In modern biomedical classification applications, data are often collected from multiple modalities, ranging from various omics technologies to brain scans. As different modalities provide complementary information, classifiers using multi-modality data usually have good classification performance. However, in many studies, due to the high cost of measures, in a lot of samples, some modalities are missing and therefore all data from those modalities are missing completely. In this case, the training data set is a block-missing multi-modality data set. In this paper, considering such classification problems, we develop a new weighted nearest neighbors classifier, called the integrative nearest neighbor (INN) classifier. INN harnesses all available information in the training data set and the feature vector of the test data point effectively to predict the class label of the test data point without deleting or imputing any missing data. Given a test data point, INN determines the weights on the training samples adaptively by minimizing the worst-case upper bound on the estimation error of the regression function over a convex class of functions. Our simulation study shows that INN outperforms common weighted nearest neighbors classifiers that only use complete training samples or modalities that are available in each sample. It performs better than methods that impute the missing data as well, even for the case where some modalities are missing not at random. The effectiveness of INN has been also demonstrated by our theoretical studies and a real application from the Alzheimer’s disease neuroimaging initiative.
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