A survival analysis model for measuring association between bivariate censored outcomes: validation using mathematical simulation

Abstract

Bivariate censored data occur in follow-up studies of events that can result in two different outcomes. Many studies have explored methods for inference about the marginal recurrence times of these outcomes. However, very few have focused on the dependence structures between their occurrences or recurrence times especially when these outcomes are censored as evidence in the current study. This theoretical and empirical study used simulated data to monitor and validate the survival analysis model for measuring association between recurrence times of bivariate censored outcomes. Bivariate outcomes would naturally fall into one of four possibilities: only the first, only the second, none or both conditions occurring with different and distinct likelihoods. Using predetermined correlation coefficients, n=100000 bivariate standardized binormal data were simulated. The simulated data were then subjected to different censoring chances while contributions of the likelihoods of the four possibilities were examined and Maximum Likelihood Estimate (MLE) of the association parameter determined. For the data simulated at 50% censoring, MLE of the association parameter tended to zero as the predetermined correlation coefficients fell from +1.0 to -1.0. However, at 0% censoring, the MLE were approximates of the predetermined correlation coefficients. The developed model was robust as the model responded adequately to the dynamics of the predetermined correlation and censoring conditions. The model would be appropriate in studying associations between two censored survival times.