of estimated effect of biomarker variability (\(\widehat{{\gamma }_{3}}\)) on survival outcome and its standard error (SE) from the joint model and two-stage methods based on the first simulation

Simulated scenarios					naive		LMA		td-Cox		RC		Joint model
Frequency of visits	Min #visits (lead-in time)	β₁	\({\gamma }_{3}\)	Scenario#	\(\widehat{{\gamma }_{3}}\)	SE	\(\widehat{{\gamma }_{3}}\)	SE	\(\widehat{{\gamma }_{3}}\)	SE	\(\widehat{{\gamma }_{3}}\)	SE	\(\widehat{{\gamma }_{3}}\)	SE
Semi-annually	3 (1-yr)	0.0	0.0	1	-0.353	0.053	0.002	0.034	0.001	0.042	0.039	0.129	0.011	0.150
		0.0	0.5	2	-0.238	0.060	0.067	0.038	0.076	0.046	0.372	0.128	0.507	0.154
		-0.5	0.0	3	-0.355	0.054	0.002	0.035	0.003	0.042	0.018	0.127	-0.017	0.149
		-0.5	0.5	4	-0.226	0.060	0.074	0.039	0.088	0.045	0.419	0.126	0.528	0.161
	7 (3-yr)	0.0	0.0	5	-0.129	0.081	-0.019	0.081	-0.018	0.075	0.044	0.117	0.002	0.129
		0.0	0.5	6	0.197	0.084	0.243	0.085	0.259	0.078	0.483	0.115	0.499	0.132
		-0.5	0.0	7	-0.121	0.081	-0.014	0.080	-0.005	0.075	0.003	0.117	-0.010	0.127
		-0.5	0.5	8	0.191	0.084	0.243	0.083	0.258	0.077	0.452	0.121	0.521	0.136
Quarterly	5 (1-yr)	0.0	0.0	9	-0.214	0.083	-0.006	0.068	-0.012	0.069	0.002	0.114	-0.015	0.124
		0.0	0.5	10	0.122	0.086	0.218	0.073	0.232	0.072	0.452	0.115	0.489	0.129
		-0.5	0.0	11	-0.222	0.084	0.004	0.068	-0.013	0.069	0.017	0.112	0.011	0.124
		-0.5	0.5	12	0.102	0.086	0.205	0.073	0.222	0.072	0.413	0.113	0.524	0.131
	13 (3-yr)	0.0	0.0	13	-0.080	0.090	-0.014	0.097	-0.025	0.087	0.008	0.107	0.005	0.113
		0.0	0.5	14	0.299	0.092	0.313	0.098	0.321	0.088	0.474	0.109	0.515	0.115
		-0.5	0.0	15	-0.074	0.091	-0.024	0.096	-0.023	0.087	0.001	0.108	-0.005	0.111
		-0.5	0.5	16	0.302	0.091	0.314	0.098	0.321	0.088	0.462	0.108	0.519	0.119

RC Regression calibration; Naïve: simple OLS; LMA Landmark analysis, td-Cox Time-dependent Cox model

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