Analysis of Survival Data: Challenges and Algorithm-Based Model Selection

Survival data is a special form of time to event data that is often encountered while modelling risk. The classical Cox proportional hazard model, that is popularly used to analyse survival data, cannot be used for modelling risk when the proportional hazard assumption is violated or when there is recurrent time to event data. In this context we conducted this narrative review to develop an algorithm for selection of advanced methods of analysing survival data in the above-mentioned situations. Findings were synthesized from literature retrieved from searches of Pubmed, Embase, and Google Scholar. Existing literature suggest that for non-proportionality, especially due to categorical predictors stratified Cox model may be useful. An accelerated failure time model is applicable in case of different follow-up time among different experimental groups and the median time to event is the outcome of interest instead of hazard. Extended Cox models and marginal models are used in case of multivariate ordered failure events and the type of model depends upon the presence of clustering and nature of ordering. In the presence of heterogeneity, a shared frailty model is used that is analogous to mixed models. More advanced models, including competing risk and multistate models are required for modelling competing risk, multiple states and multiple transitions. Joint models are used for multiple time dependent outcomes with different attributes. We have developed an algorithm based on the review for appropriate model selection to curb the challenge of modeling survival data and the algorithm is expected to help the naive researchers in analysing survival data.