Comparison of Cox Proportional Hazards Model and Lognormal Accelerated Failure Time Model: Application in Time to Event Analysis of Acute Liver Failure Patients in India

Abstract

Background: Different survival analysis techniques such as nonparametric, semi-parametric, parametric Accelerated Failure Time (AFT) models have been generally applied to analyze time to event data. In order to identify the prognostic factors for survival of Acute Liver Failure (ALF) patients, previous studies applied Cox Proportional hazards (CPH) model, Lognormal AFT and Log-Logistic AFT model satisfying respective model’s assumptions and goodness of fit of each model. However, comparison of CPH model and AFT model has not been reported so far for ALF data with short follow up time.

Objective: To compare CPH model and Lognormal AFT model based on different parameters for assessing the model performance and prospective validation of the finally selected model.

Materials and Methods: Altogether 1099 ALF patients’ data from liver clinic of All India Institute of Medical Sciences, New Delhi India were analyzed based on the retrospective cohort study design. For validating the final model, a separate data set of 138 ALF patients from the same clinic was used. CPH model and Lognormal model’s performance was assessed through selection of variables in the final model, R2 type statistic, goodness of fit of the model, visual assessment of Cox-Snell’s residuals plot and robustness of the model. The prospective validation of the over scored CPH model was done by comparing overall survival, regression coefficients, observed and predicted survival curves between original and validation data set.

Results: It is found that 60% of variation in the partial log-likelihood is explained by the CPH model whereas 39% of variation in full log-likelihood is explained by Lognormal AFT model. Cox-Snell residuals plot for CPH model seems less deviated from the line of ideal fit, replications of variables measured through bootstrapping resampling technique in CPH model are on the higher side, model predicted and observed survival curves in each risk stratum were closer than that of Lognormal model. The survival experience of original data and validation data set for CPH model does not seem to be very different (p = 0.07) at 5% level of significance.

Conclusion: Both CPH and Lognormal AFT model are found well fitted and can be applied either of them for this ALF data. While comparing the model performance, the CPH model for the identification of prognostic factors for the survival of ALF patients is found comparatively better.