证明一下survival likelihood

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2024-04-05 更新 🔗

  1. 写likelihood第一步,想一下 what is Y. in survival analysis, the observed outcome, is observed T + status. where T is either censoring time(C_i) or event time (T~_i)
  2. 两个假设很重要: 1. independent censoring (C_i and T~_i independent); 2. non-informative censoring C_i does not involve theta (params of interest)
  3. 因为我们观测到的结局包括了两种情况有人censor有人developed outcome,i)censored+censoring time or ii).event+event time. 那么我们就分情况写likelihood。这是因为我们的数据产生机制就是有censoring dist and event time dist (参考我们practicum是如何产生observed time的,我们是假设censoring time ~ some dist, e.g., uniform, exp; event time ~ some dist T = min{C, T~})

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