A review on missing values for main challenges and methods

ObjectivesTo describe how systematic reviewers are reporting missing data for dichotomous outcomes, handling them in the analysis and assessing the risk of associated bias.MethodsWe searched MEDLINE and the Cochrane Database...

Missing data are uncollected data but meaningful for the statistical analysis due to clinical relevancy of the data for properly specified estimands in clinical trials. Meanwhile the efforts to prevent or minimize missing data are commonly applied in clinical trials, in practice, missing data still occurs. Choosing a statistical method for imputation that deals with missing data targeting specified estimands provides the more reliable estimates of treatment effects. We considered longitudinal clinical settings that have different degrees of missing data and treatment effects, and simulated different missing mechanisms using data from randomized, double-blind, placebo-controlled phase 3 confirmatory clinical trials of approved drugs. We compared four commonly used statistical methods to deal with missing data in clinical trials. We find that, when the data are missing not at random (MNAR) with higher missing rates, mixed model for repeated measurements (MMRM) method overestimates treatment difference. Pattern-mixture model estimates were seen to be more conservative in our studies than MMRM given MNAR assumptions, which are more realistic with missing datain clinical trials. We emphasize the importance of prevention of missing data and specifying the estimand based on trial objectives beforehand. The specified proper estimand and the proper statistical method might be key features to value the clinical trial results despite missing data.

Background . Properly constructed decision support systems (DSS) for modelling and forecasting behaviour of dynamic systems provide a possibility for taking into consideration uncertainties of probabilistic, statistical and structural types what results in higher quality of developed models and estimated forecasts. Objective . To consider general reasons for loosing (missing) data in statistical data analysis; to provide categorization of missing data into several groups, and identify the reasons for missing measurements; to provide stepwise system methodology for uncertainty analysis and selection of data imputation techniques; to give an insight into some popular missing values imputation techniques regarding their possible applications. Methods . To solve the problems mentioned the following methods have been used: data categorization approach from business or practical point of view that is necessary for discovering the reasons for availability of systemic and/or random missing values; the modern systemic methodology was hired for analysis of uncertainty causes and missing values imputation; the decision tree based imputation procedures; EM algorithm and regression model approach to forecasting missing data using forecasting functions. Results . The main results of the study are in categorization of the missing data into groups; development of systemic methodology for analysis of uncertainty causes and missing values imputation; providing an analysis for possibilities of missing values imputation with decision trees, EM algorithm and regression models; development of multistep forecasting functions on the basis of autoregression models; illustration of application of some selected perspective methods for missing data imputation. Conclusions . We proposed the six steps system methodology for data imputation which stresses that selection of correct method for imputation is tightly connected with the step-by-step analysis of the gaps causes and finding an appropriate technique for their imputation. The results of imputation sometimes are rather far from the existing data and should be smoothed or even broken from the sample due to their incorrectness. For such cases it should be proposed a new probabilistic-regression method which allows define parameters of the probability interval for the regression aiming missing data imputation. A series of computing experiments performed with EM algorithm, forecast regression based imputation technique and some other approaches shows that it is possible to reach high quality results regarding correct processing of data with missing values.

Focus of presentation Missing data are ubiquitous in medical research. Although there is increasing guidance on how to handle missing data, practice is changing slowly and misapprehensions abound, particularly in observational research. We present a practical framework for handling and reporting the analysis of incomplete data in observational studies, which we illustrate using a case study from the Avon Longitudinal Study of Parents and Children. Findings The framework consists of three steps: 1) Develop an analysis plan specifying the analysis model and how missing data are going to be addressed. Important considerations are whether a complete records analysis is likely to be valid, whether multiple imputation or an alternative approach is likely to offer benefits, and whether a sensitivity analysis regarding the missingness mechanism is required. 2) Explore the data, checking the methods outlined in the analysis plan are appropriate, and conduct the pre-planned analysis. 3) Report the results, including a description of the missing data, details on how missing data were addressed, and the results from all analyses, interpreted in light of the missing data and clinical relevance. Conclusions/Implications This framework encourages researchers to think carefully about their missing data and be transparent about the potential effect on the study results. This will increase confidence in the reliability and reproducibility of results from published papers. Key messages Researchers need to develop a plan for missing data prior to conducting their analysis, and be transparent about how they handled the missing data and its potential effect when reporting their results.

Missing data are frequently encountered in various disciplines and can be divided into three categories: missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR). Valid statistical approaches to missing data depend crucially on correct identification of the underlying missingness mechanism. Although the problem of testing whether this mechanism is MCAR or MAR has been extensively studied, there has been very little research on testing MAR versus MNAR. A critical challenge that is faced when dealing with this problem is the issue of model identification under MNAR. In this paper, under a logistic model for the missing probability, we develop two score tests for the problem of whether the missingness mechanism is MAR or MNAR under a parametric model and a semiparametric location model on the regression function. The implementation of the score tests circumvents the identification issue as it requires only parameter estimation under the null MAR assumption. Our simulations and analysis of human immunodeficiency virus data show that the score tests have well-controlled type I errors and desirable powers.

We aimed to investigate the association between body mass index (BMI) at the time of intensive care unit (ICU) admission and 90-day mortality risk in complete-case datasets that ignore missing data as well as in datasets with multiple imputation for missing data. This retrospective study analysed the medical records of adult patients admitted to ICUs in a single tertiary academic hospital. For BMI analysis, data were classified into four groups: underweight (<20 kg/m2 ), normal (20-24.9 kg/m2 ), overweight (25-29.9 kg/m2 ), and obese (≥30 kg/m2 ). A total of 24,928 patients were examined. Among them, 5,916 (23.7%) patients had missing BMI data at ICU admission, and the missing mechanism was not missing completely at random. In the multivariable Cox regression analysis, the 90-day mortality risk of underweight patients in the complete-case group increased by 1.49 times compared with that of normal BMI patients with a hazard ratio (HR) of 1.49 (95% confidence interval: 1.34-1.66; P<0.001), whereas the 90-day mortality risk of underweight patients in the multiple imputation group increased by 1.36 times compared with that of normal BMI patients (HR: 1.36, 95% confidence interval: 1.24-1.49; P<0.001). We showed that the occurrence of missing BMI data at ICU admission could affect the prediction of 90-day mortality in critically ill patients. Particularly, missing BMI data had the potential to slightly overestimate the 90-day mortality of underweight patients. Therefore, multiple imputation for missing BMI data can be an appropriate statistical option to reduce bias.

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

Propensity score analysis is a popular method to control for confounding in observational studies. A challenge in propensity methods is missing values in confounders. Several strategies for handling missing values exist, but guidance in choosing the best method is needed. In this simulation study, we compared four strategies of handling missing covariate values in propensity matching and propensity weighting. These methods include: complete case analysis, missing indicator method, multiple imputation and combining multiple imputation and missing indicator method. Concurrently, we aimed to provide guidance in choosing the optimal strategy. Simulated scenarios varied regarding missing mechanism, presence of effect modification or unmeasured confounding. Additionally, we demonstrated how missingness graphs help clarifying the missing structure. When no effect modification existed, complete case analysis yielded valid causal treatment effects even when data were missing not at random. In some situations, complete case analysis was also able to partially correct for unmeasured confounding. Multiple imputation worked well if the data were missing (completely) at random, and if the imputation model was correctly specified. In the presence of effect modification, more complex imputation models than default options of commonly used statistical software were required. Multiple imputation may fail when data are missing not at random. Here, combining multiple imputation and the missing indicator method reduced the bias as the missing indicator variable can be a proxy for unobserved confounding. The optimal way to handle missing values in covariates of propensity score models depends on the missing data structure and the presence of effect modification. When effect modification is present, default settings of imputation methods may yield biased results even if data are missing at random.

Missing data (MD) is a common and inevitable problem facing data mining (DM)-based decision systems in e-health since many medical historical datasets contain a huge number of missing values. Therefore, a pre-processing stage is usually required to deal with missing values before building any DM-based decision system. The purpose of this paper is to evaluate the impact of MD techniques on classification systems in cardiovascular dysautonomias diagnosis. We analyzed and compared the accuracy rates of four classification techniques: random forest (RF), support vector machines (SVM), C4.5 decision tree, and Naive Bayes (NB), using two MD techniques: deletion or imputation with k-nearest neighbors (KNN). A total of 216 experiments were therefore carried out using three missingness mechanisms (MCAR: missing completely at random, MAR: missing at random and NMAR: not missing at random), two MD techniques (deletion and KNN imputation), nine MD percentages from 10 to 90% over a dataset collected from the autonomic nervous system (ANS) unit of the University Hospital Avicenne in Morocco. The results obtained suggest that using KNN imputation rather than deletion enhances the accuracy rates of the four classifiers. Moreover, the MD percentages have a negative impact on the performance of classification techniques regardless of the MD mechanisms and MD techniques used. In fact, the accuracy rates of the four classifiers decrease as the MD percentage increases. Graphical abstract.

Comparing Methods for Handling Missing Data

Incomplete data is a pervasive challenge across a wide range of data types, including tabular, sensor, time-series, image, and textual data. Its presence stems from various real-world factors and gives rise to different missingness mechanisms. While much of the existing research focuses on the Missing Completely At Random (MCAR) assumption, the more complex and realistic mechanisms-Missing At Random (MAR) and Missing Not At Random (MNAR)-remain relatively underexplored despite their prevalence and impact. This PhD project aims to systematically investigate the challenges posed by diverse Incomplete data mechanisms and to develop robust machine learning methods that can perform reliably across MCAR, MAR, and MNAR scenarios. The research spans multiple data modalities and focuses on improving both the theoretical understanding and practical handling of incomplete data. By addressing mechanism-specific imputation challenges and proposing broadly applicable solutions, this work contributes to building more resilient and trustworthy data-driven systems in real-world settings.

We illustrate a class of conditional models for the analysis of longitudinal data suffering attrition in random effects models framework, where the subject-specific random effects are assumed to be discrete and to follow a time-dependent latent process. The latent process accounts for unobserved heterogeneity and correlation between individuals in a dynamic fashion, and for dependence between the observed process and the missing data mechanism. Of particular interest is the case where the missing mechanism is non-ignorable. To deal with the topic we introduce a conditional to dropout model. A shape change in the random effects distribution is considered by directly modeling the effect of the missing data process on the evolution of the latent structure. To estimate the resulting model, we rely on the conditional maximum likelihood approach and for this aim we outline an EM algorithm. The proposal is illustrated via simulations and then applied on a dataset concerning skin cancers. Comparisons with other well-established methods are provided as well.

After a short introduction of the model, the missing mechanism and the method of inference some imputation procedures are introduced with special focus on the simulation experiment. Within this experiment, the simple additive model y = f(x) + e is assumed to have missing values in the independent variable according to MCAR. Besides the well-known complete case analysis, mean imputation plus random noise, a single imputation and two ways of nearest neighbor imputation are used. These methods are compared within a simulation experiment based on the average mean square error, variances and biases of \hat{f}(x) at the knots.

SummaryLinear regression (LR) is vastly used in data analysis for continuous outcomes in biomedicine and epidemiology. Despite its popularity, LR is incompatible with missing data, which frequently occur in health sciences. For parameter estimation, this short-coming is usually resolved by complete-case analysis or imputation. Both workarounds, however, are inadequate for prediction, since they either fail to predict on incomplete records or ignore missingness-induced reduction in prediction accuracy and rely on (unrealistic) assumptions about the missing mechanism. Here, we derive adaptive predictor-set linear model (aps-lm), capable of making predictions for incomplete data without the need for imputation. It is derived by using a predictor-selection operation, the Moore-Penrose pseudoinverse and the reduced QR-decomposition. aps-lm is an LR generalization that inherently handles missing values. It is applied on a reference dataset, where complete predictors and outcome are available, and yields a set of privacy-preserving parameters. In a second stage, these are shared for making predictions of the outcome on external datasets with missing entries for predictors without imputation. Moreover, aps-lm computes prediction errors that account for the pattern of missing values even under extreme missingness. We benchmark aps-lm in a simulation study. aps-lm showed greater prediction accuracy and reduced bias compared to popular imputation strategies under a wide range of scenarios including variation of sample size, goodness-of-fit, missing value type and covariance structure. Finally, as a proof-of-principle, we apply aps-lm in the context of epigenetic aging clocks, linear models that predict a person’s biological age from epigenetic data with promising clinical applications.

This thesis deals with recurrent neural networks, a particular class of artificial neural networks which can learn a generative model of input sequences. The input is mapped, through a feedback loop and a non-linear activation function, into a hidden state, which is then projected into the output space, obtaining either a probability distribution or the new input for the next time-step. This work consists mainly of two parts: a theoretical study for helping the understanding of recurrent neural networks framework, which is not yet deeply investigated, and their application to non-linear prediction problems, since recurrent neural networks are really powerful models suitable for solving several practical tasks in different fields. For what concerns the theoretical part, we analyse the weaknesses of state-of-the-art models and tackle them in order to improve the performance of a recurrent neural network. Firstly, we contribute in the understanding of the dynamical properties of a recurrent neural network, highlighting the close relation between the definition of stable limit cycles and the echo state property of an echo state network. We provide sufficient conditions for the convergence of the hidden state to a trajectory, which is uniquely determined by the input signal, independently of the initial states. This may help extend the memory of the network and increase the design options for the network. Moreover, we develop a novel approach to address the main problem in training recurrent neural networks, the so-called vanishing gradient problem. Our new method allows us to train a very simple recurrent neural network, making the gradient not to vanish even after many time-steps. Exploiting the singular value decomposition of the vanishing factors in the gradient and random matrices theory, we find that the singular values have to be confined in a narrow interval and derive conditions about their root mean square value. Then, we also improve the efficiency of the training of a recurrent neural network, defining a new method for speeding up this process. Thanks to a least square regularization, we can initialize the parameters of the network, in order to set them closer to the minimum and running fewer epochs of classical training algorithms. Moreover, it is also possible to completely train the network with our initialization method, running more iterations of it without losing in performance with respect to classical training algorithms. Finally, it is also possible to use it as a real-time learning algorithm, adjusting the parameters to the new data through one iteration of our initialization. In the last part of this thesis, we apply recurrent neural networks to non-linear prediction problems. We consider prediction of numerical sequences, estimating the following input choosing it from a probability distribution. We study an automatic text generation problem, where we need to predict the following character in order to compose words and sentences, and a path prediction of walking mobile users in the central area of a city, as a sequence of crossroads. Then, we analyse the prediction of video frames, discovering a wide range of applications related to the prediction of movements. We study the collision problem of bouncing balls, taking into account only the sequence of video frames without any knowledge about the physical characteristics of the problem, and the distribution over days of mobile user in a city and in a whole region. Finally, we address the state-of-the-art problem of missing data imputation, analysing the incomplete spectrogram of audio signals. We restore audio signals with missing time-frequency data, demonstrating via numerical experiments that a performance improvement can be achieved involving recurrent neural networks.