Wearable devices collect time-varying biobehavioral data, offering opportunities to investigate how behaviors influence health outcomes. However, these data often contain measurement error and excess zeros (due to nonwear, sedentary behavior, or connectivity issues), each characterized by subject-specific distributions. Current statistical methods fail to address these issues simultaneously. We introduce a novel modeling framework for zero-inflated and error-prone functional data by incorporating a subject-specific time-varying validity indicator that explicitly distinguishes structural zeros from intrinsic values. We iteratively estimate the latent functional covariates and zero-inflation probabilities via maximum likelihood, using basis expansions and linear mixed models to adjust for measurement error. To assess the effects of the recovered latent covariates, we apply joint quantile regression across multiple quantile levels. Through extensive simulations, we demonstrate that our approach significantly improves estimation accuracy over methods that only address measurement error, and joint estimation yields substantial improvements compared with fitting separate quantile regressions. Applied to a childhood obesity study, our approach effectively corrects for zero inflation and measurement error in step counts, yielding results that closely align with energy expenditure and supporting their use as a proxy for physical activity.

翻译：可穿戴设备收集随时间变化的生物行为数据，为探究行为如何影响健康结局提供了契机。然而，这类数据常包含测量误差与过量零值（由设备未佩戴、久坐行为或连接问题导致），且两者均呈现个体特异性分布特征。现有统计方法无法同时处理这些问题。本文提出一种针对零膨胀含误差函数型数据的新型建模框架，通过引入个体特异性时变有效性指标，显式区分结构性零值与内在真值。我们采用基函数展开与线性混合模型校正测量误差，通过最大似然估计迭代求解潜函数型协变量及零膨胀概率。为评估复原后潜协变量的效应，我们在多重分位数水平上应用联合分位数回归方法。大量模拟研究表明：相较于仅处理测量误差的方法，本方法显著提升了估计精度；且与独立拟合分位数回归相比，联合估计能带来实质性改进。在儿童肥胖研究中的应用表明，本方法能有效修正步数数据中的零膨胀与测量误差，所得结果与能量消耗高度吻合，支持将步数作为体力活动的有效代理指标。