. Author manuscript; available in PMC: 2017 Mar 24.

Published in final edited form as: Biometrics. 2016 Jul 26;73(1):294–304. doi: 10.1111/biom.12564

Table 4.

Estimated treatment effect on CD4 counts from real data of the Aquitaine cohort and SHCS: Model 1: Naive regression; Model 2: MSM on $Y_{t}^{i}$ ; Model 3: MSM on $Z_{t}^{i}$ ; Model 4: Simple LIM; Model 5: autoregressive LIM; Model 6: LIM system; Model 7: mechanistic model.

		Real Dataset observational studies
		SHCS			Aquitaine Cohort
Model	β treatment	Effect	Sd.	Z-stat^†	Effect	Sd.	Z-stat^†
Model 1	< 1 yr	6	16	0.34	−94	12	−7.55
	> 1 yr	30	6	5.42	30	3	9.75
	∞	+∞	-	-	+∞	-	-
Model 2	< 1 yr	208	18	11.31	36	19	1.87
	> 1 yr	50	9	5.79	53	5	9.62
	∞	+∞	-	-	+∞	-	-

Model 3	< 1 yr	174	10	17.29	27	14	1.99
	> 1 yr	61	5	12.37	34	5	6.3
	∞	+∞	-	-	+∞	-	-

Model 4	< 1 yr	189	11	17.33	109	9	12.03
	> 1 yr	73	8	9.07	55	6	8.99
	∞	+∞	-	-	+∞	-	-
Model 5	< 1 yr	26	^*	^*	45	^*	^*
	> 1 yr	14	^*	^*	19	^*	^*
	∞	55	^*	^*	79	^*	^*
	β ₁	60	4	16.04	14	3	4.12
Model 6	< 1 yr	73	^*	^*	92	^*	^*
	> 1 yr	26	^*	^*	16	^*	^*
	∞ CD4	104	^*	^*	111	^*	^*
	∞ VL	−2.0	^*	^*	−2.3	^*	^*
	β ₁	80	16	5	28	18	1.53
	α ₁	−3.29	0.09	−38.4	−3.19	0.1	−30.55

Model 7	< 1 yr	104	^*	^*	71	^*	^*
	> 1 yr	18	^*	^*	9	^*	^*
	∞ CD4	127	^*	^*	86	^*	^*
	∞ VL	−4.09	^*	^*	−3.14	^*	^*
	β	−1.73	0.05	−34.79	−0.89	0.01	−85.77

^†

Estimates for treatment effect (β) are significant at level 10% if the Z-stat is greater than 1.64 and significant at level 5% if the Z-stat is greater than 1.96.

Simulated delta-method can lead to estimation of these values, but is not implemented here. Indeed, for Model 5, 6 and 7 significance of the treatment effect has to be evaluated through the mechanistic parameters β₁,α₁ and β.