康威-馬克士威-泊松分配（Conway-Maxwell-Poisson)可以用於描述存活資料中之治癒 比例，基於此模型，在文獻中已有兩種最大概似估計量之計算方法被提出，一種方法爲R gamlss套件所使用的方法，其利用了對數概似函數之一階導數，另一種方法則是使用了完整 資料概似函數之最大期望演算法。在本篇文章中，我們提出了一個穩健的牛頓-拉弗森演算法, 其穩健性是來自於對起始值之隨機擾動，以及對恆正參數之對數轉換，在伯努力治癒模型下，我 們提供了概似函數之導數表示法與電腦程式碼給讀者使用。由於牛頓-拉弗森演算法使用了概 似函數之一、二階導數，故其收斂速度較R gamlss套件快，同時我們也回顧了最大期望演算法, 並利用模擬分析將其表現與牛頓-拉弗森演算法做比較，除此之外，我們還提出了一筆新的資料 來配適康威-馬克士威-泊松治癒模型，並且討論使用兩種演算法之結果。

The Conway-Maxwell-Poisson (COM-Poisson) distribution is useful to account for a cure proportion in survival data. With this model, two computational approaches for calculating maximum likelihood estimates have been developed in the literature: one based on the method in the gamlss R package that employs the first-order derivatives of the log-likelihood, and the other based on the EM algorithm that employs the completedata likelihood. In this paper, we propose a robust version of the Newton-Raphson (NR) algorithm, where the robustness is introduced by random perturbations to the initial values and by log-transformations to positive parameters. We provide the expressions of the derivatives of the log-likelihood under the Bernoulli cure model and computer codes for implementation. Since the NR algorithm employs the first- and secondderivatives of the log-likelihood, it converges more quickly than the method of the gamlss R package. We also review the EM algorithms and compare the computational performance between the NR and EM algorithms via simulations. We also include a novel data to be fitted to the COM-Poisson cure model, and discuss the consequence of performing the two algorithms.