“Spatial heterogeneity of environmental risk in randomized prevention trials: consequences and modeling”

Guindo, Abdoulaye; Sagara, Issaka; Ouedraogo, Boukary; Sallah, Kankoe; Assadou, Mahamadoun Hamady; Healy, Sara; Duffy, Patrick; Doumbo, Ogobara K.; Dicko, Alassane; Giorgi, Roch; Gaudart, Jean

doi:10.1186/s12874-019-0759-z

BMC Medical Research Methodology

Table 1: Model performance measures for estimation of the treatment effect (baseline risk 0.37)

From: “Spatial heterogeneity of environmental risk in randomized prevention trials: consequences and modeling”

RRb	RRt	Model	Breeding site density
			0.25						0.75
			Population density						Population density
			0.2			0.8			0.2			0.8
			Bias	CR	SR	Bias	CR	SR	Bias	CR	SR	Bias	CR	SR
1.05	0.95	Cox-PH	0.014	0.96	0.06	0.015	0.88	0.08	0.016	0.92	0.06	\|< 0.001\|	0.96	0.04
		GAM	0.014	0.98	0.06	0.015	0.86	0.08	0.015	0.92	0.06	\|< 0.001\|	0.94	0.04
		Cox-SPDE	0.012	0.98	0.08	0.016	0.86	0.08	0.014	0.94	0.06	-0.002	0.96	0.04
		P-SPDE	0.013	0.98	0.08	0.016	0.86	0.1	0.014	0.94	0.06	-0.002	0.96	0.04
	0.80	Cox-PH	-0.011	0.98	0.74	-0.005	0.98	0.92	-0.018	0.96	0.92	0.013	0.96	0.76
		GAM	-0.012	0.98	0.74	-0.006	0.98	0.9	-0.018	0.96	0.92	0.014	0.96	0.74
		Cox-SPDE	-0.017	0.94	0.74	-0.007	0.98	0.9	-0.026	0.94	0.92	0.011	0.96	0.76
		P-SPDE	-0.012	0.96	0.76	-0.004	0.98	0.9	-0.018	0.96	0.9	0.016	0.96	0.76
	0.60	Cox-PH	-0.003	0.84	1.00	-0.005	0.94	1.00	-0.015	0.94	1.00	-0.008	0.94	1.00
		GAM	-0.004	0.88	1.00	-0.008	0.94	1.00	-0.015	0.96	1.00	-0.01	0.94	1.00
		Cox-SPDE	-0.017	0.8	1.00	-0.011	0.94	1.00	-0.027	0.96	1.00	-0.015	0.94	1.00
		P-SPDE	-0.007	0.88	1.00	-0.002	0.94	1.00	-0.011	0.98	1.00	-0.011	0.96	1.00
	0.25	Cox-PH	0.009	0.98	1.00	-0.011	0.98	1.00	-0.018	0.96	1.00	0.012	0.9	1.00
		GAM	0.005	0.96	1.00	-0.016	0.96	1.00	-0.02	0.96	1.00	0.007	0.92	1.00
		Cox-SPDE	-0.039	0.9	1.00	-0.033	0.92	1.00	-0.055	0.9	1.00	-0.008	0.9	1.00
		P-SPDE	0.008	0.94	1.00	-0.008	0.96	1.00	-0.01	0.96	1.00	0.016	0.96	1.00
3	0.95	Cox-PH	0.005	1.00	0.02	0.009	0.94	0.06	0.027	0.96	0.04	0.009	0.94	0.06
		GAM	0.005	1.00	0.02	0.007	0.94	0.08	0.027	0.96	0.04	0.01	0.98	0.08
		Cox-SPDE	\|< 0.001\|	1.00	0.02	-0.002	0.94	0.08	0.024	0.92	0.04	0.007	1.00	0.04
		P-SPDE	-0.002	1.00	0.02	-0.002	0.94	0.08	0.023	0.9	0.04	0.006	1.00	0.04
	0.80	Cox-PH	0.01	0.96	0.78	0.016	0.92	0.8	0.045	0.92	0.6	0.069	0.84	0.5
		GAM	0.008	0.98	0.78	0.013	0.92	0.8	0.044	0.94	0.58	0.068	0.86	0.5
		Cox-SPDE	-0.002	0.98	0.78	-0.003	0.96	0.82	0.004	1.00	0.64	0.025	0.98	0.48
		P-SPDE	-0.011	0.98	0.8	-0.008	0.96	0.82	-0.008	1.00	0.64	0.023	1.00	0.5
	0.60	Cox-PH	0.036	0.9	1.00	0.072	0.86	1.00	0.139	0.62	1.00	0.121	0.64	1.00
		GAM	0.035	0.92	1.00	0.067	0.86	1.00	0.135	0.6	1.00	0.104	0.78	1.00
		Cox-SPDE	0.006	0.96	1.00	0.032	0.94	1.00	0.053	0.92	1.00	\|< 0.001\|	0.96	1.00
		P-SPDE	-0.012	0.96	1.00	0.027	0.92	1.00	0.025	0.92	1.00	-0.003	0.96	1.00
	0.25	Cox-PH	0.125	0.78	1.00	0.136	0.58	1.00	0.32	0.02	1.00	0.33	0.06	1.00
		GAM	0.121	0.78	1.00	0.123	0.68	1.00	0.309	0.02	1.00	0.293	0.1	1.00
		Cox-SPDE	0.045	0.94	1.00	0.004	0.98	1.00	0.067	0.94	1.00	0.011	0.94	1.00
		P-SPDE	-0.006	1.00	1.00	0.002	1.00	1.00	-0.021	0.98	1.00	-0.004	0.92	1.00

CR Coverage Rate, SR Significance Rate, Cox-PH Cox Proportional Hazard model, GAM Generalized Additive Model, Cox-SPDE Cox-Stochastic Partial Differential Equation Model, P-SPDE Poisson-Stochastic Partial Differential Equation Model, RRt Treatment Relative Risk, RRb Breeding site Relative Risk. See Additional file 6 for MSE Mean Square Error

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