We develop a state space model documenting Gompertz behaviour of tumour growth. The state space model consists of two sub-models: a stochastic system model that is an extension of the deterministic model proposed by Gyllenberg and Webb (1991), and an observation model that is a statistical model based on data for the total number of tumour cells over time. In the stochastic system model we derive through stochastic equations the probability distributions of the numbers of different types of tumour cells. Combining with the statistic model, we use these distribution results to develop a generalized Bayesian method and a Gibbs sampling procedure to estimate the unknown parameters and to predict the state variables (number of tumour cells). We apply these models and methods to real data and to computer simulated data to illustrate the usefulness of the models, the methods, and the procedures.

中文翻译：

---

肿瘤生长和应用的随机状态空间模型

我们开发了一个状态空间模型，记录了肿瘤生长的Gompertz行为。状态空间模型包括两个子模型：随机系统模型，是Gyllenberg和Webb（1991）提出的确定性模型的扩展；观察模型，是基于肿瘤总数数据的统计模型。细胞随着时间的流逝。在随机系统模型中，我们通过随机方程得出不同类型肿瘤细胞数量的概率分布。结合统计模型，我们使用这些分布结果来开发广义贝叶斯方法和吉布斯采样程序，以估计未知参数并预测状态变量（肿瘤细胞数）。