Multi-state models are considered in the field of survival analysis for modelling illnesses that evolve through several stages over time. Multi-state models can be developed by applying several techniques, such as non-parametric, semi-parametric and stochastic processes, particularly Markov processes. When the development of an illness is being analysed, its progression is tracked periodically. Medical reviews take place at discrete times, and a panel data analysis can be formed. In this paper, a discrete-time piecewise non-homogeneous Markov process is constructed for modelling and analysing a multi-state illness with a general number of states. The model is built, and relevant measures, such as survival function, transition probabilities, mean total times spent in a group of states and the conditional probability of state change, are determined. A likelihood function is built to estimate the parameters and the general number of cut-points included in the model. Time-dependent covariates are introduced, the results are obtained in a matrix algebraic form and the algorithms are shown. The model is applied to analyse the behaviour of breast cancer. A study of the relapse and survival times of 300 breast cancer patients who have undergone mastectomy is developed. The results of this paper are implemented computationally with MATLAB and R.

在生存分析领域中考虑使用多状态模型来建模随时间演变为多个阶段的疾病。可以通过应用多种技术来开发多状态模型，例如非参数，半参数和随机过程，尤其是马尔可夫过程。在分析疾病的发展时，会定期跟踪疾病的进展。医学检查在不连续的时间进行，并且可以形成面板数据分析。在本文中，构造了离散时间分段非齐次马尔可夫过程，用于建模和分析具有多个状态的多状态疾病。建立模型，并确定相关度量，例如生存函数，过渡概率，在一组状态中花费的平均总时间以及状态改变的条件概率。建立似然函数来估计参数和模型中包含的切点的总数。引入了时变协变量，以矩阵代数形式获得了结果，并给出了算法。该模型用于分析乳腺癌的行为。开展了对300例接受乳房切除术的乳腺癌患者的复发和生存时间的研究。本文的结果是使用MATLAB和R计算实现的。开展了对300例接受乳房切除术的乳腺癌患者的复发和生存时间的研究。本文的结果是使用MATLAB和R计算实现的。开展了对300例接受乳房切除术的乳腺癌患者的复发和生存时间的研究。本文的结果是使用MATLAB和R计算实现的。