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Exploration and analysis of massive datasets has recently generatedincreasing interest in the research and development communities. It has longbeen a recognized problem that many datasets contain significant levels ofmissing numerical data. We introduce a mathematically principled stochasticoptimization imputation method based on the theory of Kriging. This is shown tobe a powerful method for imputation. However, its computational effort andpotential numerical instabilities produce costly and/or unreliable predictions,potentially limiting its use on large scale datasets. In this paper, we apply arecently developed multi-level stochastic optimization approach to the problemof imputation in massive medical records. The approach is based oncomputational applied mathematics techniques and is highly accurate. Inparticular, for the Best Linear Unbiased Predictor (BLUP) this multi-levelformulation is exact, and is also significantly faster and more numericallystable. This permits practical application of Kriging methods to dataimputation problems for massive datasets. We test this approach on data fromthe National Inpatient Sample (NIS) data records, Healthcare Cost andUtilization Project (HCUP), Agency for Healthcare Research and Quality.Numerical results show the multi-level method significantly outperforms currentapproaches and is numerically robust. In particular, it has superior accuracyas compared with methods recommended in the recent report from HCUP on theimportant problem of missing data, which could lead to sub-optimal and poorlybased funding policy decisions. In comparative benchmark tests it is shown thatthe multilevel stochastic method is significantly superior to recommendedmethods in the report, including Predictive Mean Matching (PMM) and PredictedPosterior Distribution (PPD), with up to 75% reductions in error.

Multilevel Stochastic Optimization for Imputation in Massive Medical Data Records