This document provides a clear and practical guide to understanding missing data mechanisms, including Missing Completely At Random (MCAR), Missing At Random (MAR), and Missing Not At Random (MNAR). Through real-world scenarios and examples, it explains how different types of missingness impact data analysis and decision-making. It also outlines common strategies for handling missing data, including deletion techniques and imputation methods such as mean imputation, regression, and stochastic modeling.Designed for researchers, analysts, and students working with real-world datasets, this guide helps ensure statistical validity, reduce bias, and improve the overall quality of analysis in fields like public health, behavioral science, social research, and machine learning.

R code to impute binary outcome. (R 1 kb)

Imputation methods for missing data on a time-dependent variable within time-dependent Cox models are investigated in a simulation study. Quality of life (QoL) assessments were removed from the complete simulated datasets, which have a positive relationship between QoL and disease-free survival (DFS) and delayed chemotherapy and DFS, by missing at random and missing not at random (MNAR) mechanisms. Standard imputation methods were applied before analysis. Method performance was influenced by missing data mechanism, with one exception for simple imputation. The greatest bias occurred under MNAR and large effect sizes. It is important to carefully investigate the missing data mechanism.

MAPE and PB statistics for IBFI compared with other imputation methods (mean, median, mode, PMM, and Hotdeck) for 20% missingness of type MAR and all parameters tested (RN, TH, TC, RH, and PR).

The integration of proteomic datasets, generated by non-cooperating laboratories using different LC-MS/MS setups can overcome limitations in statistically underpowered sample cohorts but has not been demonstrated to this day. In proteomics, differences in sample preservation and preparation strategies, chromatography and mass spectrometry approaches and the used quantification strategy distort protein abundance distributions in integrated datasets. The Removal of these technical batch effects requires setup-specific normalization and strategies that can deal with missing at random (MAR) and missing not at random (MNAR) type values at a time. Algorithms for batch effect removal, such as the ComBat-algorithm, commonly used for other omics types, disregard proteins with MNAR missing values and reduce the informational yield and the effect size for combined datasets significantly. Here, we present a strategy for data harmonization across different tissue preservation techniques, LC-MS/MS instrumentation setups and quantification approaches. To enable batch effect removal without the need for data reduction or error-prone imputation we developed an extension to the ComBat algorithm, ´ComBat HarmonizR, that performs data harmonization with appropriate handling of MAR and MNAR missing values by matrix dissection The ComBat HarmonizR based strategy enables the combined analysis of independently generated proteomic datasets for the first time. Furthermore, we found ComBat HarmonizR to be superior for removing batch effects between different Tandem Mass Tag (TMT)-plexes, compared to commonly used internal reference scaling (iRS). Due to the matrix dissection approach without the need of data imputation, the HarmonizR algorithm can be applied to any type of -omics data while assuring minimal data loss

Statistical details of the SRGC time series dataset.

Conventional survey tools such as weighting do not address non-ignorable nonresponse that occurs when nonresponse depends on the variable being measured. This paper describes non-ignorable nonresponse weighting and imputation models using randomized response instruments, which are variables that affect response but not the outcome of interest \citep{SunEtal2018}. The paper uses a doubly robust estimator that is valid if one, but not necessarily both, of the weighting and imputation models is correct. When applied to a national 2019 survey, these tools produce estimates that suggest there was non-trivial non-ignorable nonresponse related to turnout, and, for subgroups, Trump approval and policy questions. For example, the conventional MAR-based weighted estimates of Trump support in the Midwest were 10 percentage points lower than the MNAR-based estimates. Data to replicate estimation described in "Countering Non-Ignorable Nonresponse in Survey Models with Randomized Response Instruments and Doubly Robust Estimation"

Currently, various methods have been proposed to handle missing data in clinical trials. Some methods assume that the missing data are missing at random (MAR), which means that it is assumed that subjects who stopped treatment would still maintain the treatment effect. In many cases, however, researchers often assume that the missing data are missing not at random (MNAR) to conduct additional sensitivity analyses. Under the MNAR assumption, whether using some conservative imputation methods such as RTB (return to baseline) method, J2R (jump to reference) method, and CR (copy reference) method, or optimistic imputation methods like multiple imputation (MI) and its derivative RD (retrieved dropout) method, biases compared to the true treatment effect can occur in some scenarios. This paper aims to propose a method that can impute results while considering the occurrence of intercurrent events, thereby reducing the bias compared to the true treatment effect. This method combines the RD method with the RTB formula, reducing the biases and standard errors associated with using either method alone. Considering the differing treatment effects between RD subjects and non-RD subjects, our imputation results often align more closely with the true drug efficacy.

Summary statistics for the complete-case data, original data, and original data with imputed values.

Clustering assessed at the 0.10 threshold, with m = 100 deletions. Clus stands for clustering; Obs for observed data; In-Obs for ncomplete-observed data; Impute-Com for imputed-complete data; Cov stands for coverage.Estimated overall proportion of clustering for observed, incomplete-observed and imputed-complete datasets under MNAR.