Errors in interpreting abstinence curves in studies of smoking cessation

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Abstract
Articles on smoking cessation often present curves representing the percentage of smokers still abstinent over time. The purpose of this paper is to illustrate how common conclusions from inspecting these curves may be misleading because they are based on assumptions of which readers are not aware. For example, when active and control abstinence curves converge, this is often interpreted to indicate a diminution of treatment effect size over time. We use illustrative data to show that this interpretation is correct if one assumes a treatment has a constant additive effect; however, if one assumes treatment has a constant multiplicative effect, then converging curves can still indicate a constant treatment effect. Converging abstinence curves are also often interpreted to indicate that the rate of relapse is greater in the active than the control group. We illustrate that this interpretation is correct if one is interested in cumulative relapse rate and uses all subjects in the denominator; however, if one is interested in relapse over a discrete subperiod of time (e.g., immediately after treatment stops), and thus uses only those at risk for relapse, then converging curves can still indicate a constant relapse rate. When trials interpret abstinence curves, they should make clear whether they are assuming additive or multiplicative effects of treatment and are discussing overall or local relapse rates. They should also report both additive and multiplicative effect sizes.