Random intercepts and random coefficients
Exponential, loglogistic, Weibull, lognormal, gamma, survival distributions
Graphs of marginal survivor, cumulative hazard, and hazard functions
Fully integrated with stset
Fully integrated with xtset
Survival models concern time-to-event outcomes. The outcomes can be anything: death, myopia, employment, etc. The outcomes can be good or bad, such as recovery or relapse, or marriage or divorce, which is worth mentioning because the jargon of survival analysis suggests the outcomes are unpleasant. The word survival itself suggests time until death.
The data on which survival models are fit are often right-censored. Data are collected for a while and, as of some date, data collection ends before everyone has "failed". Two types of survival models are popular for right-censord data: semiparametric and parametric. Semiparametric means Cox proportional hazards. Parametric means a distributional assumption is made, typically exponential, Weibull, lognormal, conditional log log, etc.
Panel data concerns repeated observations of the primary analysis unit. For instance, let's assume we are analyzing data on individuals. Obviously, in survival data, we have repeated observations on the same person because we observed them over a period of time, from onset of risk until failure or the calling off of the data collection effort. Sometimes the multiple observations on a person are explicit; the data themselves contain multiple observations for some or all the individuals. That happens when covariates change over time. Other times, the multiple observations on the individuals are implicit; there is only one physical observation for each, but still that observation records a span of time.
Those kinds of repeated observations have nothing to do with panel data. Panel data arises, for instance, when individuals are from different countries and it was believed that country affects survival. In that case, in a panel-data model, there would be a random effect or, if you prefer, an unobserved latent effect for each country.
We can, however, write models in which the random effect occurs at the individual level if we have repeated failure events for them.
Panel-data random effects are similar to frailty, a survival-analysis concept. In frailty, related observations (individuals) are grouped and viewed as sharing a latent component. Stata offers gamma- or inverse-Gaussian-distributed frailty for parametric models, and gamma-distributed frailty for semiparametric models; see the manual entries [ST] streg and [ST] stcox. Panel-data random effects are assumed to be normally distributed and are available with parametric survival models. Frailty is assumed to be gamma- or inverse-Gaussian distributed, and that is mainly for computational rather than substantive reasons. Panel-data's normal random effects are a more plausible assumption. They are equivalent to lognormal frailties.
Stata provides two commands, xtstreg and mestreg, for fitting parametric survival models with panel-data. Examples of survival outcomes in panel data are the number of years until a new recession occurs for a group of countries that belong to different regions, or unemployed weeks for individuals who might experience multiple unemployment episodes.
Read more about panel-data survival models in Stata Longitudinal-Data/Panel-Data Reference Manual; see [XT] xtstreg.