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Inferring causal effects of treatments is a central goal in many disciplines. The potential outcomes framework is a main statistical approach to causal inference, in which a causal effect is defined as a comparison of the potential outcomes of the same units under different treatment conditions. Because for each unit at most one of the potential outcomes is observed and the rest are missing, causal inference is inherently a missing data problem. Indeed, there is a close analogy in the terminology and the inferential framework between causal inference and missing data. Despite the intrinsic connection between the two subjects, statistical analyses of causal inference and missing data also have marked differences in aims, settings and methods. This article provides a systematic review of causal inference from the missing data perspective. Focusing on ignorable treatment assignment mechanisms, we discuss a wide range of causal inference methods that have analogues in missing data analysis, such as imputation, inverse probability weighting and doubly robust methods. Under each of the three modes of inference—Frequentist, Bayesian and Fisherian randomization—we present the general structure of inference for both finite-sample and super-population estimands, and illustrate via specific examples. We identify open questions to motivate more research to bridge the two fields.

Background Missing data are common in statistical analyses, and imputation methods based on random forests (RF) are becoming popular for handling missing data especially in biomedical research. Unlike standard imputation approaches, RF-based imputation methods do not assume normality or require specification of parametric models. However, it is still inconclusive how they perform for non-normally distributed data or when there are non-linear relationships or interactions. Methods To examine the effects of these three factors, a variety of datasets were simulated with outcome-dependent missing at random (MAR) covariates, and the performances of the RF-based imputation methods missForest and CALIBERrfimpute were evaluated in comparison with predictive mean matching (PMM). Results Both missForest and CALIBERrfimpute have high predictive accuracy but missForest can produce severely biased regression coefficient estimates and downward biased confidence interval coverages, especially for highly skewed variables in nonlinear models. CALIBERrfimpute typically outperforms missForest when estimating regression coefficients, although its biases are still substantial and can be worse than PMM for logistic regression relationships with interaction. Conclusions RF-based imputation, in particular missForest, should not be indiscriminately recommended as a panacea for imputing missing data, especially when data are highly skewed and/or outcome-dependent MAR. A correct analysis requires a careful critique of the missing data mechanism and the inter-relationships between the variables in the data.

Background Multiple imputation (MI) is now widely used to handle missing data in longitudinal studies. Several MI techniques have been proposed to impute incomplete longitudinal covariates, including standard fully conditional specification (FCS-Standard) and joint multivariate normal imputation (JM-MVN), which treat repeated measurements as distinct variables, and various extensions based on generalized linear mixed models. Although these MI approaches have been implemented in various software packages, there has not been a comprehensive evaluation of the relative performance of these methods in the context of longitudinal data. Method Using both empirical data and a simulation study based on data from the six waves of the Longitudinal Study of Australian Children ( N  = 4661), we investigated the performance of a wide range of MI methods available in standard software packages for investigating the association between child body mass index (BMI) and quality of life using both a linear regression and a linear mixed-effects model. Results In this paper, we have identified and compared 12 different MI methods for imputing missing data in longitudinal studies. Analysis of simulated data under missing at random (MAR) mechanisms showed that the generally available MI methods provided less biased estimates with better coverage for the linear regression model and around half of these methods performed well for the estimation of regression parameters for a linear mixed model with random intercept. With the observed data, we observed an inverse association between child BMI and quality of life, with available data as well as multiple imputation. Conclusion Both FCS-Standard and JM-MVN performed well for the estimation of regression parameters in both analysis models. More complex methods that explicitly reflect the longitudinal structure for these analysis models may only be needed in specific circumstances such as irregularly spaced data.

We present and compare multiple imputation methods for multilevel continuous and binary data where variables are systematically and sporadically missing. The methods are compared from a theoretical point of view and through an extensive simulation study motivated by a real dataset comprising multiple studies. The comparisons show that these multiple imputation methods are the most appropriate to handle missing values in a multilevel setting and why their relative performances can vary according to the missing data pattern, the multilevel structure and the type of missing variables. This study shows that valid inferences can only be obtained if the dataset includes a large number of clusters. In addition, it highlights that heteroscedastic multiple imputation methods provide more accurate inferences than homoscedastic methods, which should be reserved for data with few individuals per cluster. Finally, guidelines are given to choose the most suitable multiple imputation method according to the structure of the data.

Missing data is a common problem encountered in various fields, including clinical research, environmental sciences and hydrology. In order to obtain reliable results from the analysis, the data inventory must be completed. This paper presents a methodology for addressing the missing data problem by examining the missing data structure and missing data techniques. Simulated datasets were created by considering the number of missing data, missing data pattern and missing data mechanism of real datasets containing missing values, which are often overlooked in hydrology. Considering the missing data pattern, the most commonly used methods for missing data analysis in hydrology and other fields were applied to the created simulated datasets. Simple imputation techniques and expectation maximization (EM) were implemented in SPSS software and machine learning techniques such as k-nearest neighbor (kNN), together with the hot-deck were implemented in the Python programming language. In the performance evaluation based on error metrics, it is concluded that the EM method is the most suitable completion method. Homogeneity analyses were performed in the Mathematica programming language to identify possible changes and inconsistencies in the completed rainfall dataset. Homogeneity analyses revealed that most of the completed rainfall datasets are homogeneous at class 1 level, consistent and reliable and do not show systematic changes in time.

Multiple imputation is a straightforward method for handling missing data in a principled fashion. This paper presents an overview of multiple imputation, including important theoretical results and their practical implications for generating and using multiple imputations. A review of strategies for generating imputations follows, including recent developments in flexible joint modeling and sequential regression/chained equations/fully conditional specification approaches. Finally, we compare and contrast different methods for generating imputations on a range of criteria before identifying promising avenues for future research.

As a result of the development of sophisticated techniques, such as multiple imputation, the interest in handling missing data in longitudinal studies has increased enormously in past years. Within the field of longitudinal data analysis, there is a current debate on whether it is necessary to use multiple imputations before performing a mixed-model analysis to analyze the longitudinal data. In the current study this necessity is evaluated. The results of mixed-model analyses with and without multiple imputation were compared with each other. Four data sets with missing values were created—one data set with missing completely at random, two data sets with missing at random, and one data set with missing not at random). In all data sets, the relationship between a continuous outcome variable and two different covariates were analyzed: a time-independent dichotomous covariate and a time-dependent continuous covariate. Although for all types of missing data, the results of the mixed-model analysis with or without multiple imputations were slightly different, they were not in favor of one of the two approaches. In addition, repeating the multiple imputations 100 times showed that the results of the mixed-model analysis with multiple imputation were quite unstable. It is not necessary to handle missing data using multiple imputations before performing a mixed-model analysis on longitudinal data.

In data analytics, missing data is a factor that degrades performance. Incorrect imputation of missing values could lead to a wrong prediction. In this era of big data, when a massive volume of data is generated in every second, and utilization of these data is a major concern to the stakeholders, efficiently handling missing values becomes more important. In this paper, we have proposed a new technique for missing data imputation, which is a hybrid approach of single and multiple imputation techniques. We have proposed an extension of popular Multivariate Imputation by Chained Equation (MICE) algorithm in two variations to impute categorical and numeric data. We have also implemented twelve existing algorithms to impute binary, ordinal, and numeric missing values. We have collected sixty-five thousand real health records from different hospitals and diagnostic centers of Bangladesh, maintaining the privacy of data. We have also collected three public datasets from the UCI Machine Learning Repository, ETH Zurich, and Kaggle. We have compared the performance of our proposed algorithms with existing algorithms using these datasets. Experimental results show that our proposed algorithm achieves 20% higher F-measure for binary data imputation and 11% less error for numeric data imputations than its competitors with similar execution time.

In environmental research, missing data are often a challenge for statistical modeling. This paper addressed some advanced techniques to deal with missing values in a data set measuring air quality using a multiple imputation (MI) approach. MCAR, MAR, and NMAR missing data techniques are applied to the data set. Five missing data levels are considered: 5%, 10%, 20%, 30%, and 40%. The imputation method used in this paper is an iterative imputation method, missForest, which is related to the random forest approach. Air quality data sets were gathered from five monitoring stations in Kuwait, aggregated to a daily basis. Logarithm transformation was carried out for all pollutant data, in order to normalize their distributions and to minimize skewness. We found high levels of missing values for NO2 (18.4%), CO (18.5%), PM10 (57.4%), SO2 (19.0%), and O3 (18.2%) data. Climatological data (i.e., air temperature, relative humidity, wind direction, and wind speed) were used as control variables for better estimation. The results show that the MAR technique had the lowest RMSE and MAE. We conclude that MI using the missForest approach has a high level of accuracy in estimating missing values. MissForest had the lowest imputation error (RMSE and MAE) among the other imputation methods and, thus, can be considered to be appropriate for analyzing air quality data.

No clear guidance exists on handling missing data at each stage of developing, validating and implementing a clinical prediction model (CPM). We aimed to review the approaches to handling missing data that underly the CPMs currently recommended for use in UK healthcare. A descriptive cross-sectional meta-epidemiological study aiming to identify CPMs recommended by the National Institute for Health and Care Excellence (NICE), which summarized how missing data is handled across their pipelines. A total of 23 CPMs were included through “sampling strategy.” Six missing data strategies were identified: complete case analysis (CCA), multiple imputation, imputation of mean values, k-nearest neighbours imputation, using an additional category for missingness, considering missing values as risk-factor-absent. 52% of the development articles and 48% of the validation articles did not report how missing data were handled. CCA was the most common approach used for development (40%) and validation (44%). At implementation, 57% of the CPMs required complete data entry, whilst 43% allowed missing values. Three CPMs had consistent paths in their pipelines. A broad variety of methods for handling missing data underly the CPMs currently recommended for use in UK healthcare. Missing data handling strategies were generally inconsistent. Better quality assurance of CPMs needs greater clarity and consistency in handling of missing data.