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Chen, L.‐W., Cheng, Y., Ding, Y. and Li, R. (2020), Quantile association regression on bivariate survival data. Can J Statistics. https://doi.org/10.1002/cjs.11577
The association between two event times is of scientific importance in various fields. The local association measures capture the dynamic pattern of association and thereby provide much richer information than the global association measures. Due to the heterogeneity of the population, it is desirable to examine the degree to which local association depends on different characteristics of the population. In this work, we propose a quantile-based regression model for the association between two event times that may be censored (i.e., event not observed yet when a study ends). The proposed quantile-based association regression model enables the evaluation of the strength of the local dependency between different quantiles (e.g., medians) of marginal event times. We apply the model to an age-related macular degeneration (AMD) dataset, where we explore the association between AMD progression times in the two eyes of the same patient. Our analysis suggests that the associational strength between the progression times of the two eyes is stronger among those with higher AMD severity score at baseline, and the impact of the baseline AMD severity score on the odds ratio is higher at short progression times (low quantiles) than at long progression times (high quantiles) while conditioning on age and smoking status. This suggests a varying effect of the baseline AMD severity score on the local association, which cannot be captured by global association models. The findings have important clinical implications. For a person who has a large AMD severity score at baseline, if she/he suffers the progression to late-AMD in one eye in a short period, it is of importance to monitor the other eye as soon as possible.