Restricted Boltzmann machine for missing data imputation in biomedical datasets

Abstract

In biology and medicine, conservative patient and data collection malpractice can lead to missing or incorrect values in patient registries, which can affect both diagnosis and prognosis. Insufficient or biased patient information significantly impedes the sensitivity and accuracy of predicting cancer survival. In bioinformatics, making a best guess of the missing values and identifying the incorrect values are collectively called “imputation”. Existing imputation methods work by establishing a model based on the data mechanism of the missing values. Existing imputation methods work well under two assumptions: 1) the data is missing completely at random, and 2) the percentage of missing values is not high. These are not cases found in biomedical datasets, such as the Cancer Genome Atlas Glioblastoma Copy-Number Variant dataset (TCGA: 108 columns), or the North Central Cancer Treatment Group Lung Cancer (NCCTG) dataset (NCCTG: 9 columns). We tested six existing imputation methods, but only two of them worked with these datasets: The Last Observation Carried Forward (LOCF) and K-nearest Algorithm (KNN). Predictive Mean Matching (PMM) and Classification and Regression Trees (CART) worked only with the NCCTG lung cancer dataset with fewer columns, except when the dataset contains 45% missing data. The quality of the imputed values using existing methods is bad because they do not meet the two assumptions. In our study, we propose a Restricted Boltzmann Machine (RBM)-based imputation method to cope with low randomness and the high percentage of the missing values. RBM is an undirected, probabilistic and parameterized two-layer neural network model, which is often used for extracting abstract information from data, especially for high-dimensional data with unknown or non-standard distributions. In our benchmarks, we applied our method to two cancer datasets: 1) NCCTG, and 2) TCGA. The running time, root mean squared error (RMSE) of the different methods were gauged. The benchmarks for the NCCTG dataset show that our method performs better than other methods when there is 5% missing data in the dataset, with 4.64 RMSE lower than the best KNN. For the TCGA dataset, our method achieved 0.78 RMSE lower than the best KNN. In addition to imputation, RBM can achieve simultaneous predictions. We compared the RBM model with four traditional prediction methods. The running time and area under the curve (AUC) were measured to evaluate the performance. Our RBM-based approach outperformed traditional methods. Specifically, the AUC was up to 19.8% higher than the multivariate logistic regression model in the NCCTG lung cancer dataset, and the AUC was higher than the Cox proportional hazard regression model, with 28.1% in the TCGA dataset. Apart from imputation and prediction, RBM models can detect outliers in one pass by allowing the reconstruction of all the inputs in the visible layer with in a single backward pass. Our results show that RBM models have achieved higher precision and recall on detecting outliers than other methods.