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I work with learning and predicting events (of various kinds) in time and space. The data is completely observable without censoring. Even so, survival analysis is a useful tool to learn a distribution over time and sample from it to predict future events (deaths). A potential challenge is the inclusion of time-varying covariates in the model. While the Cox's regression model can easily accommodate such covariates, predicting survival times is not easy due to the implicit assumption of treating the baseline hazard as unimportant (unspecified). On the other hand, the inclusion of time-varying covariates is not straight forward in the parametric models.

What is the best way to go about this? Given that the data lacks censoring but includes time varying covariates, is there another tool that is better suited to handle such a problem?

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While the baseline hazard is not specified in the Cox model, it is obtainable for predictions following model estimation. Most software packages allow you to obtain the baseline hazard for all observed event times. You can then use the linear predictor to predict a cumulative hazard from values of your observations or create a new dataset with candidate variable values for prediction.

See the UCLA IDRE for an example using Stata.

I cannot comment with authority on predictions with time-dependent covariates. Predictions from Cox models use covariate values to modify the baseline hazard at a given time. I see no reason why time-dependent covariates would create a false prediction, as long as you provide the exact time and a candidate time-dependent covariate value for each time.

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