Vandamme Lode K J, Wouters Peter A A F, Slooter Gerrit D, de Hingh Ignace H J T
Department of Electrical Engineering, Eindhoven University of Technology, 5612AE Eindhoven, The Netherlands.
Department of Surgical Oncology, Máxima Medical Center, 5504DB Veldhoven, The Netherlands.
Healthcare (Basel). 2019 Oct 28;7(4):123. doi: 10.3390/healthcare7040123.
Survival functions are often characterized by a median survival time or a 5-year survival. Whether or not such representation is sufficient depends on tumour development. Different tumour stages have different mean survival times after therapy. The validity of an exponential decay and the origins of deviations are substantiated. The paper shows, that representation of survival data as logarithmic functions visualizes differences better, which allows for differentiating short- and long-term dynamic lifetime. It is more instructive to represent the changing lifetime expectancy for an individual who has survived a certain time, which can be significantly different from the initial expectation just after treatment. Survival data from 15 publications on cancer are compared and re-analysed based on the well-established: (i) exponential decay (ii) piecewise constant hazard (iii) Weibull model and our proposed parametric survival models, (iv) the two-τ and (v) the sliding-τ model. The new models describe either accelerated aging or filtering out of defects with numerical parameters with a physical meaning and add information to the usually provided log-rank -value or median survival. The statistical inhomogeneity in a group by mixing up different tumour stages, metastases and treatments is the main origin for deviations from the exponential decay.
生存函数通常由中位生存时间或5年生存率来表征。这种表征是否足够取决于肿瘤的发展情况。不同的肿瘤阶段在治疗后的平均生存时间不同。指数衰减的有效性以及偏差的来源得到了证实。本文表明，将生存数据表示为对数函数能更好地直观呈现差异，这有助于区分短期和长期的动态生存期。对于在一定时间后存活的个体，呈现其不断变化的预期寿命更具启发性，这可能与治疗刚结束时的初始预期有显著差异。基于以下成熟方法，对来自15篇癌症相关出版物的生存数据进行了比较和重新分析：(i)指数衰减；(ii)分段恒定风险；(iii)威布尔模型以及我们提出的参数化生存模型；(iv)双τ模型；(v)滑动τ模型。新模型通过具有物理意义的数值参数描述加速衰老或缺陷筛选，并为通常提供的对数秩值或中位生存增加了信息。通过混合不同肿瘤阶段、转移情况和治疗方法导致的组内统计不均匀性是偏离指数衰减的主要原因。
