Time-dependent Cox model with endogenous time-varying cofactor

TomHsiung — Tue, 14 Oct 2025 14:07:46 GMT

I read from a textbook saying the traditional (partial) likelihood function does not hold if the time-varying cofactor is endogenous (if the person dies, the factor will not exist anymore). If we are dealing with exogenous time-varying cofactor such as switch between treatment strategies, we can use the Andersen-Gill model with a robust (clustered) variance estimator to get the model parameters.

I read further and know the joint model could be used to serve the purpose - a shared random eﬀect model, which includes a submodel to depict the trajectory of the time-varying endogenous cofactor (e.g., serum albumin, CD4 cell count, etc.) and the other submodel to describe the survival function. The two parts can be linked together.

I wonder if there is a SAS procedure to fit dataset into this joint model and output estimation of parameters. Thank you.

PS: They just jointed the two part independently for the full likelihood function.

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Time-dependent Cox model with endogenous time-varying cofactor