Women are at increased risk of bone loss during the menopausal transition; in fact, nearly 50\% of women's lifetime bone loss occurs during this time. The longitudinal relationships between estradiol (E2) and follicle-stimulating hormone (FSH), two hormones that change have characteristic changes during the menopausal transition, and bone health outcomes are complex. However, in addition to level and rate of change in E2 and FSH, variability in these hormones across the menopausal transition may be an important predictor of bone health, but this question has yet to be well explored. We introduce a joint model that characterizes individual mean estradiol (E2) trajectories and the individual residual variances and links these variances to bone health trajectories. In our application, we found that higher FSH variability was associated with declines in bone mineral density (BMD) before menopause, but this association was moderated over time after the menopausal transition. Additionally, higher mean E2, but not E2 variability, was associated with slower decreases in during the menopausal transition. We also include a simulation study that shows that naive two-stage methods often fail to propagate uncertainty in the individual-level variance estimates, resulting in estimation bias and invalid interval coverage

翻译：女性在绝经过渡期骨丢失风险增加；事实上，女性近50%的终身骨量损失发生在此阶段。雌二醇（E2）与促卵泡激素（FSH）——两种在绝经过渡期呈现特征性变化的激素——与骨骼健康结局之间存在复杂的纵向关联。然而，除E2和FSH的水平及变化速率外，这些激素在绝经过渡期的变异性可能是骨骼健康的重要预测因子，但该问题尚未得到充分探索。我们提出一种联合模型，该模型可刻画个体平均雌二醇（E2）轨迹及其个体残差方差，并将这些方差与骨骼健康轨迹建立关联。在应用中我们发现：高FSH变异性与绝经前骨矿物质密度（BMD）下降相关，但这种关联在绝经过渡期后随时间减弱；此外，较高的平均E2（而非E2变异性）与绝经过渡期内BMD减缓下降相关。我们还通过模拟研究证明，朴素的两阶段方法通常无法传播个体水平方差估计的不确定性，导致估计偏差和区间覆盖失效。