Missing value imputation for physical activity data measured by accelerometer

An accelerometer, a wearable motion sensor on the hip or wrist, is becoming a popular tool in clinical and epidemiological studies for measuring the physical activity. Such data provide a series of activity counts at every minute or even more often and displays a person's activity pattern throughout a day. Unfortunately, the collected data can include irregular missing intervals because of noncompliance of participants and therefore make the statistical analysis more challenging. The purpose of this study is to develop a novel imputation method to handle the multivariate count data, motivated by the accelerometer data structure. We specify the predictive distribution of the missing data with a mixture of zero-inflated Poisson and Log-normal distribution, which is shown to be effective to deal with the minute-by-minute autocorrelation as well as under- and over-dispersion of count data. The imputation is performed at the minute level and follows the principles of multiple imputation using a fully conditional specification with the chained algorithm. To facilitate the practical use of this method, we provide an R package accelmissing. Our method is demonstrated using 2003-2004 National Health and Nutrition Examination Survey data.