In experimental studies the most commonly used survival analysis technique is likely to be the (non-parametric) Kaplan-Meier method (1958). In epidemiology the most popular one is the (semi-parametric) Cox regression model (1972). Very often in cancer clinical trials the primary comparison between treatment and control groups is based on the Kaplan-Meier method. A secondary analysis with adjustment for covariates based on the Cox regression model is then reported (see example 2). Example 1 and 3 used the Cox model and a parametric model, respectively.

Kaplan EL, Meier P. Nonparametric estimation from incomplete observations. J Am Stat Asso 1958; 53: 457-481.

Cox DR. Regression models and life tables (with discussion). J Royal Stat Soc B 1972; 34: 187-220.