Single Imputation Methods and Confidence Intervals for the Gini Index

The problem of missing data is a common feature in any study, and a single imputation method is often applied to deal with this problem. The first contribution of this paper is to analyse the empirical performance of some traditional single imputation methods when they are applied to the estimation of the Gini index, a popular measure of inequality used in many studies. Various methods for constructing confidence intervals for the Gini index are also empirically evaluated. We consider several empirical measures to analyse the performance of estimators and confidence intervals, allowing us to quantify the magnitude of the non-response bias problem. We find extremely large biases under certain non-response mechanisms, and this problem gets noticeably worse as the proportion of missing data increases. For a large correlation coefficient between the target and auxiliary variables, the regression imputation method may notably mitigate this bias problem, yielding appropriate mean square errors. We also find that confidence intervals have poor coverage rates when the probability of data being missing is not uniform, and that the regression imputation method substantially improves the handling of this problem as the correlation coefficient increases.

Incomplete Data Analysis

This chapter discusses missing-value problems from the perspective of machine learning. Missing values frequently occur during data acquisition. When a dataset contains missing values, nonvectorial data are generated. This subsequently causes a serious problem in pattern recognition models because nonvectorial data need further data wrangling before models are built. In view of such, this chapter reviews the methodologies of related works and examines their empirical effectiveness. At present, a great deal of effort has been devoted in this field, and those works can be roughly divided into two types — Multiple imputation and single imputation, where the latter can be further classified into subcategories. They include deletion, fixed-value replacement, K-Nearest Neighbors, regression, tree-based algorithms, and latent component-based approaches. In this chapter, those approaches are introduced and commented. Finally, numerical examples are provided along with recommendations on future development.

Evaluating Methods for Imputing Missing Data from Longitudinal Monitoring of Athlete Workload

Missing data can influence calculations of accumulated athlete workload. The objectives were to identify the best single imputation methods and examine workload trends using multiple imputation. External (jumps per hour) and internal (rating of perceived exertion; RPE) workload were recorded for 93 (45 females, 48 males) high school basketball players throughout a season. Recorded data were simulated as missing and imputed using ten imputation methods based on the context of the individual, team and session. Both single imputation and machine learning methods were used to impute the simulated missing data. The difference between the imputed data and the actual workload values was computed as root mean squared error (RMSE). A generalized estimating equation determined the effect of imputation method on RMSE. Multiple imputation of the original dataset, with all known and actual missing workload data, was used to examine trends in longitudinal workload data. Following multiple imputation, a Pearson correlation evaluated the longitudinal association between jump count and sRPE over the season. A single imputation method based on the specific context of the session for which data are missing (team mean) was only outperformed by methods that combine information about the session and the individual (machine learning models). There was a significant and strong association between jump count and sRPE in the original data and imputed datasets using multiple imputation. The amount and nature of the missing data should be considered when choosing a method for single imputation of workload data in youth basketball. Multiple imputation using several predictor variables in a regression model can be used for analyses where workload is accumulated across an entire season.

Multiple imputation and direct estimation for qPCR data with non-detects

Background Quantitative real-time PCR (qPCR) is one of the most widely used methods to measure gene expression. An important aspect of qPCR data that has been largely ignored is the presence of non-detects: reactions failing to exceed the quantification threshold and therefore lacking a measurement of expression. While most current software replaces these non-detects with a value representing the limit of detection, this introduces substantial bias in the estimation of both absolute and differential expression. Single imputation procedures, while an improvement on previously used methods, underestimate residual variance, which can lead to anti-conservative inference. Results We propose to treat non-detects as non-random missing data, model the missing data mechanism, and use this model to impute missing values or obtain direct estimates of model parameters. To account for the uncertainty inherent in the imputation, we propose a multiple imputation procedure, which provides a set of plausible values for each non-detect. We assess the proposed methods via simulation studies and demonstrate the applicability of these methods to three experimental data sets. We compare our methods to mean imputation, single imputation, and a penalized EM algorithm incorporating non-random missingness (PEMM). The developed methods are implemented in the R/Bioconductor package . Conclusions The statistical methods introduced here reduce discrepancies in gene expression values derived from qPCR experiments in the presence of non-detects, providing increased confidence in downstream analyses.

THU0556 MISSING DATA AND MULTIPLE IMPUTATION IN RHEUMATOID ARTHRITIS REGISTRIES USING SEQUENTIAL RANDOM FOREST METHOD

Background:Missing data in clinical epidemiological researches violate the intention to treat principle,reduce statistical power and can induce bias if they are related to patient’s response to treatment. In multiple imputation (MI), covariates are included in the imputation equation to predict the values of missing data.Objectives:To find the best approach to estimate and impute the missing values in Kuwait Registry for Rheumatic Diseases (KRRD) patients data.Methods:A number of methods were implemented for dealing with missing data. These includedMultivariate imputation by chained equations(MICE),K-Nearest Neighbors(KNN),Bayesian Principal Component Analysis(BPCA),EM with Bootstrapping(Amelia II),Sequential Random Forest(MissForest) and mean imputation. Choosing the best imputation method wasjudged by the minimum scores ofRoot Mean Square Error(RMSE),Mean Absolute Error(MAE) andKolmogorov–Smirnov D test statistic(KS) between the imputed datapoints and the original datapoints that were subsequently sat to missing.Results:A total of 1,685 rheumatoid arthritis (RA) patients and 10,613 hospital visits were included in the registry. Among them, we found a number of variables that had missing values exceeding 5% of the total values. These included duration of RA (13.0%), smoking history (26.3%), rheumatoid factor (7.93%), anti-citrullinated peptide antibodies (20.5%), anti-nuclear antibodies (20.4%), sicca symptoms (19.2%), family history of a rheumatic disease (28.5%), steroid therapy (5.94%), ESR (5.16%), CRP (22.9%) and SDAI (38.0%), The results showed that among the methods used, MissForest gave the highest level of accuracy to estimate the missing values. It had the least imputation errors for both continuous and categorical variables at each frequency of missingness and it had the smallest prediction differences when the models used imputed laboratory values. In both data sets, MICE had the second least imputation errors and prediction differences, followed by KNN and mean imputation.Conclusion:MissForest is a highly accurate method of imputation for missing data in KRRD and outperforms other common imputation techniques in terms of imputation error and maintenance of predictive ability with imputed values in clinical predictive models. This approach can be used in registries to improve the accuracy of data, including the ones for rheumatoid arthritis patients.References:[1]Junninen, H.; Niska, H.; Tuppurainen, K.; Ruuskanen, J.; Kolehmainen, M. Methods for imputation ofmissing values in air quality data sets.Atmospheric Environment2004,38, 2895–2907.[2]Norazian, M.N.; Shukri, Y.A.; Azam, R.N.; Al Bakri, A.M.M. Estimation of missing values in air pollutiondata using single imputation techniques.ScienceAsia2008,34, 341–345.[3]Plaia, A.; Bondi, A. Single imputation method of missing values in environmental pollution data sets.Atmospheric Environment2006,40, 7316–7330.[4]Kabir, G.; Tesfamariam, S.; Hemsing, J.; Sadiq, R. Handling incomplete and missing data in water networkdatabase using imputation methods.Sustainable and Resilient Infrastructure2019, pp. 1–13.[5]Di Zio, M.; Guarnera, U.; Luzi, O. Imputation through finite Gaussian mixture models.ComputationalStatistics & Data Analysis2007,51, 5305–5316.Disclosure of Interests:None declared

Multiply robust bootstrap variance estimation in the presence of singly imputed survey data

Item nonresponse in surveys is usually dealt with through single imputation. It is well known that treating the imputed values as if they were observed values may lead to serious underestimation of the variance of point estimators. In this article, we propose three pseudo-population bootstrap schemes for estimating the variance of imputed estimators obtained after applying a multiply robust imputation procedure. The proposed procedures can handle large sampling fractions and enjoy the multiple robustness property. Results from a simulation study suggest that the proposed methods perform well in terms of relative bias and coverage probability, for both population totals and quantiles.