Instrumental variable estimation for a time-varying treatment and a time-to-event outcome via structural nested cumulative failure time models

Table 1 Mean, standard deviation (SD), bias and mean squared error (MSE) of psi estimates using different g-estimation approaches under different data-generating mechanisms

DAG	Under the null	Measure	Confounding-adjusted analysis	IV analysis	IV analysis of nested case-control sample	Unadjusted analysis
Time-fixed exposure and outcome	Yes	Mean	0.0013	0.0044	0.0102	0.2468
		SD	0.0655	0.2001	0.2665	0.0563
		Bias	+0.0013	+0.0044	+ 0.0102	+ 0.2468
		MSE	0.0043	0.0400	0.0711	0.0641
	No	Mean	0.4591	0.4655	0.5010	0.7016
		SD	0.0579	0.1885	0.2563	0.0478
		Bias	0.0000	+0.0064	+0.0419	+0.2424
		MSE	0.0034	0.0355	0.0674	0.0611
Time-fixed exposure and time-varying outcome	Yes	Mean	−0.0024	−0.0018	0.0021	0.2410
		SD	0.0473	0.1446	0.1950	0.0401
		Bias	−0.0024	− 0.0018	+0.0021	+0.2410
		MSE	0.0022	0.0209	0.0380	0.0597
	No	Mean	0.4523	0.4489	0.5015	0.6923
		SD	0.0417	0.1365	0.1833	0.0348
		Bias	0.0000	−0.0033	+0.0492	+0.2400
		MSE	0.0017	0.0186	0.0360	0.0588
Time-varying exposure and outcome	Yes	Mean	−0.0018	0.0061	0.0122	0.1717
		SD	0.0539	0.1428	0.1861	0.0470
		Bias	−0.0018	+0.0061	+0.0122	+0.1717
		MSE	0.0029	0.0204	0.0348	0.0317
	No	Mean	0.4600	0.4588	0.4974	0.6316
		SD	0.0448	0.1293	0.1706	0.0378
		Bias	0.0000	−0.0012	+0.0374	+0.1716
		MSE	0.0020	0.0167	0.0305	0.0309

ISSN: 1471-2288