本篇論文主要有兩個目標，第一個目標為找出對於每位病患適合之治療方式；第二個目標為在最佳醫療決策下估計病患之倖存函數。因此我們根據梯度提升演算法(gradient boosting machine)架構，提出RAINBOW演算法，達成此兩項目的。從模擬結果可知，藉由給予適當的懲罰項，即便在自變數的個數大於樣本數的情況下，仍可精確的估計倖存函數與醫療決策。

We consider the problem of identifying patients who may take medication. To deal with the problem, we use gradient boosting to train the Cox model, involves estimating survival function for treatment and control for each patient. The difference in these survival function is then used to make the optimal decision which patient should be treated and estimate the survival function with optimal treatment regime which maps observed patient characteristics to a recommended treatment. From our simulation, we get the good performance even the number of covariates is larger than the sample size. As an illustration, we apply the proposed method to survival data of non-small cell lung cancer.

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