Analytic Methods for Elucidating Continuous Dose-response Associations in the Presence of Spike-effects: Avoiding the Illusion of a Safe Dose

Background: Determining the dose-response association between continuously measured drug exposures and outcomes can help substantiate observations in pharmacoepidemiologic research. Traditionally employed approaches for modeling continuous dose exposures (e.g., natural cubic splines) presume the effect of continuous exposure to continuously shrink toward zero with smaller doses, potentially creating a false sense of safety when caution would be warranted.

Objectives: To develop analytic approaches to accommodate the relative effect of any dose exposure (e.g., through a nocebo-like effect), and to compare these methods to other commonly implemented models.

Methods: We propose a semi-continuous "spike-and-spline" approach to accommodate exposure distributions characterized by a "spike" at zero followed by a continuous dose range. Furthermore, we extended this method and introduced a "slab-and-spline" approach that can be used when there are sparse data available at low doses. We conducted a comprehensive range of simulations with semi-continuous exposures and continuous outcomes to evaluate the operating characteristics of each approach including bias, coverage, and power when the spike effect was and was not present. Specific comparator methods included linear regression modeling and analyses of users only (i.e., those with a positive dose).

Results: Simulations reveal the spike-and-spline approach to provide substantive reductions in bias and improved coverage compared to traditional approaches when a there are effects at low doses present, with comparatively small costs in power when the effect is not present. Yet, when data are sparse at low-dose ranges, the spike-and-spline approach may not have appropriate degrees of freedom to provide meaningful insights into the dose-response association. Our proposed slab-and-spline approach provides efficiency gains in this setting. When spike or slab terms are not included, the dose-response curve is forced through the origin, creating a sense of a range of safe doses where none exist. Of note, spline approaches capture the dose-response association at higher doses, irrespective of inclusion of spike or slab terms.

Conclusions: The spike/slab-and-spline approaches provide advantages over traditional approaches in elucidating dose-response associations between continuous exposures and outcomes with markedly less bias, particularly at lower dose ranges. Given the relative ease of implementing these approaches, along with the very low cost in power, we recommend inclusion of these terms to better capture full dose-response relationships in pharmacoepidemiologic drug exposure studies.