An overview of semiparametric models in survival analysis

• We review commonly used semiparametric models for time to event.
• The models include the Cox proportional hazards models, linear transformation models and the accelerated failure time model.
• Nonparametric maximum likelihood estimation provides efficient estimators.
• The reviewed models can be applied to univariate and multivariate censored data.
• Semiparametric models are also used for analyzing interval censored data and joint analysis of multiple outcomes.

We provide an overview of semiparametric models commonly used in survival analysis, including proportional hazards model, proportional odds models and linear transformation models. The applications of these models to different types of censored data, either univariate or multivariate survival analysis, are given. For each case, inference procedures using censored observations are discussed.