Evaluating Additive Interaction Using Survival Percentiles.

Evaluation of statistical interaction in time-to-event analysis is usually limited to the study of multiplicative interaction, via inclusion of a product term in a Cox proportional-hazard model. Measures of additive interaction are available but seldom used. All measures of interaction in survival analysis, whether additive or multiplicative, are in the metric of hazard, usually assuming that the interaction between two predictors of interest is constant during the follow-up period. We introduce a measure to evaluate additive interaction in survival analysis in the metric of time. This measure can be calculated by evaluating survival percentiles, defined as the time points by which different subpopulations reach the same incidence proportion. Using this approach, the probability of the outcome is fixed and the time variable is estimated. We also show that by using a regression model for the evaluation of conditional survival percentiles, including a product term between the two exposures in the model, interaction is evaluated as a deviation from additivity of the effects. In the simple case of two binary exposures, the product term is interpreted as excess/decrease in survival time (i.e., years, months, days) due to the presence of both exposures. This measure of interaction is dependent on the fraction of events being considered, thus allowing evaluation of how interaction changes during the observed follow-up. Evaluation of interaction in the context of survival percentiles allows deriving a measure of additive interaction without assuming a constant effect over time, overcoming two main limitations of commonly used approaches.