Functional linear regression model with an error-prone zero inflated functional predictor

Music City Center 

Because measures of physical activity derived from accelerometers are used to monitor physical activity behavior, the data may contain measurement error. Due to sedentary behavior, non-wear, or device malfunctions, the data may also contain excess zeroes. Limited options exist for analyzing zero-inflated functional data measured with error. Prior estimation methods were based on the assumption that the zero-inflated data were observed without errors, and assumed marginal distributions, such as a mixture of a degenerate distribution with a Gaussian distribution. However, these methods are not applicable for bias reduction of error-prone zero-inflated functional data. We propose semi-parametric Bayesian approaches that incorporate more flexible marginal distributions and priors while accounting for measurement error biases. We conduct simulations and sensitivity analyses to assess the performance of our proposed methods and compare them to current approaches. Our proposed method reduces biases due to measurement errors under the different simulation settings. We apply our methods to investigate the relationship between school-based physical activity and body mass index.

measurement error

zero-inflation

functional data

physical activity

wearable device

accelerometer 

Section on Statistics in Epidemiology