. Author manuscript; available in PMC: 2021 Apr 15.

Published in final edited form as: Stat Med. 2020 Jan 29;39(8):1167–1182. doi: 10.1002/sim.8469

Table 5:

Application to the Pima Indians diabetes data: fitting a logistic regression change-point model for T2D diagnosis including age, BMI and glucose as covariates with age experiencing one change-point, BMI having two change-points and glucose having a linear effect (no change-point). ${\hat{θ}}_{I}$ represents the proposed estimator; ${\hat{θ}}_{M}$ denotes Muggeo’s estimator.

	${\hat{θ}}_{M}$			${\hat{θ}}_{I}$
Parameter	Estimate	SE	95% CI	Estimate	SE	95% CI
β₀	−15.656	1.918	(−19.53, −11.98)	−15.628	1.925	(−19.40, −11.86)
β_1x	0.066	0.012	(0.04, 0.09)	0.069	0.013	(0.04, 0.10)
β_1z	0.281	0.064	(0.16, 0.41)	0.276	0.065	(0.15, 0.40)
β_w	0.037	0.004	(0.03, 0.04)	0.037	0.004	(0.03, 0.04)
β_2x	−0.237	0.072	(−0.36, −0.11)	−0.204	0.050	(−0.30, −0.11)
β_21z	−0.355	0.086	(−0.52, −0.18)	−0.347	0.086	(−0.52, −0.18)
β_22z	0.221	0.089	(0.04, 0.39)	0.218	0.089	(0.04, 0.39)
τ_x	52.060	2.879	(46.91, 56.86)	49.811	13.88	(22.61, 77.02)
τ_1z	31.602	1.053	(29.42, 33.54)	31.60	1.830	(28.01, 35.19)
τ_2z	40.066	2.245	(35.67, 44.63)	40.105	1.433	(37.33, 42.91)

Note: β₀ is the intercept; τ_x is the change-point for age; τ_1z and τ_2z are the two change-points for BMI; β_1x is the slope for age before τ_x; β_2x is the difference in slopes for age before and after τ_x; β_1z is the slope for BMI before τ_1z; β_21z is the difference in slopes between the two segments of BMI joining at τ_1z; β_22z is the difference in slopes between the two segments of BMI joining at τ_2z; β_w is the slope for glucose concentration levels.