Table 1. Simulation study: bias and root mean squared error (RMSE) of regression coefficients of a continuous exposure variable in unselected models, models selected by backward elimination (BE) and models selected by augmented backward elimination (ABE) for linear, logistic and Cox regression.

VIF		Variable selection among	Bias (×100)	RMSE (×100)	Selected models (%)
			of		Biased	Correct	Inflated
Linear regression
		No selection	1	24			100
2	0	BE,	3	21	33	35	32
		ABE,	2	22	28	34	38
		No selection	1	24			100
2	1	BE,	3	21	33	35	32
		ABE,	2	21	29	35	36
		No selection	1	57			100
4	0	BE,	6	50	39	34	27
		ABE,	2	56	25	14	61
		No selection	1	57			100
4	1	BE,	6	50	40	34	27
		ABE,	2	56	28	17	56
Logistic regression
		No selection	1	20			100
2	0	BE,	1	17	7	48	45
		ABE,	1	20	1	4	95
		No selection	6	25			100
2	1	BE,	5	21	11	43	46
		ABE,	6	25	2	3	95
		No selection	2	47			100
4	0	BE, Geben Sie hier eine Formel ein.	4	38	12	46	42
		ABE,	2	47	1	2	97
		No selection	6	55			100
4	1	BE,	7	46	17	41	43
		ABE,	6	55	1	1	98
Cox regression
		No selection	−1	22			100
2	0	BE, Geben Sie hier eine Formel ein.	1	19	20	40	40
		ABE,	−1	22	7	13	80
		No selection	2	23			100
2	1	BE, Geben Sie hier eine Formel ein.	3	20	19	40	41
		ABE,	2	23	7	13	80
		No selection	−2	52			100
4	0	BE,	4	47	26	36	38
		ABE,	−2	52	6	5	89
		No selection	1	52			100
4	1	BE, Geben Sie hier eine Formel ein.	6	46	28	36	36
		ABE,	1	52	7	4	89

Abbreviations and symbols: , significance threshold; ABE, augmented backward elimination; BE, backward elimination; RMSE, root mean squared error; , change-in-estimate threshold; VIF, variance inflation factor of conditional on . Sample size, subjects; Number of simulations, ; Variables selection based on six continuous candidate adjustment variables , among which three are truly associated with the outcome and five are correlated with the exposure; ‘Biased’, at least one variable from the true model was not selected; ‘Correct’, selected set of variables matches the true model; ‘Inflated’, selected set of variables contains all variables of the true model and at least one further variable. Full details on the simulation setup are contained in the Methods section.