Subgroup Identification For Time-to-event Data Based On Accelerated Failure Time Model

BackgroundSubgroup identification is an important means of precision medicine,while survival data commonly arises in clinical trials.It is urgent to reliably identify the subpopulation of enhanced treatment effect in a randomized clinical trial with respect to survival time.When interest lies in the relationship between covariates and duration time,the most popular regression model in survival analysis is Cox proportional hazards model,but its assumption often doesn’t hold.An alternative is the accelerated failure time(AFT)model which doesn’t rely on the proportional hazard assumption.In survival analysis,the popular models are usually suitable for data with few covariates and many observations.In the case where the number of covariates exceeds the sample size,it is necessary to apply the penalty to regression model so as to reduce instabilities in variable selection.Therefore,our study proposes applying the univariate AFT model and penalized AFT model regularized by adaptive elastic net to subgroup identification with respect to survival time.ObjectiveConsidering the problem of identifying subgroup in a randomized clinical trial with respect to survival time,we present an analysis strategy to find subgroup of enhanced treatment effect based on AFT model.MethodsWe fitted univariate AFT models,applied adaptive elastic net to the AFT model(designated as the penalized model)and identified the candidate covariates based on covariate-treatment interactions.Based on the identified covariates,predictive score of each patient was computed.To classify patient subgroups,we utilized the classifier based on change-point algorithm to find the threshold cutoff-point.A two-stage adaptive design was adopted to verify if the treatment effect exists within certain subgroups.Firstly,to evaluate the performance,simulations were conducted across different sample size,censoring rate,or subgroup proportion.Secondly,to explore how the univariate AFT model and penalized AFT model perform in the data with a sample size that did not exceed the number of covariates,evaluations were also made through simulations conducted across different scenarios.ResultsFirstly,simulations showed that the univariate AFT model without the main effect of the covariates outperformed the one with the main effect in different scenarios.The change-point algorithm noticeably outperformed the median cutoff especially when the subgroup proportion was less than 0.5.Secondly,the penalized model with the main effect of the covariates performs better than the one without the main effect.And the penalized model with the main effect of the covariates considerably outperformed the univariate model without the main effect for the trial data with a small sample size,a high censoring rate,a small subgroup size,or a sample size that did not exceed the number of covariates;in other scenarios,the latter model showed better performances.Furthermore,the adaptive design improved the power for detecting the treatment effect where subgroup effect exists,while the type I error of the univariate AFT model without main effect and that of the penalized model with the main effect showed a well-controlled type I error.ConclusionThe univariate AFT model without main effect of covariates,and the penalized AFT model with main effect both have advantage in subgroup identification with respect to survival data.In low sample size,high censoring rate,low subgroup size,or high-dimensional data,the latter one outperforms the former one.In other scenarios,the former one performs better.Adaptive design may be useful in evaluation of treatment effect when subgroup effect exists.