Modern multiple imputation with functional data

Instrumental variable estimation for functional concurrent regression models

In this work we propose a functional concurrent regression model to estimate labor supply elasticities over the years 1988 through 2014 using Current Population Survey data. Assuming, as is common, that individuals' wages are endogenous, we introduce instrumental variables in a two-stage least squares approach to estimate the desired labor supply elasticities. Furthermore, we tailor our estimation method to sparse functional data. Though recent work has incorporated instrumental variables into other functional regression models, to our knowledge this has not yet been done in the functional concurrent regression model, and most existing literature is not suited for sparse functional data. We show through simulations that this two-stage least squares approach greatly eliminates the bias introduced by a naive model (i.e. one that does not acknowledge endogeneity) and produces accurate coefficient estimates for moderate sample sizes.

Binned Data Provide Better Imputation of Missing Time Series Data from Wearables

The presence of missing values in a time-series dataset is a very common and well-known problem. Various statistical and machine learning methods have been developed to overcome this problem, with the aim of filling in the missing values in the data. However, the performances of these methods vary widely, showing a high dependence on the type of data and correlations within the data. In our study, we performed some of the well-known imputation methods, such as expectation maximization, k-nearest neighbor, iterative imputer, random forest, and simple imputer, to impute missing data obtained from smart, wearable health trackers. In this manuscript, we proposed the use of data binning for imputation. We showed that the use of data binned around the missing time interval provides a better imputation than the use of a whole dataset. Imputation was performed for 15 min and 1 h of continuous missing data. We used a dataset with different bin sizes, such as 15 min, 30 min, 45 min, and 1 h, and we carried out evaluations using root mean square error (RMSE) values. We observed that the expectation maximization algorithm worked best for the use of binned data. This was followed by the simple imputer, iterative imputer, and k-nearest neighbor, whereas the random forest method had no effect on data binning during imputation. Moreover, the smallest bin sizes of 15 min and 1 h were observed to provide the lowest RMSE values for the majority of the time frames during the imputation of 15 min and 1 h of missing data, respectively. Although applicable to digital health data, we think that this method will also find applicability in other domains.

Sequential Multiple Imputation for Real-World Health-Related Quality of Life Missing Data after Bariatric Surgery

One of the main challenges for the successful implementation of health-related quality of life (HRQoL) assessments is missing data. The current study examined the feasibility and validity of a sequential multiple imputation (MI) method to deal with missing values in the longitudinal HRQoL data from the Scandinavian Obesity Surgery Registry. All patients in the SOReg who received bariatric surgery between 1 January 2011 and 31 March 2019 (n = 47,653) were included for the descriptive analysis and missingness pattern exploration. The patients who had completed the short-form 36 (SF-36) at baseline (year 0), and one-, two-, and five-year follow-ups were included (n = 3957) for the missingness pattern simulation and the sequential MI analysis. Eleven items of the SF-36 were selected to create the six domains of SF-6D, and the SF-6D utility index of each patient was calculated accordingly. The multiply-imputed variables in previous year were used as input to impute the missing values in later years. The performance of the sequential MI was evaluated by comparing the actual values with the imputed values of the selected SF-36 items and index at all four time points. At the baseline and year 1, where missing proportions were about 20% and 40%, respectively, there were no statistically significant discrepancies between the distributions of the actual and imputed responses (all p-values > 0.05). In year 2, where the missing proportion was about 60%, distributions of the actual and imputed responses were consistent in 9 of the 11 SF-36 items. However, in year 5, where the missing proportion was about 80%, no consistency was found between the actual and imputed responses in any of the SF-36 items. Relatively high missing proportions in HRQoL data are common in clinical registries, which brings a challenge to analyzing the HRQoL of longitudinal cohorts. The experimental sequential multiple imputation method adopted in the current study might be an ideal strategy for handling missing data (even though the follow-up survey had a missing proportion of 60%), avoiding significant information waste in the multivariate analysis. However, the imputations for data with higher missing proportions warrant more research.