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.
Fractional imputation (FI) is a relatively new method of imputation for handling item nonresponse in survey sampling. In FI, several imputed values with their fractional weights are created for each missing item. Each fractional weight represents the conditional probability of the imputed value given the observed data, and the parameters in the conditional probabilities are often computed by an iterative method such as EM algorithm. The underlying model for FI can be fully parametric, semiparametric, or nonparametric, depending on plausibility of assumptions and the data structure. In this pap…
Reference based multiple imputation methods have become popular for handling missing data in randomised clinical trials. Rubin's variance estimator is well known to be biased compared to the reference based imputation estimator's true repeated sampling variance. Somewhat surprisingly given the increasingly popularity of these methods, there has been relatively little debate in the literature as to whether Rubin's variance estimator or alternative (smaller) variance estimators targeting the repeated sampling variance are more appropriate. We review the arguments made on both sides of this debat…
This chapter addresses important steps during the quality assurance and control of RWD, with particular emphasis on the identification and handling of missing values. A gentle introduction is provided on common statistical and machine learning methods for imputation. We discuss the main strengths and weaknesses of each method, and compare their performance in a literature review. We motivate why the imputation of RWD may require additional efforts to avoid bias, and highlight recent advances that account for informative missingness and repeated observations. Finally, we introduce alternative m…
We investigate the problem of calibration and assessment of predictive rules in prognostic designs when missing values are present in the predictors. Our paper has two key objectives which are entwined. The first is to investigate how the calibration of the prediction rule can be combined with the use of multiple imputation to account for missing predictor observations. The second objective is to propose such methods that can be implemented with current multiple imputation software, while allowing for unbiased predictive assessment through validation on new observations for which outcome is no…
Imputing missing values is an important preprocessing step in data analysis, but the literature offers little guidance on how to choose between different imputation models. This letter suggests adopting the imputation model that generates a density of imputed values most similar to those of the observed values for an incomplete variable after balancing all other covariates. We recommend stable balancing weights as a practical approach to balance covariates whose distribution is expected to differ if the values are not missing completely at random. After balancing, discrepancy statistics can be…
Many modern estimators require bootstrapping to calculate confidence intervals because either no analytic standard error is available or the distribution of the parameter of interest is non-symmetric. It remains however unclear how to obtain valid bootstrap inference when dealing with multiple imputation to address missing data. We present four methods which are intuitively appealing, easy to implement, and combine bootstrap estimation with multiple imputation. We show that three of the four approaches yield valid inference, but that the performance of the methods varies with respect to the nu…
Robust variance estimation for multiple imputation using predictive mean matching or parametric imputation models
University of Washington（华盛顿大学）；University of Florida（佛罗里达大学）；Wake Forest University（维克森林大学）；Kaiser Permanente Washington Health Research Institute（凯撒永久华盛顿健康研究所）；Fred Hutchinson Cancer Center（弗雷德·哈钦森癌症中心）
Multiple imputation (MI) is a popular method for handling missing data. Auxiliary variables can be added to the imputation model(s) to improve MI estimates. However, the choice of which auxiliary variables to include in the imputation model is not always straightforward. Including too few may lead to important information being discarded, but including too many can cause problems with convergence of the estimation procedures for imputation models. Several data-driven auxiliary variable selection strategies have been proposed. This paper uses a simulation study and a case study to provide a com…
Balancing the distributions of the confounders across the exposure levels in an observational study through matching or weighting is an accepted method to control for confounding due to these variables when estimating the association between an exposure and outcome and to reduce the degree of dependence on certain modeling assumptions. Despite the increasing popularity in practice, these procedures cannot be immediately applied to datasets with missing values. Multiple imputation of the missing data is a popular approach to account for missing values while preserving the number of units in the…
\Multiple imputation (MI) is a popular and well-established method for handling missing data in multivariate data sets, but its practicality for use in massive and complex data sets has been questioned. One such data set is the Panel Study of Income Dynamics (PSID), a longstanding and extensive survey of household income and wealth in the U.S. Missing data for this survey are currently handled using traditional hot deck methods because of the simple implementation; however, the univariate hot deck results in large random wealth fluctuations. MI is effective but faced with operational challenge…
Using directed acyclic graphs to determine whether multiple imputation or subsample multiple imputation estimates of an exposure-outcome association are unbiased
Although prospective logistic regression is the standard method of analysis for case-control data, it has been recently noted that in genetic epidemiologic studies one can use the ``retrospective'' likelihood to gain major power by incorporating various population genetics model assumptions such as Hardy-Weinberg-Equilibrium (HWE), gene-gene and gene-environment independence. In this article we review these modern methods and contrast them with the more classical approaches through two types of applications (i) association tests for typed and untyped single nucleotide polymorphisms (SNPs) and …
Standard approaches for variable selection in linear models are not tailored to deal properly with high-dimensional and incomplete data. Currently, methods dedicated to high-dimensional data handle missing values by ad-hoc strategies, like complete case analysis or single imputation, while methods dedicated to missing values, mainly based on multiple imputation, do not discuss the imputation method to use with high-dimensional data. Consequently, both approaches appear to be limited for many modern applications. With inspiration from ensemble methods, a new variable selection method is propose…
Multiple imputation provides us with efficient estimators in model-based methods for handling missing data under the true model. It is also well-understood that design-based estimators are robust methods that do not require accurately modeling the missing data; however, they can be inefficient. In any applied setting, it is difficult to know whether a missing data model may be good enough to win the bias-efficiency trade-off. Raking of weights is one approach that relies on constructing an auxiliary variable from data observed on the full cohort, which is then used to adjust the weights for th…
Large-sample properties of multiple imputation estimators for parameters of logistic regression with covariates missing at random separately or simultaneously
研究两组分类协变量分别或同时 MAR 时 logistic 回归 MI 估计量的渐近性质，提出修正方差估计，并通过模拟和逢甲夜市调查数据验证其优势。
The National Health and Nutrition Examination Survey (NHANES) studies the nutritional and health status over the whole U.S. population with comprehensive physical examinations and questionnaires. However, survey data analyses become challenging due to inevitable missingness in almost all variables. In this paper, we develop a new imputation method to deal with multivariate missingness at random using matrix completion. In contrast to existing imputation schemes either conducting row-wise or column-wise imputation, we treat the data matrix as a whole which allows exploiting both row and column …
Validation studies are often used to obtain more reliable information in settings with error-prone data. Validated data on a subsample of subjects can be used together with error-prone data on all subjects to improve estimation. In practice, more than one round of data validation may be required, and direct application of standard approaches for combining validation data into analyses may lead to inefficient estimators since the information available from intermediate validation steps is only partially considered or even completely ignored. In this paper, we present two novel extensions of mul…
Finite population inference is a central goal in survey sampling. Probability sampling is the main statistical approach to finite population inference. Challenges arise due to high cost and increasing non-response rates. Data integration provides a timely solution by leveraging multiple data sources to provide more robust and efficient inference than using any single data source alone. The technique for data integration varies depending on types of samples and available information to be combined. This article provides a systematic review of data integration techniques for combining probabilit…
The propensity score is a common tool for estimating the causal effect of a binary treatment in observational data. In this setting, matching, subclassification, imputation, or inverse probability weighting on the propensity score can reduce the initial covariate bias between the treatment and control groups. With more than two treatment options, however, estimation of causal effects requires additional assumptions and techniques, the implementations of which have varied across disciplines. This paper reviews current methods, and it identifies and contrasts the treatment effects that each one …
Adjusting for Outcome Reporting Bias in Meta-analysis: A Multiple Imputation Approach
Epidemiology, Biostatistics and Prevention Institute (EBPI)（流行病学、生物统计学与预防研究所）；Center for Reproducible Science and Research Synthesis (CRS)（可重复科学与研究综合中心）；University of Zurich (UZH)（苏黎世大学）
It is argued that the Calibrated Bayesian (CB) approach to statistical inference capitalizes on the strength of Bayesian and frequentist approaches to statistical inference. In the CB approach, inferences under a particular model are Bayesian, but frequentist methods are useful for model development and model checking. In this article the CB approach is outlined. Bayesian methods for missing data are then reviewed from a CB perspective. The basic theory of the Bayesian approach, and the closely related technique of multiple imputation, is described. Then applications of the Bayesian approach t…
The missing data issue is ubiquitous in health studies. Variable selection in the presence of both missing covariates and outcomes is an important statistical research topic but has been less studied. Existing literature focuses on parametric regression techniques that provide direct parameter estimates of the regression model. Flexible nonparametric machine learning methods considerably mitigate the reliance on the parametric assumptions, but do not provide as naturally defined variable importance measure as the covariate effect native to parametric models. We investigate a general variable s…
Multiple imputation (MI) inference handles missing data by imputing the missing values $m$ times, and then combining the results from the $m$ complete-data analyses. However, the existing method for combining likelihood ratio tests (LRTs) has multiple defects: (i) the combined test statistic can be negative, but its null distribution is approximated by an $F$-distribution; (ii) it is not invariant to re-parametrization; (iii) it fails to ensure monotonic power owing to its use of an inconsistent estimator of the fraction of missing information (FMI) under the alternative hypothesis; and (iv) i…
Panel studies typically suffer from attrition, which reduces sample size and can result in biased inferences. It is impossible to know whether or not the attrition causes bias from the observed panel data alone. Refreshment samples - new, randomly sampled respondents given the questionnaire at the same time as a subsequent wave of the panel - offer information that can be used to diagnose and adjust for bias due to attrition. We review and bolster the case for the use of refreshment samples in panel studies. We include examples of both a fully Bayesian approach for analyzing the concatenated p…
Robust clustering from incomplete data is an important topic because, in many practical situations, real data sets are heavy-tailed, asymmetric, and/or have arbitrary patterns of missing observations. Flexible methods and algorithms for model-based clustering are presented via mixture of the generalized hyperbolic distributions and its limiting case, the mixture of multivariate skew-t distributions. An analytically feasible EM algorithm is formulated for parameter estimation and imputation of missing values for mixture models employing missing at random mechanisms. The proposed methodologies a…
Ulster University（阿尔斯特大学）；National University of Ireland Galway（爱尔兰国立大学戈尔韦分校）；Altnagelvin Area Hospital（阿尔特纳格尔文地区医院）；Western Health and Social Care Trust（西部健康与社会保健信托）
Data imputation is the most popular method of dealing with missing values, but in most real life applications, large missing data can occur and it is difficult or impossible to evaluate whether data has been imputed accurately (lack of ground truth). This paper addresses these issues by proposing an effective and simple principal component based method for determining whether individual data features can be accurately imputed - feature imputability. In particular, we establish a strong linear relationship between principal component loadings and feature imputability, even in the presence of ex…
Handling Missingness and Censoring in Dirichlet Models
University of Pretoria（比勒陀利亚大学）；National Institute for Theoretical and Computational Sciences (NITheCS)（国家理论与计算科学研究所）；San José State University（圣何塞州立大学）；University of Catania（卡塔尼亚大学）
Prior work has shown that combining bootstrap imputation with tree-based machine learning variable selection methods can provide good performances achievable on fully observed data when covariate and outcome data are missing at random (MAR). This approach however is computationally expensive, especially on large-scale datasets. We propose an inference-based method, called RR-BART, which leverages the likelihood-based Bayesian machine learning technique, Bayesian additive regression trees, and uses Rubin's rule to combine the estimates and variances of the variable importance measures on multip…
A key aspect of the design of evolutionary and swarm intelligence algorithms is studying their performance. Statistical comparisons are also a crucial part which allows for reliable conclusions to be drawn. In the present paper we gather and examine the approaches taken from different perspectives to summarise the assumptions made by these statistical tests, the conclusions reached and the steps followed to perform them correctly. In this paper, we conduct a survey on the current trends of the proposals of statistical analyses for the comparison of algorithms of computational intelligence and …
Marginal structural models (MSMs) are commonly used to estimate causal intervention effects in longitudinal non-randomised studies. A common issue when analysing data from observational studies is the presence of incomplete confounder data, which might lead to bias in the intervention effect estimates if they are not handled properly in the statistical analysis. However, there is currently no recommendation on how to address missing data on covariates in MSMs under a variety of missingness mechanisms encountered in practice. We reviewed existing methods to handling missing data in MSMs and per…
