Multiplicative models for survival percentiles: estimating percentile ratios and multiplicative interaction in the metric of time

Evaluating percentiles of survival was proposed as a possible method to analyze time-to-event outcomes. This approach sets the cumulative risk of the event of interest to a specific proportion and evaluates the time by which this proportion is attainedIn this context, exposure-outcome associations can be expressed in terms of differences in survival percentiles, expressing the difference in survival time by which different subgroups of the study population experience the same proportion of events, or in terms of percentile ratios, expressing the strength of the exposure in accelerating the time to the event. Additive models for conditional survival percentiles have been introduced, and their use to estimate multivariable-adjusted percentile differences, and additive interaction on the metric of time has been described. On the other hand, the percentile ratio has never been fully described, neither statistical methods have been presented for its models-based estimation. To bridge this gap, we provide a detailed presentation of the percentile ratio as a relative measure to assess exposure-outcome associations in the context of time-to-event analysis, discussing its interpretation and advantages. We then introduce multiplicative statistical models for conditional survival percentiles, and present their use in estimating percentile ratios and multiplicative interactions in the metric of time. The introduction of multiplicative models for survival percentiles allows researchers to apply this approach in a large variety of context where multivariable adjustment is required, enriching the potentials of the percentile approach as a flexible and valuable tool to evaluate time-to-event outcomes in medical research