Table 4:

Results of the analysis of the HIV-surveillance data: fitting a two-phase piecewise linear model (with an unknown change-point) to the jurisdiction-specific L2C measures in the HPTN 065 study based on the proposed estimator solving (5).

		City jurisdiction
		DC	Miami	Chicago	New york	Philadelphia	Houston
		Estimation of the change-point model parameters
β0	Estimate	71.25	42.21	74.13	78.60	74.19	49.43
	SE	0.76	0.70	1.15	1.22	0.06	0.86
	95% CI	(69.76, 72.74)	(40.84, 43.59)	(71.88, 76.38)	(76.21, 81.00)	(74.07, 74.31)	(47.74, 51.12)
β1	Estimate	3.29	3.13	0.96	3.58	2.92	16.37
	SE	0.61	0.39	0.27	0.67	0.05	1.26
	95% CI	(2.09, 4.48)	(2.37, 3.90)	(0.44, 1.49)	(2.26, 4.90)	(2.82, 3.02)	(13.90, 18.83)
β2	Estimate	−3.01	−2.93	−0.96	−3.87	−3.0	−16.04
	SE	0.61	0.39	0.77	0.69	0.05	1.26
	95% CI	(−4.21, −1.80)	(−3.70, −2.16)	(−2.47, 0.55)	(−5.22, −2.52)	(−3.10, −2.90)	(−18.50, −13.57)
τ	Estimate	2.96	3.35	7.52	3.38	2.34	1.55
	SE	0.46	0.39	1.96	0.47	0.03	0.10
	95% CI	(2.05, 3.87)	(2.66, 4.04)	(3.67, 11.36)	(2.46, 4.31)	(2.28, 2.40)	(1.36, 1.74)
		Annual percentage of linkage to care
%	Estimate	82.13	53.54	81.44	89.68	80.62	76.42

Note: β₀ is the intercept; β₁ is the slope of the first segment; β₂ is the difference in slopes between the two segments; τ is the jurisdiction change-point.