# Survival analysis and regression models

2018 Feb 21
**Abstract**: Time-to-event outcomes are common in medical research as they offer more information than simply whether or not an event occurred. To handle these outcomes, as well as censored observations where the event was not observed during follow-up, survival analysis methods should be used. Kaplan-Meier estimation can be used to create graphs of the observed survival curves, while the log-rank test can be used to compare curves from different groups. If it is desired to test continuous predictors or to test multiple covariates at once, survival regression models such as the Cox model or the accelerated failure time model (AFT) should be used. The choice of model should depend on whether or not the assumption of the model (proportional hazards for the Cox model, a parametric distribution of the event times for the AFT model) is met. The goal of this paper is to review basic concepts of survival analysis. Discussions relating the Cox model and the AFT model will be provided. The use and interpretation of the survival methods model are illustrated using an artificially simulated dataset.

**SUMMARY AND CONCLUSIONS** This paper reviews some basic concepts of survival analyses including discussions and comparisons between the semiparametric Cox proportional hazards model and the parametric AFT model. The appeal of the AFT model lies in the ease of interpreting the results, because the AFT models the effect of predictors and covariates directly on the survival time instead of through the hazard function. If the assumption of proportional hazards of the Cox model is met, the AFT model can be used with the Weibull distribution, while if proportional hazard is violated, the AFT model can be used with distributions other than Weibull.

It is essential to consider the model assumptions and recognize that if the assumptions are not met, the results may be erroneous or misleading. The AFT model assumes a certain parametric distribution for the failure times and that the effect of the covariates on the failure time is multiplicative. Several different distributions should be considered before choosing one. The Cox model assumes proportional hazards of the predictors over time. Model diagnostic tools and goodness of fit tests should be utilized to assess the model assumptions before statistical inferences are made.

In conclusion, although the Cox proportional hazards model tends to be more popular in the literature, the AFT model should also be considered when planning a survival analysis. It should go without saying that the choice should be driven by the desired outcome or the fit to the data, and never by which gives a significant P value for the predictor of interest. The choice should be dictated only by the research hypothesis and by which assumptions of the model are valid for the data being analyzed.