Generating Synthetic Missing Data: A Review by Missing Mechanism <s> III. MISSING DATA MECHANISMS <s> D, Center for ResearchMethods and Data Analysis, University of Kansas, Lawrence, KS 66045, USA. E-mail: yhat@ku.eduReceived February 28, 2013; revisions received and accepted May 30, 2013We provide conceptual introductions to missingness mechanisms—missing completely at random, missing atrandom, and missing not at random—and state-of-the-art methods of handling missing data—full-informa-tion maximum likelihood and multiple imputation—followed by a discussion of planned missing designs:Multiform questionnaire protocols, 2-method measurement models, and wave-missing longitudinal designs.We reviewed 80 articles of empirical studies published in the 2012 issues of the Journal of PediatricPsychology to present a picture of how adequately missing data are currently handled in this field. Toillustrate the benefits of using multiple imputation or full-information maximum likelihood and incorporatingplanned missingness into study designs, we provide example analyses of empirical data gathered using a3-form planned missing design.Key words full-information maximum likelihood; missing data analysis; missingness mechanisms; multipleimputation; planned missing design.Missing data are not problematic, per se—how weapproach and treat missing data, on the other hand, canbe highly problematic. In fact, all of the traditionalmethods that are still popular in pediatric research sufferfrom many drawbacks that introduce bias and lack ofpower (Enders, 2010; Graham, 2012; van Buuren,2011). In contrast to the drawbacks of traditional app-roaches (e.g., listwise or pairwise deletion, mean substitu-tion), modern treatments for missing data such as multipleimputation (MI) and full-information maximum likelihood(FIML) easily accommodate valid inferences when thestudy design includes careful consideration of the reasonsfor why data might go missing. We provide a conceptualintroduction to the steadily growing literature on modernmissing data treatments. Admittedly, the devil is in thedetails of how to best minimize any deleterious effects ofmissing data, and we provide citations to ample resourceswhere these details are carefully described. In this article,therefore, we only highlight the many ways that missingdata can and should be addressed in pediatric research.When a sample of participants is used to make infer-ences about a population of persons, three issues arisewhen data are missing: power, bias, and recoverability.How much power has been lost? Are the remaining datanow a biased representation of the population? Can thepower loss be recovered? Can the bias be recovered?With modern treatments for missing data, the answer toeach of these questions depends on which of three possiblemechanisms (Rubin, 1976) is responsible for the missingdata. All missing data happen because of one of these threemechanisms, and in any data collection endeavor, all threemechanisms are likely to be involved to some degree. <s> BIB001 </s> Generating Synthetic Missing Data: A Review by Missing Mechanism <s> III. MISSING DATA MECHANISMS <s> Breast cancer is the most frequently diagnosed cancer in women. Using historical patient information stored in clinical datasets, data mining and machine learning approaches can be applied to predict the survival of breast cancer patients. A common drawback is the absence of information, i.e., missing data, in certain clinical trials. However, most standard prediction methods are not able to handle incomplete samples and, then, missing data imputation is a widely applied approach for solving this inconvenience. Therefore, and taking into account the characteristics of each breast cancer dataset, it is required to perform a detailed analysis to determine the most appropriate imputation and prediction methods in each clinical environment. This research work analyzes a real breast cancer dataset from Institute Portuguese of Oncology of Porto with a high percentage of unknown categorical information (most clinical data of the patients are incomplete), which is a challenge in terms of complexity. Four scenarios are evaluated: (I) 5-year survival prediction without imputation and 5-year survival prediction from cleaned dataset with (II) Mode imputation, (III) Expectation-Maximization imputation and (IV) K-Nearest Neighbors imputation. Prediction models for breast cancer survivability are constructed using four different methods: K-Nearest Neighbors, Classification Trees, Logistic Regression and Support Vector Machines. Experiments are performed in a nested ten-fold cross-validation procedure and, according to the obtained results, the best results are provided by the K-Nearest Neighbors algorithm: more than 81% of accuracy and more than 0.78 of area under the Receiver Operator Characteristic curve, which constitutes very good results in this complex scenario. HighlightsA 5-year survival model is constructed in a real breast cancer context.The dataset is a challenge in terms of complexity due to its high missing data ratio.Several representative imputation and decision methods are analyzed.Obtained results are very interesting and accurate for this complex clinical dataset. <s> BIB002 </s> Generating Synthetic Missing Data: A Review by Missing Mechanism <s> III. MISSING DATA MECHANISMS <s> Display Omitted Survival prediction of HCC patients is modeled in a real and high complex scenario.Its complexity is due to a small dataset with heterogeneous and missing input data.We propose a new cluster-based oversampling method to overcome these drawbacks.Neural networks and logistic regression are applied in the classification stage.Experimental results show that our method outperforms previous existing approaches. Liver cancer is the sixth most frequently diagnosed cancer and, particularly, Hepatocellular Carcinoma (HCC) represents more than 90% of primary liver cancers. Clinicians assess each patients treatment on the basis of evidence-based medicine, which may not always apply to a specific patient, given the biological variability among individuals. Over the years, and for the particular case of Hepatocellular Carcinoma, some research studies have been developing strategies for assisting clinicians in decision making, using computational methods (e.g. machine learning techniques) to extract knowledge from the clinical data. However, these studies have some limitations that have not yet been addressed: some do not focus entirely on Hepatocellular Carcinoma patients, others have strict application boundaries, and none considers the heterogeneity between patients nor the presence of missing data, a common drawback in healthcare contexts. In this work, a real complex Hepatocellular Carcinoma database composed of heterogeneous clinical features is studied. We propose a new cluster-based oversampling approach robust to small and imbalanced datasets, which accounts for the heterogeneity of patients with Hepatocellular Carcinoma. The preprocessing procedures of this work are based on data imputation considering appropriate distance metrics for both heterogeneous and missing data (HEOM) and clustering studies to assess the underlying patient groups in the studied dataset (K-means). The final approach is applied in order to diminish the impact of underlying patient profiles with reduced sizes on survival prediction. It is based on K-means clustering and the SMOTE algorithm to build a representative dataset and use it as training example for different machine learning procedures (logistic regression and neural networks). The results are evaluated in terms of survival prediction and compared across baseline approaches that do not consider clustering and/or oversampling using the Friedman rank test. Our proposed methodology coupled with neural networks outperformed all others, suggesting an improvement over the classical approaches currently used in Hepatocellular Carcinoma prediction models. <s> BIB003
We now formally characterize the different missing data mechanisms, p(M | X, ξ )  , illustrating each one with an example. For this purpose, consider Table 2 which represents a simulated dataset of a study regarding adolescent tobacco use, with 20 participants. Feature ''Age'' is completely observed while the ''Number of Cigarettes'', is missing according to different mechanisms, as explained in what follows. In Missing Completely At Random (MCAR) mechanism, M is completely unrelated to the input data X -completely unrelated to both X obs and X miss BIB002 . For MCAR, the probability of missingness depends only on parameters ξ ; or in other words, the probability of missing values in a feature x j is completely random. Considering Table 2 , MCAR values were produced by random deletion: the missing values are not located in a particular range of ''Age'' or ''Number of Cigarettes'' values. This mechanism can, therefore, be due to unexpected events during the study: a participant had a flat tire and could not attend the appointment or was with the flue. Missing At Random (MAR) mechanism occurs when the probability of missingness depends on the observed information X obs , but not on X miss BIB003 . In other words, the probability of missing values in a feature x j may depend on the observed values of other features in the dataset, but not on the values of x j itself. In Table 2 , MAR scenario is created by the missing values of ''Number of Cigarettes'' for younger participants (aged between 15 and 16 years). It could be the case that younger adolescents are less likely to fill in their number of smoked cigarettes per day because they do not want to admit that they are regular smokers. However, the missingness is unrelated to the number of cigarettes smoked by these teenagers, had it been reported (note the ''Complete'' column, where a low and high number of cigarettes would be found among the missing values, had they been observed). The probability of missing values in ''Number of Cigarettes'' is therefore a function of the observed information X obs only, unrelated to the missing values in the study, X miss . Finally, in Missing Not At Random (MNAR) mechanism, the missingness may depend on both observed and unobserved information -both X obs and X miss -and the general expression of the missing data model cannot be simplified BIB001 . In a simple manner, this means that the probability of missing values occurring in a feature x j may be related to the observed values of other features in the dataset (X obs ), as well as the underlying, unknown values of x j itself (X miss ). In Table 2 , MNAR values are missing for higher values of ''Number of Cigarettes'': the probability of missing values in ''Number of Cigarettes'' is related to the missing values themselves, had they been observed (note the ''Complete'' column). This would be the case of teenagers that refused to report their number of smoked cigarettes per day since they smoked a very large quantity.