When a joint model should be preferred over a linear mixed model for analysis of longitudinal health-related quality of life data in cancer clinical trials

Touraine, Célia; Cuer, Benjamin; Conroy, Thierry; Juzyna, Beata; Gourgou, Sophie; Mollevi, Caroline

doi:10.1186/s12874-023-01846-3

Table 2 Results^a of the simulation study on the main parameters^b

From: When a joint model should be preferred over a linear mixed model for analysis of longitudinal health-related quality of life data in cancer clinical trials

		LMM					JM
	True	Mean	Bias	RB	RMSE	Cov.	Mean	Bias	RB	RMSE	Cov.
SCENARIO 0
HRQoL
β₁	0.3	0.603	0.303	1.010	0.371	70.8	0.297	− 0.003	− 0.011	0.22	95.7
β₂	1.2	1.141	−0.059	− 0.049	0.287	93.1	1.215	0.015	0.012	0.284	93.3
β₁ + β₂	1.5	1.744	0.244	0.163	–	–	1.512	0.012	0.008	–	–
Risk of dropout
γ₁	− 0.4	–	–	–	–	–	− 0.403	− 0.003	0.007	0.103	93.8
α	−0.02	–	–	–	–	–	− 0.02	0	0.003	0.003	95.2
SCENARIO 1
HRQoL
β₁	0	−0.007	−0.007	NA	0.183	94.1	−0.008	−0.008	NA	0.184	94.2
β₂	1.5	1.508	0.008	0.005	0.253	93.4	1.508	0.008	0.005	0.253	93.3
β₁ + β₂	1.5	1.501	0.001	0.001	–	–	1.5	0	0	–	–
Risk of dropout
γ₁	0	–	–	–	–	–	−0.002	−0.002	NA	0.102	93.4
α	0	–	–	–	–	–	0	0	NA	0.002	94.9
SCENARIO 2
HRQoL
β₁	0	0.356	0.356	NA	0.404	52.7	0.004	0.004	NA	0.198	94.3
β₂	1.5	1.465	−0.035	−0.023	0.255	93.1	1.517	0.017	0.011	0.260	93.4
β₁ + β₂	1.5	1.821	0.321	0.214	–	–	1.521	0.021	0.014	–	–
Risk of dropout
γ₁	0	–	–	–	–	–	−0.003	− 0.003	NA	0.110	94.3
α	−0.03	–	–	–	–	–	−0.03	0	0	0.003	95.5
SCENARIO 3
HRQoL
β₁	0	0.343	0.343	NA	0.391	53.0	−0.003	−0.003	NA	0.193	94.2
β₂	1.5	1.359	−0.141	− 0.094	0.274	88.6	1.515	0.015	0.01	0.240	93.0
β₁ + β₂	1.5	1.702	0.202	0.135	–	–	1.512	0.012	0.008	–	–
Risk of dropout
γ₁	−0.7	–	–	–	–	–	− 0.704	−0.004	0.006	0.115	94.4
α	−0.03	–	–	–	–	–	−0.03	0	0.001	0.003	95.4
SCENARIO 4
HRQoL
β₁	0	0.352	0.352	NA	0.397	51.8	0.002	0.002	NA	0.190	95.2
β₂	0	−0.098	−0.098	NA	0.255	91.7	0.014	0.014	NA	0.241	93.8
β₁ + β₂	0	0.254	0.254	NA	–	–	0.016	0.016	NA	–	–
Risk of dropout
γ₁	−0.7	–	–	–	–	–	− 0.706	−0.006	0.009	0.108	94.1
α	−0.03	–	–	–	–	–	−0.030	0.000	0.002	0.003	94.8
SCENARIO 5
HRQoL
β₁	0	0.342	0.342	NA	0.39	54.2	−0.009	−0.009	NA	0.194	94.8
β₂	−1.5	−1.551	−0.051	0.034	0.245	93.9	−1.482	0.018	−0.012	0.245	94.4
β₁ + β₂	−1.5	−1.209	0.291	0.582	–	–	−1.491	0.009	−0.006	–	–
Risk of dropout
γ₁	−0.7	–	–	–	–	–	−0.7	0	0	0.115	93.9
α	−0.03	–	–	–	–	–	−0.03	0	−0.003	0.003	94.5

^amean, bias, relative bias (RB), root mean square error (RMSE) and coverage rate (Cov.) based on 1000 generated datasets of 500 patients
^b β₁ and β₂: time and interaction parameters characterizing the slope of the HRQoL trajectory in the control and experimental arms; γ₁ and α: effects of treatment and HRQoL on risk of dropout
HRQoL, Health-related quality of life; JM, Joint model; LMM, Linear mixed model

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