Table 4.

Regression coefficient estimation under an additive hazards model

				t = 1		t = 2		t = 3		t = 4
Orig			B	1	−6	3	−13	5	−15	−12	−4
			SD	52	119	104	232	187	444	354	863
			SE	52	116	104	231	186	426	340	824
			CI	93.8	94.2	95.0	94.2	95.4	94.8	94.0	94.9
$\text{AI-}\widehat{𝕏}$	MAE	0.83	B	9	−19	11	−22	15	−20	1	36
	RMISE	0.94	SD	48	112	101	224	179	417	326	772
	BRK	0.31	CI	96.3	94.8	95.0	95.2	96.6	95.5	95.5	96.9
Adapted estimators from curve monotonization
AI-{x}	MAE	0.92	B	10	−10	14	−14	27	−7	44	49
	RMISE	0.99	SD	49	116	102	230	184	438	352	847
	BRK	0.94	CI	96.2	94.7	95.2	94.8	96.5	94.8	95.2	95.5
LY	MAE	0.92	B	9	−12	11	−17	19	−14	18	32
	RMISE	0.97	SD	49	115	101	228	183	434	344	834
	BRK	0.94	CI	96.3	94.8	95.5	94.8	96.3	95.0	94.8	95.9
RA	MAE	5.75	B	−29	−329	−5	−73	−16	−86	−64	−147
	RMISE	4.05	SD	607	4819	109	356	197	479	349	799
	BRK	1.96	CI	95.0	86.9	93.5	89.2	93.3	91.8	92.8	94.9
RA, limited	MAE	0.87	B	2	−7	3	−14	2	−17	−25	−34
	RMISE	0.96	SD	49	116	102	230	183	431	337	776
	BRK	1.93	CI	95.5	94.5	95.4	94.4	95.7	95.4	94.9	96.3

Orig: the original estimator; $\text{AI-}\widehat{𝕏}$: the proposed adaptive interpolation estimator with $\widehat{𝕏}$; AI-{x}: the adaptive interpolation method with $𝕏S$ taking the singleton of a given covariate; LY: the Lin–Ying method; RA: the rearrangement method; RA, limited: the rearrangement limited to interval [0, 5].

MAE: maximum absolute error over [0, 4]; RMISE: root mean integrated squared error over [0, 4]; BRK: number of knots or breakpoints. All are average measures, reported as relative to the original estimator. B: Empirical bias (×1000); SD: Empirical standard deviation (×1000); SE: Average standard error (×1000); CI: Empirical coverage (%) of 95% Wald confidence interval.

Two columns under each t value correspond to the estimated intercept and slope.