A Bayesian path analysis to estimate causal effects of bazedoxifene acetate on incidence of vertebral fractures, either directly or through non-linear changes in bone mass density

Abstract

Background/Aims Bone mass density values have been related with risk of vertebral fractures in post-menopausal women. However, bone mass density is not perfectly accurate in predicting risk of fracture, which decreases its usefulness as a surrogate in clinical trials. We propose a modeling framework with three interconnected parts to improve the evaluation of bone mass density accuracy in forecasting fractures after treatment. Methods The modeling framework includes: (1) a piecewise regression to describe non-linear temporal BMD changes more accurately than crude percent changes, (2) a structural equation model to analyze interdependencies among vertebral fractures and their potential risk factors in preference to regression techniques that consider only directional associations, and (3) a counterfactual causal interpretation of the direct and indirect relationships between treatment and occurrence of vertebral fractures. We apply the methods to BMD repeated measurements from a study of the effect of bazedoxifene acetate on incident vertebral fractures in three different geographical regions. Results We made four observations: (1) bone mass density changes varied largely across participants, (2) baseline age and body mass index influenced baseline bone mass density that, in turn, had an effect on prevalent fractures, (3) direct and/or indirect effects of bazedoxifene acetate on incident fractures were different across regions, and (4) estimates of indirect effects were sensible to the presence of post-treatment unmeasured confounders. In one region, around 40% of the bazedoxifene acetate effect on the occurrence of fracture is explained by its effect on bone mass density. Under the counterfactual approach, these 40% represent the average difference in the occurrence of fracture observed for untreated individuals when their bone mass density values are set at the value under bazedoxifene acetate versus under placebo. Conclusions Computational methods are available to evaluate and interpret the surrogacytic capability of a biomarker of a primary outcome.