Confounding in longitudinal studies in addiction treatment research

Figures & data

Figure 1. Path diagrams representing a time varying treatment exposure (A_t), an outcome variable (Y_t) and confounding by a variable (X) that is (a) time invariant; (b) time-varying and not affected by prior treatment; and (c) time-varying and affected by prior treatment.

Figure 2. Time-invariant confounding: heat maps of the bias of the estimated treatment effect, on the log odds ratio (ln(OR)) scale, when failing to control for confounding. With varying effect of a confounding variable on being in treatment (β_XA) and outcome (β_XY). The area in blue represents negative bias, the area in red positive bias.

Figure 3. Time-varying confounding: Heat maps of the bias on the log odds ratio (ln(OR)) scale, when (a) there is no adjustment, (b) adjusting for the baseline value of the confounder only. With varying effect of a time-varying, deterministic, confounding variable on being in treatment (β_XA) and outcome (β_XY). The area in blue represents negative bias, the area in red positive bias.

Table 1. Bias on the log odds ratio (ln(OR)) scale from simulations for different effects of a time-varying variable on treatment (β_XA) and outcome (β_XY) and the effect of prior treatment on that variable (β_AXAXE); unadjusted analysis and after adjusting for the time-varying variable.

				ln(OR) bias^a
Scenario	βXA	βXY	βAX	Unadjusted analysis	Adjusted analysis
1. X is a confounder and mediator	−2	2	2	−0.61	−0.14
2. X is a confounder only	−2	2	0	−0.72	0.02
3. X is a mediator only	0	2	2	0.00	−0.40

^a Bias calculated as the difference between regression estimates and estimates using the IPTW method, full details provided in Appendix A.