Semi-Markov models are widely used for survival analysis and reliability analysis. In general, there are two competing parameterizations and each entails its own interpretation and inference properties. On the one hand, a semi-Markov process can be defined based on the distribution of sojourn times, often via hazard rates, together with transition probabilities of an embedded Markov chain. On the other hand, intensity transition functions may be used, often referred to as the hazard rates of the semi-Markov process. We summarize and contrast these two parameterizations both from a probabilistic and an inference perspective, and we highlight relationships between the two approaches. In general, the intensity transition based approach allows the likelihood to be split into likelihoods of two-state models having fewer parameters, allowing efficient computation and usage of many survival analysis tools. Nevertheless, in certain cases the sojourn time based approach is natural and has been exploited extensively in applications. In contrasting the two approaches and contemporary relevant R packages used for inference, we use two real datasets highlighting the probabilistic and inference properties of each approach. This analysis is accompanied by an R vignette.

中文翻译：

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半马尔可夫多状态模型的估计：逗留时间和过渡强度方法的比较

半马尔可夫模型广泛用于生存分析和可靠性分析。一般来说，有两个相互竞争的参数化，每个参数化都有自己的解释和推理属性。一方面，半马尔可夫过程可以基于逗留时间的分布来定义，通常通过危险率，以及嵌入马尔可夫链的转移概率。另一方面，可以使用强度转换函数，通常称为半马尔可夫过程的危险率。我们从概率和推理的角度总结和对比这两种参数化，并强调两种方法之间的关系。一般来说，基于强度转换的方法允许将似然分解为具有较少参数的两态模型的似然，允许有效计算和使用许多生存分析工具。然而，在某些情况下，基于逗留时间的方法是自然的，并且已在应用程序中得到广泛利用。对比这两种方法和用于推理的当代相关 R 包，我们使用两个真实数据集突出每种方法的概率和推理属性。此分析伴随着一个 R 小插图。