. Author manuscript; available in PMC: 2016 Jan 20.

Published in final edited form as: Comput Stat Data Anal. 2013 Nov;67:199–212. doi: 10.1016/j.csda.2013.05.011

Table 4. Sensitivity analysis: results of parameter estimates under model misspecification.

Analysis a: angle between β̂ and β₀ when the true model is the single index model

	log quardratic link						sine link

	N = 1000		N = 2000				N = 1000		N = 2000

	mean	SD	mean	SD			mean	SD	mean	SD
SI	7.371	4.174	4.548	1.909			3.441	1.543	2.238	1.071
plSI	14.827	7.493	8.469	3.945			4.559	1.787	3.059	1.305
Cox PH	71.073	32.413	71.473	32.310			5.354	2.466	3.967	1.693

Analysis b: the true model is the partially linear single index model, scenarios S1-S4

	α₁				α₂				angle (β̂,β₀)

	bias	SD	SEE	CP	bias	SD	SEE	CP	mean	SD

SI: include a noise variable in X

plSI	0.087	0.150	0.155	0.965	-0.187	0.274	0.277	0.955	8.110	5.174
Cox PH	-0.209	0.114	0.113	0.495	0.411	0.181	0.190	0.435	81.930	44.423

S2: omit a covariate in X

plSI	0.079	0.185	0.152	0.905	-0.155	0.315	0.271	0.925	11.257	8.135
Cox PH	-0.192	0.125	0.113	0.530	0.393	0.194	0.190	0.415	86.079	38.615

S3: misspecify membership of covariates, linear to nonlinear

plSI	0.049	0.160	0.150	0.930	-0.116	0.312	0.267	0.935	7.816	6.031
Cox PH	-0.243	0.108	0.109	0.385	0.465	0.179	0.182	0.260	90.100	44.880

S4: misspecify membership of covariates, nonlinear to linear

plSI	0.070	0.154	0.152	0.970	-0.140	0.272	0.270	0.950	9.668	5.006
Cox PH	-0.233	0.104	0.110	0.425	0.464	0.159	0.182	0.270	89.795	37.962

N: cohort size; bias: empirical bias; SD: sample standard deviation; SEE: standard error estimate; CP: empirical coverage probability of 95% confidence interval; SI: single index model; plSI: partially linear single index model.