Imputation Estimation Research Articles

Multiple imputation to deal with missing objectively-measured physical activity data: findings from two cohorts

The objective of this article was to describe patterns of losses of information regarding accelerometer data and to assess the use of multiple imputation to generate physical activity estimates for individuals without accelerometry data. Two birth cohort studies from Pelotas (Brazil) with participants aged 22 and 11-years old assessed objectively measured physical activity differences between complete and imputed cases. Mean values of overall physical activity for complete cases (n1993 = 2,985 and n2004 = 3,348) and for complete cases plus imputed cases (n1993 = 760 and n2004 = 79) were described according to predictors. Male individuals, participants with black skin color, and less schooled individuals presented higher averages of overall physical activity than their counterparts. Almost all imputed estimates were comparable to the complete cases, and the highest difference found was 0.7 mg for the first quintile of socioeconomic status of the 1993 birth cohort. Multiple imputation is a positive technique to deal with missing data from objectively measured physical activity. It provides a set of relevant variables to be used in order to efficiently predict accelerometer data.

Regression-type Imputation Class of Estimators using Auxiliary Attributes

Several imputation schemes and estimators have been proposed by different authors in sample survey. However, these estimators utilized quantitative information of auxiliary characters. In this study, some imputation methods were studied using qualitative information of auxiliary characters and two new imputation schemes using auxiliary attribute have been suggested. The mean squared errors of the proposed estimators were derived up to first order approximation using Taylor series approach. Numerical illustrations with two populations were conducted and the results revealed that the proposed estimator is more efficient.

Combining Non-Probability and Probability Survey Samples Through Mass Imputation

Abstract Analysis of non-probability survey samples requires auxiliary information at the population level. Such information may also be obtained from an existing probability survey sample from the same finite population. Mass imputation has been used in practice for combining non-probability and probability survey samples and making inferences on the parameters of interest using the information collected only in the non-probability sample for the study variables. Under the assumption that the conditional mean function from the non-probability sample can be transported to the probability sample, we establish the consistency of the mass imputation estimator and derive its asymptotic variance formula. Variance estimators are developed using either linearization or bootstrap. Finite sample performances of the mass imputation estimator are investigated through simulation studies. We also address important practical issues of the method through the analysis of a real-world non-probability survey sample collected by the Pew Research Centre.

The diversification of termites: Inferences from a complete species‐level phylogeny

AbstractTermites play a major role in a variety of ecological processes in tropical and subtropical biomes worldwide, such as decomposition, soil formation and aeration, and nutrient cycling. These important ecosystem services were achieved through their highly complex societies and remarkable adaptations, including the evolution of reproductive division of labour, the acquisition of endosymbionts and the capacity for extensive environmental engineering, yet the causes and consequences of their ecological success are still poorly understood. The goals of our study were (a) to provide the first complete, species‐level phylogeny of all currently recognized termite species by integrating the available genetic and taxonomic data, as well as methods of phylogenetic imputation and divergence time estimation; and (b) to explore variation in speciation rates among termite lineages. We provide the inferred relationships as a set of 1,000 pseudo‐posterior trees, which can be used in future comparative analyses. We demonstrate that speciation rates have been relatively constant throughout the history of termites, with two positive shifts in speciation rates: one at their origin of Euisoptera and the other concordant with evolution of Termitidae. On the other hand, there was no obvious trend towards deceleration in speciation rates for termites as a whole, nor within the most species‐rich families. The provided trees might represent a valuable resource for termite comparative studies by summarizing the available phylogenetic information, while accounting for uncertainty in the inferred topologies.

PCN247 Association between Health-Related Quality of Life and Productivity Loss Among Working-Age Women with Breast Cancer in the United States

Breast cancer (BC) is the second most common cancer among women in the United States (US), with a considerable economic burden in terms of direct medical cost and lost productivity. Little is known about the relationship of health-related quality of life (HRQoL) and productivity loss (PL) among women with BC. This study evaluated the PL associated with HRQoL in working-age women with BC in the US. This retrospective cross-sectional study analyzed data from 2012-2018 Medical Expenditure Panel Survey (MEPS) Household Component (HC) involving women diagnosed with BC. PL was calculated as a product of days missed from work and wage rate for employed individuals and as regression-based imputed estimates for unemployed individuals. The HRQoL was assessed using the Physical Component Summary (PCS) and Mental Component Summary (MCS) scores from the Short-Form 12 Health Survey Version 2 (SF12-v2). The generalized linear model (GLM) with gamma distribution and log link was employed to evaluate the association between HRQoL and PL, controlling for age, race/ethnicity, region, marital status, fluency in English language, education, number of priority conditions, and survey year. The study sample consisted of 734 women with BC, between 18-64 years of age, representing 1.21 million patients annually. The majority of these were aged 50 years or above (74%), non-Hispanic whites (73%), employed (70%), married (67%), fluent in English (84%), and without bachelor’s degree (59%). Mean PCS and MCS scores were 49 (SE=0.55) and 52 (SE=0.45), respectively. The average PL annually was $1,130 (SE=$104) for the study sample. The multivariable analysis demonstrated that a unit increase in the PCS score was associated with a 3.58% (beta coefficient: -0.04; 95% CI: -0.05 to -0.02, p-value<0.001) reduction in PL. Working-age women with BC experience substantial PL, and improvements in physical component scores can lead to reduced PL.

Machine learning pipeline for quantum state estimation with incomplete measurements

Two-qubit systems typically employ 36 projective measurements for high-fidelity tomographic estimation. The overcomplete nature of the 36 measurements suggests possible robustness of the estimation procedure to missing measurements. In this paper, we explore the resilience of machine-learning-based quantum state estimation techniques to missing measurements by creating a pipeline of stacked machine learning models for imputation, denoising, and state estimation. When applied to simulated noiseless and noisy projective measurement data for both pure and mixed states, we demonstrate quantum state estimation from partial measurement results that outperforms previously developed machine-learning-based methods in reconstruction fidelity and several conventional methods in terms of resource scaling. Notably, our developed model does not require training a separate model for each missing measurement, making it potentially applicable to quantum state estimation of large quantum systems where preprocessing is computationally infeasible due to the exponential scaling of quantum system dimension.

Statistical Evaluation of Item Nonresponse Methods Using the World Bank’s 2015 Philippines Enterprise Survey

The main objective of the study was to evaluate item nonresponse procedures through a simulation study of different nonresponse levels or missing rates. A simulation study was used to explore how each of the response rates performs under a variety of circumstances. It also investigated the performance of procedures suggested for item nonresponse under various conditions and variable trends. The imputation methods considered were the cell mean imputation, random hotdeck, nearest neighbor, and simple regression. These variables are some of the major indicators for measuring productive labor and decent work in the country. For the purpose of this study, the researcher is interested in evaluating methods for imputing missing data for the number of workers and total cost of labor per establishment from the World Bank’s 2015 Enterprise Survey for the Philippines.&#x0D; The performances of the imputation techniques for item nonresponse were evaluated in terms of bias and coefficient of variation for accuracy and precision. Based on the results, the cell-mean imputation was seen to be most appropriate for imputing missing values for the total number of workers and total cost of labor per establishment. Since the study was limited to the variables cited, it is recommended to explore other labor indicators. Moreover, exploring choice of other clustering groups is highly recommended as clustering groups have great effect in the resulting estimates of imputation estimation. It is also recommended to explore other imputation techniques like multiple regression and other parametric models for nonresponse such as the Bayes estimation method. For regression based imputation, since the study is limited only in using the cluster groupings estimation, it is highly recommended to use other possible variables that might be related to the variable of interest to verify the results of this study.

Selecting the model for multiple imputation of missing data: Just use an IC!

Multiple imputation and maximum likelihood estimation (via the expectation‐maximization algorithm) are two well‐known methods readily used for analyzing data with missing values. While these two methods are often considered as being distinct from one another, multiple imputation (when using improper imputation) is actually equivalent to a stochastic expectation‐maximization approximation to the likelihood. In this article, we exploit this key result to show that familiar likelihood‐based approaches to model selection, such as Akaike's information criterion (AIC) and the Bayesian information criterion (BIC), can be used to choose the imputation model that best fits the observed data. Poor choice of imputation model is known to bias inference, and while sensitivity analysis has often been used to explore the implications of different imputation models, we show that the data can be used to choose an appropriate imputation model via conventional model selection tools. We show that BIC can be consistent for selecting the correct imputation model in the presence of missing data. We verify these results empirically through simulation studies, and demonstrate their practicality on two classical missing data examples. An interesting result we saw in simulations was that not only can parameter estimates be biased by misspecifying the imputation model, but also by overfitting the imputation model. This emphasizes the importance of using model selection not just to choose the appropriate type of imputation model, but also to decide on the appropriate level of imputation model complexity.

Integrated Square Error of Hazard Rate Estimation for Survival Data with Missing Censoring Indicators

The problem of hazard rate estimation under right-censored assumption has been investigated extensively. Integrated square error (ISE) of estimation is one of the most widely accepted measurements of the global performance for nonparametric kernel estimation. But there are no results available for ISE of hazard rate estimation under right-censored model with censoring indicators missing at random (MAR) so far. This paper constructs an imputation estimator of the hazard rate function and establish asymptotic normality of the ISE for the kernel hazard rate estimator with censoring indicators MAR. At the same time, an asymptotic representation of the mean integrated square error (MISE) is also presented. The finite sample behavior of the estimator is investigated via one simple simulation.

Validation likelihood estimation method for a zero-inflated Bernoulli regression model with missing covariates

A zero-inflated Bernoulli (ZIBer) regression model is an alternative model in order to improve fitting the binary outcome data that have many more zeros than expected under a regular logistic regression model. Because some covariates often have missing values, we propose the validation likelihood (VL) method to estimate the parameters of the ZIBer regression model with covariates missing at random. We consider the true selection probability (SP) model, a parametric SP model and a nonparametric SP model to compare the efficiency of the true SP, parametric SP, and semiparametric SP VL estimators. The asymptotic results of these three estimators are studied under some regularity conditions. Both the theoretical and simulation results reveal that the parametric and semiparametric SP VL estimation methods outperform the true SP VL estimation method if the parametric SP model is correct. The simulation results also indicate that the semiparametric SP VL estimation method is preferred to the inverse probability weighting and multiple imputation estimation methods. The practical application of the proposed methodology is adorned with a survey data set of violations of traffic rules of motorcyclist respondents in Taiwan.

Response Surface Analysis with Missing Data

Response Surface Analysis (RSA) is gaining popularity in psychological research as a tool for investigating congruence hypotheses (e.g., consequences of self-other agreement, person-job fit, dyadic similarity). RSA involves the estimation of a nonlinear polynomial regression model and the interpretation of the resulting response surface. However, little is known about how best to conduct RSA when the underlying data are incomplete. In this article, we compare different methods for handling missing data in RSA. This includes different strategies for multiple imputation (MI) and maximum-likelihood (ML) estimation. Specifically, we consider the “just another variable” (JAV) approach to MI and ML, an approach that is in regular use in applications of RSA, and the more novel “substantive-model-compatible” (SMC) approach. In a simulation study, we evaluate the impact of these methods on focal outcomes of RSA, including the accuracy of parameter estimates, the shape of the response surface, and the testing of congruence hypotheses. Our findings suggest that the JAV approach can sometimes distort parameter estimates and conclusions about the shape of the response surface, whereas the SMC approach performs well overall. We illustrate applications of the methods in a worked example with real data and provide recommendations for their application in practice.

Estimating Average Treatment Effects Utilizing Fractional Imputation when Confounders are Subject to Missingness

Abstract The problem of missingness in observational data is ubiquitous. When the confounders are missing at random, multiple imputation is commonly used; however, the method requires congeniality conditions for valid inferences, which may not be satisfied when estimating average causal treatment effects. Alternatively, fractional imputation, proposed by Kim 2011, has been implemented to handling missing values in regression context. In this article, we develop fractional imputation methods for estimating the average treatment effects with confounders missing at random. We show that the fractional imputation estimator of the average treatment effect is asymptotically normal, which permits a consistent variance estimate. Via simulation study, we compare fractional imputation’s accuracy and precision with that of multiple imputation.

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

BackgroundQuantitative 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.ResultsWe 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 nondetects.ConclusionsThe 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.

Imputation of missing data from time-lapse cameras used in recreational fishing surveys

Abstract While remote camera surveys have the potential to improve the accuracy of recreational fishing estimates, missing data are common and require robust analytical techniques to impute. Time-lapse cameras are being used in Western Australia to monitor recreational boating activities, but outages have occurred. Generalized linear mixed effect models formulated in a fully conditional specification multiple imputation framework were used to reconstruct missing data, with climatic and some temporal classifications as covariates. Using a complete 12-month camera record of hourly counts of recreational powerboat retrievals, data were simulated based on ten observed camera outage patterns, with a missing proportion of between 0.06 and 0.61. Nine models were evaluated, including Poisson and negative binomial models, and their associated zero-inflated variants. The imputed values were cross-validated against actual observations using percent bias, mean absolute error, root mean square error, and skill score as performance measures. In 90% of the cases, 95% confidence intervals for the total imputed estimates from at least one of the models contained the total actual counts. With no systematic trends in performance among the models, zero-inflated Poisson and its bootstrapping variant models consistently ranked among the top 3 models and possessed the narrowest confidence intervals. The robustness and generality of the imputation framework were demonstrated using other camera datasets with distinct characteristics. The results provide reliable estimates of the number of boat retrievals for subsequent estimates of fishing effort and provide time series data on boat-based activity.

Sufficient Dimension Reduction for Feasible and Robust Estimation of Average Causal Effect

When estimating the treatment effect in an observational study, we use a semiparametric locally efficient dimension reduction approach to assess both the treatment assignment mechanism and the average responses in both treated and non-treated groups. We then integrate all results through imputation, inverse probability weighting and double robust augmentation estimators. Double robust estimators are locally efficient while imputation estimators are super-efficient when the response models are correct. To take advantage of both procedures, we introduce a shrinkage estimator to automatically combine the two, which retains the double robustness property while improving on the variance when the response model is correct. We demonstrate the performance of these estimators through simulated experiments and a real dataset concerning the effect of maternal smoking on baby birth weight.

Missing data imputation in multivariate t distribution with unknown degrees of freedom using expectation maximization algorithm and its stochastic variants

Many researchers encounter the missing data problem. The phenomenon may be occasioned by data omission, non-response, death of respondents, recording errors, among others. It is important to find an appropriate data imputation technique to fill in the missing positions. In this study, the Expectation Maximization (EM) algorithm and two of its stochastic variants, stochastic EM (SEM) and Monte Carlo EM (MCEM), are employed in missing data imputation and parameter estimation in multivariate t distribution with unknown degrees of freedom. The imputation efficiencies of the three methods are then compared using mean square error (MSE) criterion. SEM yields the lowest MSE, making it the most efficient method in data imputation when the data assumes the multivariate t distribution. The algorithm’s stochastic nature enables it to avoid local saddle points and achieve global maxima; ultimately increasing its efficiency. The EM and MCEM techniques yield almost similar results. Large sample draws in the MCEM’s E-step yield more or less the same results as the deterministic EM. In parameter estimation, it is observed that the parameter estimates for EM and MCEM are relatively close to the simulated data’s maximum likelihood (ML) estimates. This is not the case in SEM, owing to the random nature of the algorithm.

Parallel Fractional Hot-Deck Imputation and Variance Estimation for Big Incomplete Data Curing

The fractional hot-deck imputation (FHDI) is a general-purpose, assumption-free imputation method for handling multivariate missing data by filling each missing item with multiple observed values without resorting to artificially created values. The corresponding R package FHDI J. Im, I. Cho, and J. K. Kim, “An R package for fractional hot deck imputation,” <i>R J.</i> , vol. 10, no. 1, pp. 140–154, 2018 holds generality and efficiency, but it is not adequate for tackling big incomplete data due to the requirement of excessive memory and long running time. As a first step to tackle big incomplete data by leveraging the FHDI, we developed a new version of a parallel fractional hot-deck imputation (named as P-FHDI) program suitable for curing large incomplete datasets. Results show a favorable speedup when the P-FHDI is applied to big datasets with up to millions of instances or 10,000 of variables. This paper explains the detailed parallel algorithms of the P-FHDI for large instances (big- <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> ) or high-dimensionality (big- <inline-formula><tex-math notation="LaTeX">$p$</tex-math></inline-formula> ) datasets and confirms the favorable scalability. The proposed program inherits all the advantages of the serial FHDI and enables a parallel variance estimation, which will benefit a broad audience in science and engineering.

Handling Missing Data in the Short Form-12 Health Survey (SF-12): Concordance of Real Patient Data and Data Estimated by Missing Data Imputation Procedures.

If information on single items in the Short Form–12 health survey (SF-12) is missing, the analysis of only complete cases causes a loss of statistical power and, in case of nonrandom missing data (MD), systematic bias. This study aimed at evaluating the concordance of real patient data and data estimated by different MD imputation procedures in the items of the SF-12 assessment. For this ends, MD were examined in a sample of 1,137 orthopedic patients. Additionally, MD were simulated (a) in the subsample of orthopedic patients exhibiting no MD (n = 810; 71%) as well as (b) in a sample of 6,970 respondents representing the German general population (95.8% participants with complete data) using logistic regression modelling. Simulated MD were replaced by mean values as well as regression-, expectation-maximization- (EM-), and multiple imputation estimates. Higher age and lower education were associated with enhanced probabilities of MD. In terms of accuracy in both data sets, the EM-procedure (ICC2,1 = .33-.72) outperformed alternative estimation approaches substantially (e.g., regression imputation: ICC2,1 = .18-.48). The EM-algorithm can be recommended to estimate MD in the items of the SF-12, because it reproduces the actual patient data most accurately.

Uncertainty-Gated Stochastic Sequential Model for EHR Mortality Prediction.

Electronic health records (EHRs) are characterized as nonstationary, heterogeneous, noisy, and sparse data; therefore, it is challenging to learn the regularities or patterns inherent within them. In particular, sparseness caused mostly by many missing values has attracted the attention of researchers who have attempted to find a better use of all available samples for determining the solution of a primary target task through defining a secondary imputation problem. Methodologically, existing methods, either deterministic or stochastic, have applied different assumptions to impute missing values. However, once the missing values are imputed, most existing methods do not consider the fidelity or confidence of the imputed values in the modeling of downstream tasks. Undoubtedly, an erroneous or improper imputation of missing variables can cause difficulties in the modeling as well as a degraded performance. In this study, we present a novel variational recurrent network that: 1) estimates the distribution of missing variables (e.g., the mean and variance) allowing to represent uncertainty in the imputed values; 2) updates hidden states by explicitly applying fidelity based on a variance of the imputed values during a recurrence (i.e., uncertainty propagation over time); and 3) predicts the possibility of in-hospital mortality. It is noteworthy that our model can conduct these procedures in a single stream and learn all network parameters jointly in an end-to-end manner. We validated the effectiveness of our method using the public data sets of MIMIC-III and PhysioNet challenge 2012 by comparing with and outperforming other state-of-the-art methods for mortality prediction considered in our experiments. In addition, we identified the behavior of the model that well represented the uncertainties for the imputed estimates, which showed a high correlation between the uncertainties and mean absolute error (MAE) scores for imputation.

An Alternative Implementation of Reference-Based Controlled Imputation Procedures

Reference-based controlled imputations have become a popular tool to assess the sensitivity of primary analysis inference to different post-dropout assumptions and to yield an alternative effectiveness estimand of treatment effect. As the imputation and analysis models are uncongenial in this setting, Rubin’s variance estimator overestimates the repeated sampling variability of the multiple imputation estimator of treatment effect. On the other hand, since reference-based methods borrow information across arms, the sampling variance of treatment effect estimator decreases as the proportion of missing data increases, rendering it inappropriate for use in sensitivity analysis. We propose to decouple the variance estimation from information borrowing by using a delta-adjusted pattern mixture model with delta-adjustments fixed at the maximum likelihood estimate. Reference-based pattern-mixture models can thus be embedded in the sensitivity analysis using delta-adjusted pattern-mixture models by identifying a scalar sensitivity parameter value to match the treatment effect estimate. We provide both theoretical and empirical justifications of the proposed approach and illustrate its use in the analysis of a clinical trial of major depressive disorder.