Survival analysis can sometimes involve individuals who will not experience the event of interest, forming what is known as the cured group. Identifying such individuals is not always possible beforehand, as they provide only right-censored data. Ignoring the presence of the cured group can introduce bias in the final model. This paper presents a method for estimating a semiparametric additive hazards model that accounts for the cured fraction. Unlike regression coefficients in a hazard ratio model, those in an additive hazard model measure hazard differences. The proposed method uses a primal-dual interior point algorithm to obtain constrained maximum penalized likelihood estimates of the model parameters, including the regression coefficients and the baseline hazard, subject to certain non-negativity constraints.

翻译：生存分析有时涉及不会经历感兴趣事件的个体，形成所谓的治愈组。预先识别这类个体并非总是可行，因为他们仅提供右删失数据。忽略治愈组的存在可能导致最终模型产生偏差。本文提出了一种估计考虑治愈比例的半参数加性风险模型的方法。与风险比模型中的回归系数不同，加性风险模型中的回归系数测量的是风险差异。所提出的方法采用原始-对偶内点算法，在特定的非负约束条件下，获得模型参数（包括回归系数和基准风险）的约束最大惩罚似然估计值。