Missing Mechanism Research Articles

Handling missing data when estimating causal effects with targeted maximum likelihood estimation.

Targeted maximum likelihood estimation (TMLE) is increasingly used for doubly robust causal inference, but how missing data should be handled when using TMLE with data-adaptive approaches is unclear. Based on data (1992-1998) from the Victorian Adolescent Health Cohort Study, we conducted a simulation study to evaluate 8 missing-data methods in this context: complete-case analysis, extended TMLE incorporating an outcome-missingness model, the missing covariate missing indicator method, and 5 multiple imputation (MI) approaches using parametric or machine-learning models. We considered 6 scenarios that varied in terms of exposure/outcome generation models (presence of confounder-confounder interactions) and missingness mechanisms (whether outcome influenced missingness in other variables and presence of interaction/nonlinear terms in missingness models). Complete-case analysis and extended TMLE had small biases when outcome did not influence missingness in other variables. Parametric MI without interactions had large bias when exposure/outcome generation models included interactions. Parametric MI including interactions performed best in bias and variance reduction across all settings, except when missingness models included a nonlinear term. When choosing a method for handling missing data in the context of TMLE, researchers must consider the missingness mechanism and, for MI, compatibility with the analysis method. In many settings, a parametric MI approach that incorporates interactions and nonlinearities is expected to perform well.

Missing Data Analysis.

Methods for handling missing data in clinical psychology studies are reviewed. Missing data are defined, and a taxonomy of main approaches to analysis is presented, including complete-case and available-case analysis, weighting, maximum likelihood, Bayes, single and multiple imputation, and augmented inverse probability weighting. Missingness mechanisms, which play a key role in the performance of alternative methods, are defined. Approaches to robust inference, and to inference when the mechanism is potentially missing not at random, are discussed.

Global photosynthetic capacity jointly determined by enzyme kinetics and eco-evo-environmental drivers

Accurate understanding of global photosynthetic capacity (i.e. maximum RuBisCO carboxylation rate, Vc, max) variability is critical for improved simulations of terrestrial ecosystem photosynthesis metabolisms and carbon cycles with climate change, but a holistic understanding and assessment remains lacking. Here we hypothesized that Vc, max was dictated by both factors of temperature-associated enzyme kinetics (capturing instantaneous ecophysiological responses) and the amount of activated RuBisCO (indexed by Vc, max standardized at 25 ℃, Vc, max25), and compiled a comprehensive global dataset (n = 7339 observations from 428 sites) for hypothesis testing. The photosynthesis data were derived from leaf gas exchange measurements using portable gas exchange systems. We found that a semi-empirical statistical model considering both factors explained 78% of global Vc, max variability, followed by 55% explained by enzyme kinetics alone. This statistical model outperformed the current theoretical optimality model for predicting global Vc, max variability (67%), primarily due to its poor characterization on global Vc, max25 variability (3%). Further, we demonstrated that, in addition to climatic variables, belowground resource constraint on photosynthetic machinery built-up that directly structures the biogeography of Vc, max25 was a key missing mechanism for improving the theoretical modelling of global Vc, max variability. These findings improve the mechanistic understanding of global Vc, max variability and provide an important basis to benchmark process-based models of terrestrial photosynthesis and carbon cycling under climate change.

Compatibility in Missing Data Handling Across the Prediction Model Pipeline: A Simulation Study.

Careful handling of missing data is crucial to ensure that clinical prediction models are developed, validated, and implemented in a robust manner. We determined the bias in estimating predictive performance of different combinations of approaches for handling missing data across validation and implementation. We found four strategies that are compatible across the model pipeline and have provided recommendations for handling missing data between model validation and implementation under different missingness mechanisms.

Quantifying bias due to missing data in quality of life surveys of advanced-stage cancer patients.

Many studies on cancer patients investigate the impact of treatment on health-related quality of life (QoL). Typically, QoL is measured longitudinally, at baseline and at predefined timepoints thereafter. The question is whether, at a given timepoint, patients who return their questionnaire (available cases, AC) have a different QoL than those who do not return their questionnaire (non-AC). We employed augmented inverse probability weighting (AIPW) to estimate the average QoL of non-AC in two studies on advanced-stage cancer patients. The AIPW estimator assumed data to be missing at random (MAR) and used machine learning (ML)-based methods to estimate answering probabilities of individuals at given timepoints as well as their reported QoL, as a function of auxiliary variables. These auxiliary variables were selected by medical oncologists based on domain expertise. We aggregated results both by timepoint and by time until death and compared AIPW estimates to the AC averages. Additionally, we used a pattern mixture model (PMM) to check sensitivity of our AIPW estimates against violation of the MAR assumption. Our study included 1927 patients with advanced pancreatic and 797 patients with advanced breast cancer. The AIPW estimate for average QoL of non-AC was below the average QoL of AC when aggregated by timepoint. The difference vanished when aggregated by time until death. PMM estimates were below AIPW estimates. Our results indicate that non-AC have a lower average QoL than AC. However, estimates for QoL of non-AC are subject to unverifiable assumptions about the missingness mechanism.

A Model-Based Approach to the Disentanglement and Differential Treatment of Engaged and Disengaged Item Omissions

Item omissions in large-scale assessments may occur for various reasons, ranging from disengagement to not being capable of solving the item and giving up. Current response-time-based classification approaches allow researchers to implement different treatments of item omissions presumably going back to different mechanisms. These approaches, however, are limited in that they require a clear-cut decision on the underlying missingness mechanism and do not allow to take the uncertainty in classification into account. We present a response-time-based model-based mixture modeling approach that overcomes this limitation. The approach (a) facilitates disentangling item omissions stemming from disengagement from those going back to solution behavior, (b) considers the uncertainty in omission classification, (c) allows for omission mechanisms to vary on the item-by-examinee level, (d) supports investigating person and item characteristics associated with different types of omission behavior, and (e) gives researchers flexibility in deciding on how to handle different types of omissions. The approach exhibits good parameter recovery under realistic research conditions. We illustrate the approach on data from the Programme for the International Assessment of Adult Competencies 2012 and compare it against previous classification approaches for item omissions.

Missing data: Issues, concepts, methods

Missing data are a common issue in medical research. We aim to explain in non-technical language the issues and concepts around missing data, as well as discuss common methods for handling missing data. Specifically, our objectives are to answer the following questions: (1) What are missing data and why should we care about them? (2) What are the missingness mechanisms and how do they impact statistical analysis? (3) How can we explore missing values in our datasets? (4) What are ad-hoc methods for dealing with missing values and are they valid? (5) What is multiple imputation? (6) What should we consider when conducting a multiple imputation analysis? (7) Is multiple imputation always needed? (8) How should we report an analysis with missing data? We illustrate discussions with examples from an orthodontic study.

A Novel Truncated Normal Tensor Completion Method for Multi-Source Fusion Data

Completing traffic data is a basic requirement for intelligent transportation systems. However, completing spatiotemporal traffic data poses a significant challenge, especially for high-dimensional data with complex missing mechanisms. Various completion methods targeting different missing mechanisms have showcased the superiority of tensor learning by effectively characterizing intricate spatiotemporal correlations. In this study, a novel tensor completion framework, known as the multi-source tensor completion method for data fusion, is proposed. This framework incorporates passenger transfer relationships between buses and subways into subway data completion, enhancing the data completion accuracy. Moreover, by combining bus transfer passenger flow data with other data dimensions, such as the different road sections, time intervals, and days, an innovative 4D low-rank tensor completion data framework was obtained. In addition, to boost the completion accuracy, a truncated l2,p norm optimization model was derived. This model enhances the non-convex performance of the objective function throughout the tensor completion process. The results highlight the superiority of the proposed completion method, leveraging fused subway/bus data over other completion methods that rely solely on subway data.

Analysis of Incomplete Data Under Different Missingness Mechanism using Imputation Methods for Wheat Genotypes

Missing values is a persistent problem in analysis of agriculture data. To improve the quality of the data in the agriculture study, imputation has drawn a lot of research interest. Non-missing data was removed with varying frequency from the genotypic data of the wheat crop by different missingness mechanism. Imputation methods namely last observation carried forward, mean, regression and KNN are applied to these data sets and compared their parameter with the parameter of original data. The performances of imputation methods are also evaluated by root mean square error for solving missing values at different missingness mechanism.

Smdi: an R package to perform structural missing data investigations on partially observed confounders in real-world evidence studies.

Partially observed confounder data pose a major challenge in statistical analyses aimed to inform causal inference using electronic health records (EHRs). While analytic approaches such as imputation are available, assumptions on underlying missingness patterns and mechanisms must be verified. We aimed to develop a toolkit to streamline missing data diagnostics to guide choice of analytic approaches based on meeting necessary assumptions. We developed the smdi (structural missing data investigations) R package based on results of a previous simulation study which considered structural assumptions of common missing data mechanisms in EHR. smdi enables users to run principled missing data investigations on partially observed confounders and implement functions to visualize, describe, and infer potential missingness patterns and mechanisms based on observed data. The smdi R package is freely available on CRAN and can provide valuable insights into underlying missingness patterns and mechanisms and thereby help improve the robustness of real-world evidence studies.

Studying the dynamics of the drug processing of pyrazinamide in Mycobacterium tuberculosis.

Pyrazinamide (PZA) is a key drug in the treatment of Mycobacterium tuberculosis. Although not completely understood yet, the bactericidal mechanism of PZA starts with its diffusion into the cell and subsequent conversion into pyrazinoic acid (POA) after the hydrolysis of ammonia group. This leads to the acidification cycle, which involves: (1) POA extrusion into the extracellular environment, (2) reentry of protonated POA, and (3) release of a proton into the cytoplasm, resulting in acidification of the cytoplasm and accumulation of intracellular POA. To better understand this process, we developed a system of coupled non-linear differential equations, which successfully recapitulates the kinetics of PZA/POA observed in M. tuberculosis. The parametric space was explored, assessing the impact of different PZA and pH concentrations and variations in the kinetic parameters, finding scenarios of PZA susceptibility and resistance. Furthermore, our predictions show that the acidification cycle alone is not enough to result in significant intracellular accumulation of POA in experimental time scales when compared to other neutral pH scenarios. Thus, revealing the need of novel hypotheses and experimental evidence to determine the missing mechanisms that may explain the pH-dependent intracellular accumulation of POA and their subsequent effects.

Oracle-efficient estimation for the mean function of missing covariate data based on noparametrically estimated selection probabilities

A weighted local linear estimator for the mean function is constructed based on nonparametrically estimated selection probabilities when covariates are missing at random. The weighted estimator is shown to be oracle-efficient, meaning it is uniformly as efficient as the infeasible estimator that uses the true selection probabilities assumed to be known as a prior. By applying oracle efficiency and the extreme value distribution of the weighted local linear estimator, asymptotically accurate simultaneous confidence bands for the mean function are derived. This approach avoids the risk of model misspecification for the missingness mechanism. Simulation studies are conducted to examine the finite sample performance, which supports the asymptotic results. The proposed methods are illustrated through the analysis of two real data sets.

Dealing with missing observations in the outcome and covariates in randomized controlled trials

This article compares different missing data methods in randomized controlled trials, specifically addressing cases involving joint missingness in the outcome and covariates. In the existing literature, it is still unclear how advanced methods like linear mixed model (LMM) and multiple imputation (MI) perform in comparison to simpler methods regarding the estimation of treatment effects and their standard errors. We therefore evaluates the performance of LMM and MI against simple alternatives across a wide range of simulation scenarios for various realistic missingness mechanisms. The results show that no single method universally outperforms the others. However, LMM followed by MI demonstrates superior performance across most missingness scenarios. Interestingly, a simple method that combines complete case analysis for the missing outcome and mean imputation for the missing covariate (CCAME) performs similarly to LMM and MI. All methods are furthermore compared in the context of a randomized controlled trial on chronic obstructive pulmonary disease.

Bayesian second-order sensitivity of longitudinal inferences to non-ignorability: an application to antidepressant clinical trial data.

Incomplete data is a prevalent complication in longitudinal studies due to individuals' drop-out before intended completion time. Currently available methods via commercial software for analyzing incomplete longitudinal data at best rely on the ignorability of the drop-outs. If the underlying missing mechanism was non-ignorable, potential bias arises in the statistical inferences. To remove the bias when the drop-out is non-ignorable, joint complete-data and drop-out models have been proposed which involve computational difficulties and untestable assumptions. Since the critical ignorability assumption is unverifiable based on the observed part of the sample, some local sensitivity indices have been proposed in the literature. Specifically, Eftekhari Mahabadi (Second-order local sensitivity to non-ignorability in Bayesian inferences. Stat Med 2018;59:55-95) proposed a second-order local sensitivity tool for Bayesian analysis of cross-sectional studies and show its better performance for handling bias compared with the first-order ones. In this paper, we aim to extend this index for the Bayesian sensitivity analysis of normal longitudinal studies with drop-outs. The index is driven based on a selection model for the drop-out mechanism and a Bayesian linear mixed-effect complete-data model. The presented formulas are calculated using the posterior estimation and draws from the simpler ignorable model. The method is illustrated via some simulation studies and sensitivity analysis of a real antidepressant clinical trial data. Overall, the numerical analysis showed that when repeated outcomes are subject to missingness, regression coefficient estimates are nearly approximated well by a linear function in the neighbourhood of MAR model, but there are a considerable amount of second-order sensitivity for the error term and random effect variances in Bayesian linear mixed-effect model framework.

Mallows model averaging based on kernel regression imputation with responses missing at random

Missing data is a common problem in real data analysis. In this paper, a Mallows model averaging method based on kernel regression imputation is proposed for the linear regression models with responses missing at random. We prove that our method asymptotically achieves the lowest possible squared error. Compared with the existing model averaging methods, the new method does not require the use of a parameter model to characterize the missing generation mechanism. The Monte Carlo simulation and a practical application demonstrate the usefulness of the proposed method.

A modified Nadaraya–Watson procedure for variable selection and nonparametric prediction with missing data

We propose a new method for variable selection and prediction under a nonparametric regression setting, where a covariate may be missing either because its value is hidden from the observer or because it is inapplicable to the particular subject being observed. Despite its practical relevance, the problem has received little attention in the literature and its solutions are largely non-existent. Our proposal hinges on the construction of a modified Nadaraya–Watson estimator of the conditional mean regression function, with its bandwidths regularised to select variables and its weights adapted to accommodate different types of missingness. The method allows for information sharing across different missing data patterns without affecting consistency of the estimator. Unlike other conventional methods such as those based on imputations or likelihoods, our method requires only mild assumptions on the model and the missingness mechanism. For prediction we focus on finding relevant variables for predicting mean responses, conditional on covariate vectors subject to a given type of missingness. Our theoretical and numerical results show that the new method is consistent in variable selection and yields better prediction accuracy compared to existing methods.

Imputation of missing values in residential building monitored data: Energy consumption, behavior, and environment information

This study compares missing value handling algorithms based on the type of missing value occurrence for building monitored data. The study data comprised energy consumption and occupancy data for residential buildings and indoor and outdoor environmental information. The missing mechanism was assumed to be missing completely at random (MCAR), with random missing data generated by assuming missing rates of 10–50 % to simulate various missing scenarios. The missing value handling algorithms applied statistical imputation methods and data-driven approaches. The normalized root mean squared error was calculated to verify the imputation and measurement error. The results showed that the appropriate missing value handling algorithm depends on the building energy monitoring data items and type of missingness. For both temporal resolutions, the results show that the data-driven model performs well in estimating missing values for energy consumption data by use, while the linear interpolation imputation method performs well for environmental and occupancy information. These results demonstrate the effectiveness of considering the characteristics of data items and the type of missing values when dealing with missing values and implys that previously underutilized data-driven models could be valuable imputation algorithms.

A Machine Learning-Based Multiple Imputation Method for the Health and Aging Brain Study–Health Disparities

The Health and Aging Brain Study–Health Disparities (HABS–HD) project seeks to understand the biological, social, and environmental factors that impact brain aging among diverse communities. A common issue for HABS–HD is missing data. It is impossible to achieve accurate machine learning (ML) if data contain missing values. Therefore, developing a new imputation methodology has become an urgent task for HABS–HD. The three missing data assumptions, (1) missing completely at random (MCAR), (2) missing at random (MAR), and (3) missing not at random (MNAR), necessitate distinct imputation approaches for each mechanism of missingness. Several popular imputation methods, including listwise deletion, min, mean, predictive mean matching (PMM), classification and regression trees (CART), and missForest, may result in biased outcomes and reduced statistical power when applied to downstream analyses such as testing hypotheses related to clinical variables or utilizing machine learning to predict AD or MCI. Moreover, these commonly used imputation techniques can produce unreliable estimates of missing values if they do not account for the missingness mechanisms or if there is an inconsistency between the imputation method and the missing data mechanism in HABS–HD. Therefore, we proposed a three-step workflow to handle missing data in HABS–HD: (1) missing data evaluation, (2) imputation, and (3) imputation evaluation. First, we explored the missingness in HABS–HD. Then, we developed a machine learning-based multiple imputation method (MLMI) for imputing missing values. We built four ML-based imputation models (support vector machine (SVM), random forest (RF), extreme gradient boosting (XGB), and lasso and elastic-net regularized generalized linear model (GLMNET)) and adapted the four ML-based models to multiple imputations using the simple averaging method. Lastly, we evaluated and compared MLMI with other common methods. Our results showed that the three-step workflow worked well for handling missing values in HABS–HD and the ML-based multiple imputation method outperformed other common methods in terms of prediction performance and change in distribution and correlation. The choice of missing handling methodology has a significant impact on the accompanying statistical analyses of HABS–HD. The conceptual three-step workflow and the ML-based multiple imputation method perform well for our Alzheimer’s disease models. They can also be applied to other disease data analyses.

Deep Learning Methods for Omics Data Imputation.

One common problem in omics data analysis is missing values, which can arise due to various reasons, such as poor tissue quality and insufficient sample volumes. Instead of discarding missing values and related data, imputation approaches offer an alternative means of handling missing data. However, the imputation of missing omics data is a non-trivial task. Difficulties mainly come from high dimensionality, non-linear or non-monotonic relationships within features, technical variations introduced by sampling methods, sample heterogeneity, and the non-random missingness mechanism. Several advanced imputation methods, including deep learning-based methods, have been proposed to address these challenges. Due to its capability of modeling complex patterns and relationships in large and high-dimensional datasets, many researchers have adopted deep learning models to impute missing omics data. This review provides a comprehensive overview of the currently available deep learning-based methods for omics imputation from the perspective of deep generative model architectures such as autoencoder, variational autoencoder, generative adversarial networks, and Transformer, with an emphasis on multi-omics data imputation. In addition, this review also discusses the opportunities that deep learning brings and the challenges that it might face in this field.

Assessable and interpretable sensitivity analysis in the pattern graph framework for nonignorable missingness mechanisms.

The pattern graph framework solves a wide range of missing data problems with nonignorable mechanisms. However, it faces two challenges of assessability and interpretability, particularly important in safety-critical problems such as clinical diagnosis: (i) How can one assess the validity of the framework's apriori assumption and make necessary adjustments to accommodate known information about the problem? (ii) How can one interpret the process of exponential tilting used for sensitivity analysis in the pattern graph framework and choose the tilt perturbations based on meaningful real-world quantities? In this paper, we introduce Informed Sensitivity Analysis, an extension of the pattern graph framework that enables us to incorporate substantive knowledge about the missingness mechanism into the pattern graph framework. Our extension allows us to examine the validity of assumptions underlying pattern graphs and interpret sensitivity analysis results in terms of realistic problem characteristics. We apply our method to a prevalent nonignorable missing data scenario in clinical research. We validate and compare our method'sresults of our method with a number of widely-used missing data methods, including Unweighted CCA, KNN Imputer, MICE, and MissForest. The validation is done using both boot-strapped simulated experiments as well as real-world clinical observations in the MIMIC-III public dataset.