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I have a standard time to event data set, with both time-independent and time-varying covariates.

I assume the time to event is a discrete random variable, and construct the extended data set to estimate a logistic model (following this link: http://data.princeton.edu/wws509/notes/c7s6.html).

My questions are:

  1. What is the independence assumption for the observations in the extended dataset?

  2. My goal is the predict if $T_{i,t}$ will be an event for individual $i$ at time point $t$ with the trained logistic regression above. How should I split the extended dataset into training and testing set? Split by individuals or split by individual-time observations?

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What is the independence assumption for the observations in the extended dataset?

That individuals are independent. There are dependence between each of your rows in the extended data within individual as each outcome at $t$ is conditional on having survived at time $t - 1$.

How should I split the extended dataset into training and testing set? Split by individuals or split by individual-time observations?

I would split by individuals due to the former mentioned dependence. You are observing failure times $T_i$ and not binary indicators $y_{i1},\dots,y_{iT_i}$ in your initial non-extended dataset.

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