Personalized treatment selection via the covariate-specific treatment effect curve for longitudinal data

Figures & data

Table 1. Simulation results for parametric estimates with binary data.

			GPLSIMM			GPLSIM
n	Parameters	True value	Mean	Sd	$\mathrm{M}\mathrm{S}\mathrm{E}\times 10$	Mean	Sd	$\mathrm{M}\mathrm{S}\mathrm{E}\times 10$
100	${\alpha }_1$	0.500	0.438	0.124	0.192	0.442	0.123	0.184
	${\alpha }_2$	1.000	0.894	0.126	0.271	0.884	0.128	0.297
	${\alpha }_3$	−0.500	−0.439	0.119	0.178	−0.425	0.117	0.193
	${\text{β}}_1$	0.707	0.694	0.092	0.086	0.696	0.107	0.116
	${\text{β}}_2$	0.707	0.709	0.089	0.080	0.702	0.106	0.113
300	${\alpha }_1$	0.500	0.447	0.067	0.074	0.430	0.069	0.096
	${\alpha }_2$	1.000	0.892	0.076	0.175	0.859	0.075	0.255
	${\alpha }_3$	−0.500	−0.450	0.067	0.070	−0.430	0.066	0.093
	${\text{β}}_1$	0.707	0.702	0.051	0.027	0.701	0.055	0.031
	${\text{β}}_2$	0.707	0.708	0.051	0.026	0.709	0.054	0.029
500	${\alpha }_1$	0.500	0.447	0.055	0.058	0.429	0.050	0.076
	${\alpha }_2$	1.000	0.892	0.059	0.151	0.857	0.058	0.239
	${\alpha }_3$	−0.500	−0.446	0.052	0.056	−0.427	0.051	0.080
	${\text{β}}_1$	0.707	0.707	0.042	0.018	0.706	0.044	0.020
	${\text{β}}_2$	0.707	0.705	0.042	0.018	0.706	0.045	0.020

Table 2. Simulation results for parametric estimates with count data.

			GPLSIMM			GPLSIM
n	Parameters	True value	Mean	Sd	$\mathrm{M}\mathrm{S}\mathrm{E}\times {10}^2$	Mean	Sd	$\mathrm{M}\mathrm{S}\mathrm{E}\times {10}^2$
100	${\alpha }_1$	0.500	0.508	0.048	0.236	0.505	0.129	1.671
	${\alpha }_2$	1.000	1.020	0.047	0.262	1.004	0.138	1.908
	${\alpha }_3$	−0.500	−0.508	0.054	0.302	−0.511	0.134	1.800
	${\text{β}}_1$	0.707	0.703	0.063	0.395	0.706	0.082	0.666
	${\text{β}}_2$	0.707	0.703	0.089	0.790	0.685	0.164	2.757
300	${\alpha }_1$	0.500	0.512	0.021	0.060	0.504	0.093	0.860
	${\alpha }_2$	1.000	1.023	0.024	0.108	1.016	0.096	0.954
	${\alpha }_3$	−0.500	−0.511	0.023	0.068	−0.505	0.090	0.815
	${\text{β}}_1$	0.707	0.708	0.017	0.030	0.706	0.048	0.234
	${\text{β}}_2$	0.707	0.706	0.021	0.046	0.705	0.049	0.242
500	${\alpha }_1$	0.500	0.512	0.015	0.037	0.516	0.073	0.560
	${\alpha }_2$	1.000	1.028	0.018	0.108	1.015	0.079	0.642
	${\text{β}}_1$	−0.500	−0.512	0.016	0.041	−0.515	0.076	0.596
	${\text{β}}_2$	0.707	0.706	0.011	0.013	0.708	0.039	0.156
	${\text{β}}_3$	0.707	0.708	0.011	0.012	0.704	0.039	0.153

Table 3. MISE for nonparametric estimate with binary data.

	GPLSIMM		GPLSIM
n	Mean	Sd	Mean	Sd
100	0.287	0.182	0.291	0.186
300	0.155	0.085	0.163	0.085
500	0.106	0.052	0.112	0.052

Table 4. MISE for nonparametric estimate with count data.

	GPLSIMM		GPLSIM
n	Mean	Sd	Mean	Sd
100	0.191	0.135	0.243	0.172
300	0.169	0.090	0.193	0.111
500	0.168	0.062	0.191	0.082

Figure 1. Estimate of nonparametric function $f(\cdot )$ (real line) and its 95% pointwise confidence interval (dashed line).

Figure 2. Relationship of treatment effect with MMSE score and Age: the estimated curve represented by real line and the corresponding 95% pointwise confidence interval by dashed line.

Table 5. Estimated $\alpha \alpha$ and $\text{β}\text{β}$.

Estimated $\alpha \alpha$	Estimate	Sd
Intercept	6.450	2.754
Visit year	0.029	0.026
Age	0.029	0.019
EDUC	−0.012	0.037
DIABETES	0.062	0.416
DEP	0.454	0.179
MMSE	−0.384	0.095
Estimated $\text{β}\text{β}$	Estimate	Sd
MMSE	0.842	0.115
Age	−0.540	0.304