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- Title
Missing data and prediction: the pattern submodel.
- Authors
Mercaldo, Sarah Fletcher; Blume, Jeffrey D; Fletcher Mercaldo, Sarah
- Abstract
Missing data are a common problem for both the construction and implementation of a prediction algorithm. Pattern submodels (PS)-a set of submodels for every missing data pattern that are fit using only data from that pattern-are a computationally efficient remedy for handling missing data at both stages. Here, we show that PS (i) retain their predictive accuracy even when the missing data mechanism is not missing at random (MAR) and (ii) yield an algorithm that is the most predictive among all standard missing data strategies. Specifically, we show that the expected loss of a forecasting algorithm is minimized when each pattern-specific loss is minimized. Simulations and a re-analysis of the SUPPORT study confirms that PS generally outperforms zero-imputation, mean-imputation, complete-case analysis, complete-case submodels, and even multiple imputation (MI). The degree of improvement is highly dependent on the missingness mechanism and the effect size of missing predictors. When the data are MAR, MI can yield comparable forecasting performance but generally requires a larger computational cost. We also show that predictions from the PS approach are equivalent to the limiting predictions for a MI procedure that is dependent on missingness indicators (the MIMI model). The focus of this article is on out-of-sample prediction; implications for model inference are only briefly explored.
- Subjects
FORECASTING; MISSING data (Statistics); PREDICTION models; DATA; STATISTICS; RESEARCH; RESEARCH methodology; EVALUATION research; MEDICAL cooperation; COMPARATIVE studies; RESEARCH funding; STATISTICAL models; DATA analysis; MEDICAL research
- Publication
Biostatistics, 2020, Vol 21, Issue 2, p236
- ISSN
1465-4644
- Publication type
journal article
- DOI
10.1093/biostatistics/kxy040