# Survival analysis, repeated measurements, large samples

My basic question

What are some standard time-dependent, repeated measures, full longitudinal survival analysis models?

The more precise question and context is as follows.

Context

Suppose we have $N$ = 1 million samples $\{Y_k(T)\}_{1\leq k\leq N}$ and we wish to predict the longevity of each $Y$ using the following information. Each $Y$ consists of $p$ (e.g. $p=25$) time-dependent covariates $x_1(t), \ldots, x_p(t)$, a binary censor (event) variable $c$ and current age $d(t)$. We would like to model $d(t)$ based on the covariates and censor variable.

Recall that in basic survival models such as Aalen's additive model (AAM) or CoxPH, we traditionally train the model on exactly one snapshot of data, i.e. we fix exactly one $\hat{t}>0$ and restrict the training to the set $\{Y_{k'}(T=\hat{t}\,)\}_{k'}$, for some $k'\leq N$.

Goal

Now, since my data has several time values $x_p(t')$ whenever $d(t)>0$ for $t\geq t'$, my goal is to do survival analysis'' for more than one snapshot. For this goal, the (standard) AAM or CoxPH do not suffice.

Question

What are other models or extensions of AAM/CoxPH that might help achieve the above goal?

It would be great if, for example, suggested models account for rates $dx_i/dt$ for each $1\leq i\leq p$.

As a concrete example, if we have two samples $Y_1$ and $Y_2$ and we know that the velocity'' of $x_1$ for $Y_1$ is greater than the corresponding velocity for $Y_2$, then this information should impact the expected duration for $Y_1$ differently than for $Y_2$.

Literature references would be highly appreciated, as well as Python, R, or SAS, though literature with a mathematical tone is favored.