Missing-Data Handling Methods for Lifelogs-Based Wellness Index Estimation: Comparative Analysis With Panel Data

A lifelogs-based wellness index (LWI) is a function for calculating wellness scores based on health behavior lifelogs (eg, daily walking steps and sleep times collected via a smartwatch). A wellness score intuitively shows the users of smart wellness services the overall condition of their health behaviors. LWI development includes estimation (ie, estimating coefficients in LWI with data). A panel data set comprising health behavior lifelogs allows LWI estimation to control for unobserved variables, thereby resulting in less bias. However, these data sets typically have missing data due to events that occur in daily life (eg, smart devices stop collecting data when batteries are depleted), which can introduce biases into LWI coefficients. Thus, the appropriate choice of method to handle missing data is important for reducing biases in LWI estimations with panel data. However, there is a lack of research in this area.

This study aims to identify a suitable missing-data handling method for LWI estimation with panel data.

Listwise deletion, mean imputation, expectation maximization-based multiple imputation, predictive-mean matching-based multiple imputation, k-nearest neighbors-based imputation, and low-rank approximation-based imputation were comparatively evaluated by simulating an existing case of LWI development. A panel data set comprising health behavior lifelogs of 41 college students over 4 weeks was transformed into a reference data set without any missing data. Then, 200 simulated data sets were generated by randomly introducing missing data at proportions from 1% to 80%. The missing-data handling methods were each applied to transform the simulated data sets into complete data sets, and coefficients in a linear LWI were estimated for each complete data set. For each proportion for each method, a bias measure was calculated by comparing the estimated coefficient values with values estimated from the reference data set.

Methods performed differently depending on the proportion of missing data. For 1% to 30% proportions, low-rank approximation-based imputation, predictive-mean matching-based multiple imputation, and expectation maximization-based multiple imputation were superior. For 31% to 60% proportions, low-rank approximation-based imputation and predictive-mean matching-based multiple imputation performed best. For over 60% proportions, only low-rank approximation-based imputation performed acceptably.

Low-rank approximation-based imputation was the best of the 6 data-handling methods regardless of the proportion of missing data. This superiority is generalizable to other panel data sets comprising health behavior lifelogs given their verified low-rank nature, for which low-rank approximation-based imputation is known to perform effectively. This result will guide missing-data handling in reducing coefficient biases in new development cases of linear LWIs with panel data.