Modeling Discrete Time-to-Event Data
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This result is analogous to the result linking the survival function in continuous time to the integrated or cumulative hazard at all previous times. An example of a survival process that takes place in discrete time is time to conception measured in menstrual cycles.
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Specifically, he proposed the model. In fact, the analogy with logistic regression goes further: we can fit the discrete-time proportional-hazards model by running a logistic regression on a set of pseudo observations generated as follows. The proportional hazards model 7. More generally, we can group pseudo-observations with identical covariate values.
The proof of this result runs along the same lines as the proof of the equivalence of the Poisson likelihood and the likelihood for piece-wise exponential survival data under non-informative censoring in Section 7. It is important to note that we do not assume that the pseudo-observations are independent and have a Bernoulli or binomial distribution. Rather, we note that the likelihood function for the discrete-time survival model under non-informative censoring coincides with the binomial likelihood that would be obtained by treating the death indicators as independent Bernoulli or binomial.
Time-varying covariates and time-dependent effects can be introduced in this model along the same lines as before. Recalling Equation 7.
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The transformation that makes the right hand side a linear function of the parameters is the complementary log-log. Applying this transformation we obtain the model. This model can be fitted to discrete survival data by generating pseudo-observations as before and fitting a generalized linear model with binomial error structure and complementary log-log link. In other words, the equivalence between the binomial likelihood and the discrete-time survival likelihood under non-informative censoring holds both for the logit and complementary log-log links.
It is interesting to note that this model can be obtained by grouping time in the continuous-time proportional-hazards model.
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Good text to introduce concepts of discrete time-to-event analyses and some relevant applications. The book includes some useful introduction to discrete time analyses, and more generally survival analysis, but also some more specific applications e. Was hoping for R code to be included in the text, although the book does reference useful R packages for performing each type of analysis, and includes example analyses including datasets and results in each chapter which can be replicated by the reader.
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