資料中的遺失值是統計分析時常見的現象，若未妥善處理，可能使後續推論產生偏誤。以插補方式將遺失值補齊，是常見的做法之一。本研究延續以決策樹插補遺失值的方向，提出兩種新的插補方法，並比較文獻上數個既有做法 ; 除沿用經典的 CART 外，也會嘗試使用卡方檢定來找分割變數。相較於 Rahman與Islam (2013) 的 DMI (Decision tree-based Missing value Imputation) 方法僅採用毫無遺失的觀測值，本研究採取待插補變數有觀測到的資料皆可當作訓練資料，能更充分地運用觀測值。又因建樹時所選的分割變數本身也可能含有遺失值，本研究除採用文獻上以平均數或眾數讓其通過的做法外，亦運用 MIA (Missingness Incorporated in Attributes ; Twala et al., 2008) 將遺失本身直接納入分割判斷。此外，本研究提出兩種新方法。在本研究中，第一個方法是在 MIA 的基礎上，結合疊代插補與葉節點不確定性指標，將各變數的遺失值疊代插補直到收斂，以應用變數之間的關係，並加入葉節點不確定性指標排除不可信的預測，避免偏差較大的插補值在疊代中被反覆引用而放大誤差 ; 另一方法則在建樹前兩層改採聯合搜尋，取代傳統的逐層貪婪做法，期望於建樹初期即掌握變數間的交互作用。本研究透過四種相關性與三種遺失機制所構成的情境進行模擬研究，以比較各方法的表現，並將兩個所提方法應用於心臟病真實資料，檢視其實際表現。

Missing values are common in statistical analysis and, if not properly handled, may bias subsequent inferences; imputation is one common remedy. This study follows the line of research on decision-tree-based imputation, proposing two new imputation methods and comparing several existing methods. In addition to the classical CART method, chi-square tests are also used to identify splitting variables. Unlike the DMI method of ~Rahman and Islam (2013), which uses only fully observed cases, this study treats any observation with an observed target variable as training data, making fuller use of the sample. Moreover, since a chosen splitting variable may itself be missing, this study adopts both the conventional mean or mode substitution and MIA, which incorporates missingness directly into the splitting decision. Two new methods are further proposed. In the current study, the first extends MIA with iterative imputation, which updates each variable until convergence to exploit inter-variable relationships, and adds a leaf-node uncertainty measure that withholds unreliable predictions, preventing biased values from being reused and amplifying error across iterations. The second replaces the layer-by-layer greedy strategy with a joint search over the first two layers, so that interactions among variables can be captured early in developing the CART. Simulation studies covering four levels of correlation and three missing-data mechanisms have been conducted to compare these methods across scenarios. The practical performance of the two proposed methods is further evaluated using a real-world heart disease dataset.

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