Multiple Imputation Approaches Applied to the Missing Value Problem in Bottom-Up Proteomics

Analysis of differential abundance in proteomics data sets requires careful application of missing value imputation. Missing abundance values widely vary when performing comparisons across different sample treatments. For example, one would expect a consistent rate of “missing at random” (MAR) across batches of samples and varying rates of “missing not at random” (MNAR) depending on the inherent difference in sample treatments within the study. The missing value imputation strategy must thus be selected that best accounts for both MAR and MNAR simultaneously. Several important issues must be considered when deciding the appropriate missing value imputation strategy: (1) when it is appropriate to impute data; (2) how to choose a method that reflects the combinatorial manner of MAR and MNAR that occurs in an experiment. This paper provides an evaluation of missing value imputation strategies used in proteomics and presents a case for the use of hybrid left-censored missing value imputation approaches that can handle the MNAR problem common to proteomics data.

Data Missing Not at Random in Mobile Health Research: Assessment of the Problem and a Case for Sensitivity Analyses

Background Missing data are common in mobile health (mHealth) research. There has been little systematic investigation of how missingness is handled statistically in mHealth randomized controlled trials (RCTs). Although some missing data patterns (ie, missing at random [MAR]) may be adequately addressed using modern missing data methods such as multiple imputation and maximum likelihood techniques, these methods do not address bias when data are missing not at random (MNAR). It is typically not possible to determine whether the missing data are MAR. However, higher attrition in active (ie, intervention) versus passive (ie, waitlist or no treatment) conditions in mHealth RCTs raise a strong likelihood of MNAR, such as if active participants who benefit less from the intervention are more likely to drop out. Objective This study aims to systematically evaluate differential attrition and methods used for handling missingness in a sample of mHealth RCTs comparing active and passive control conditions. We also aim to illustrate a modern model-based sensitivity analysis and a simpler fixed-value replacement approach that can be used to evaluate the influence of MNAR. Methods We reanalyzed attrition rates and predictors of differential attrition in a sample of 36 mHealth RCTs drawn from a recent meta-analysis of smartphone-based mental health interventions. We systematically evaluated the design features related to missingness and its handling. Data from a recent mHealth RCT were used to illustrate 2 sensitivity analysis approaches (pattern-mixture model and fixed-value replacement approach). Results Attrition in active conditions was, on average, roughly twice that of passive controls. Differential attrition was higher in larger studies and was associated with the use of MAR-based multiple imputation or maximum likelihood methods. Half of the studies (18/36, 50%) used these modern missing data techniques. None of the 36 mHealth RCTs reviewed conducted a sensitivity analysis to evaluate the possible consequences of data MNAR. A pattern-mixture model and fixed-value replacement sensitivity analysis approaches were introduced. Results from a recent mHealth RCT were shown to be robust to missing data, reflecting worse outcomes in missing versus nonmissing scores in some but not all scenarios. A review of such scenarios helps to qualify the observations of significant treatment effects. Conclusions MNAR data because of differential attrition are likely in mHealth RCTs using passive controls. Sensitivity analyses are recommended to allow researchers to assess the potential impact of MNAR on trial results.

Sensitivity to missing not at random dropout in clinical trials: use and interpretation of the Trimmed Means Estimator

Outcome values in randomized controlled trials (RCTs) may be missing not at random (MNAR), if patients with extreme outcome values are more likely to drop out (e.g., due to perceived ineffectiveness of treatment, or adverse effects). In such scenarios, estimates from complete case analysis (CCA) and multiple imputation (MI) will be biased. The trimmed means (TM) estimator operates by setting missing values to the most extreme value, and then “trimming” away equal fractions of both treatment groups, estimating the treatment effect using the remaining data. The TM estimator relies on two assumptions, which we term the “strong MNAR” and “location shift” assumptions. In this article, we derive formulae for the bias resulting from the violation of these assumptions for normally distributed outcomes. We propose an adjusted estimator, which relaxes the location shift assumption and detail how our bias formulae can be used to establish the direction of bias of CCA, MI and TM estimates under a range of plausible data scenarios, to inform sensitivity analyses. The TM approach is illustrated with simulations and in a sensitivity analysis of the CoBalT RCT of cognitive behavioural therapy (CBT) in 469 individuals with 46 months follow-up. Results were consistent with a beneficial CBT treatment effect. The MI estimates are closer to the null than the CCA estimate, whereas the TM estimate was further from the null. We propose using the TM estimator as a sensitivity analysis for data where it is suspected that extreme outcome values are missing.

Missing not at random in end of life care studies: multiple imputation and sensitivity analysis on data from the ACTION study

Background Missing data are common in end-of-life care studies, but there is still relatively little exploration of which is the best method to deal with them, and, in particular, if the missing at random (MAR) assumption is valid or missing not at random (MNAR) mechanisms should be assumed. In this paper we investigated this issue through a sensitivity analysis within the ACTION study, a multicenter cluster randomized controlled trial testing advance care planning in patients with advanced lung or colorectal cancer. Methods Multiple imputation procedures under MAR and MNAR assumptions were implemented. Possible violation of the MAR assumption was addressed with reference to variables measuring quality of life and symptoms. The MNAR model assumed that patients with worse health were more likely to have missing questionnaires, making a distinction between single missing items, which were assumed to satisfy the MAR assumption, and missing values due to completely missing questionnaire for which a MNAR mechanism was hypothesized. We explored the sensitivity to possible departures from MAR on gender differences between key indicators and on simple correlations. Results Up to 39% of follow-up data were missing. Results under MAR reflected that missingness was related to poorer health status. Correlations between variables, although very small, changed according to the imputation method, as well as the differences in scores by gender, indicating a certain sensitivity of the results to the violation of the MAR assumption. Conclusions The findings confirmed the importance of undertaking this kind of analysis in end-of-life care studies.