Background: In the absence of unmeasured confounding, standard methods for estimating the effects of time-varying treatments on an event are biased when a time-dependent risk factor for the event also predicts subsequent treatments and when past treatment history predicts subsequent risk factor levels. In contrast, structural models provide unbiased estimates of effects when unmeasured confounding is absent.
Methods: We describe a multiplicative structural mean model and use it to estimate the effects of time-varying osteoporosis treatments on incidence of fractures among 1328 postmenopausal women over 40 years of age in a hospital-based cohort study in Japan. The parameters of the structural mean model are estimated by g-estimation.
Results: The number of vertebral fractures and bone mineral density levels predicted the selection of subsequent treatments and were affected by the previous treatments. Incidence rate ratios of bisphosphonates, active vitamin D3, and conjugated estrogen compared with no drug therapy were 0.58 (95% confidence interval = 0.44-0.77), 0.82 (0.48-1.38), and 0.60 (0.47-0.76), respectively, after adjusting time-dependent confounders. For initial treatments estimated by the standard Poisson-GEE, incidence rate ratios were 1.61 (1.23-2.10), 1.16 (0.96-1.40), and 0.73 (0.52-1.02), respectively.
Conclusions: Our analysis using the structural mean model showed that bisphosphonates, active vitamin D3, and conjugated estrogen all had preventive effects on the incidence of fractures by appropriate adjustments for time-dependent confounders. The results from standard Poisson-GEE analysis were the opposite of these results and of evidence from randomized trials. We consider our methods useful to estimate time-varying treatments within observational data.