Fotios Siannis, Konstantina Konidari, University of Athens, Greece

Context: Meta-analysis of time-to-event data is of great interest. Standard methodology based on analyzing quantities such as the hazard ratios completely ignore the time aspect that is a key element to this type of data. As such, any meta-analysis performed on time-to-event data is based on a set of assumptions of proportionality on all participating studies and offers a rather one dimensional analytic approach.
Objective(s): Our aim is to introduce a methodology that allows time to be part of the meta-analysis. In this way we can explore how the quantity of interest behaves at various percentile (time) points as well as investigate the changes that occur over time. This definitely offers a more comprehensive analytic approach.
Method(s): We allow the percentile ratio of survival times of competing groups to serve as the quantity of interest in meta-analysis. As a result, time is incorporated in the analysis through the percentiles. We then introduce a quantile regression model where percentiles of the log-survival times of the two groups under investigation can be estimated as well as their ratio. The explanatory variables in the model may depend on the chosen percentile. Hence, different models with different set of parameters can be used to investigate how the effect changes over percentile time. Censoring can be incorporated in order to provide a real life analysis.
Results: In a large meta-analysis involving newborns, the indicated association between breastfeeding and a child's reduced risk of being overweight didn't lead to a difference in mean BMI between the two groups. However, quantile regression demonstrated that significant changes in BMI could be observed in both upper and lower percentiles. Additionally, for data simulated from Cox proportional hazards model the results from the Cox and quantile regression approaches appeared similar while when data were simulated from a quantile regression model this was not the case. This suggests that both approaches should be applied in order to obtain a more complete analysis.
Conclusions: Meta-analysis of time-to-event data using quantile regression doesn't depend on restrictive assumptions about the distribution or the structure of the data, offering a quite flexible and robust analysis.

References
Beyerlein, A. (2014). Quantile Regression-Opportunities and Challenges From a User’s Perspective. American Journal of Epidemiology, 180(3), 330–331.
Portnoy S. (2003) Censored Regression Quantiles. Journal of the American Statistical Association,98(464), 1001-1012