中国乳腺癌自然史参数选择的优化方法

An optimization approach for parameter selection in natural history of breast cancer in China

乳腺癌是女性最常见的恶性肿瘤之一。为了提出有效的筛查策略并评估其效果,一个基本且重要的步骤是在中国乳腺癌自然史模型中选择合适的参数,即转移概率.选择合理的转移概率有两个挑战.首先,由于乳腺癌的流行病学特性,其他国家使用的转移概率不一定适用于中国.其次,可用的筛查样本数据很少,这使得传统的基于统计的方法(如极大似然估计法)失效.本文从优化角度提出一种乳腺癌自然史参数选择的方法,基于公布的统计数据建立数学优化模型.该模型的挑战在于目标函数高度非线性且无显式表达式,本文提出一种坐标下降算法来处理这个挑战.最后,本文提出一种最佳匹配方法来估计每个转移概率的分布.本文所提出的方法为进一步提出合理的中国乳腺癌筛查策略和分析乳腺癌的经济负担提供了坚实的基础.

Breast cancer is one of the most common cancers for females.In order to propose efficient screening strategies and evaluate the effect,one fundamental and important step is to choose proper parameters,i.e.,transition rates,in the natural history model of breast cancer in China.There are two challenges to choosing reasonable transition rates.Firstly,the transition rates used in other countries may be not applicable to China,due to the cancer epidemiology.Secondly,little screening sample data are available,making the traditional statistical based approaches such as maximum likelihood methods fail.In this paper,we propose an optimization approach for parameter selection in the natural history of breast cancer in China.A mathematical optimization model is established based on the published statistical data.A coordinate descent algorithm is proposed to solve the resulting box-constrained and highly nonlinear problem,whose objective function does not have an explicit form.Finally,the best matching method is proposed to estimate the distributions of each transition rate.Our approach provides solid foundations to further propose reasonable screening strategies for breast cancer in China and analyze the economic burden of breast cancer.