Abstract
BACKGROUND: Reporting treatment effects from clinical trials on both relative and absolute scales is crucial. While absolute measures like the Number Needed to Treat (NNT) are well-established for binary outcomes, their calculation for time-to-event outcomes remains challenging due to time-dependence, which hinders interpretation and communication. Traditional additive hazard models, while addressing time-dependence, have been limited by restrictive assumptions regarding outcome distributions. METHODS: This paper proposes to use a recently introduced class of parametric additive hazard models to compute time-constant absolute effect measures for time-to-event outcomes. These models allow for a wide range of parametric distributions, overcoming the limitations of previous approaches. The approach provides a single, absolute effect size (e.g., hazard difference or NNT) summarizing the effect over the entire study duration. We illustrate this method using digitized Kaplan-Meier data from the EMPA-REG OUTCOME trial, focusing on all-cause mortality, and fit six different parametric distributions (exponential, linear hazard rate, Weibull, log-logistic, Gompertz, and Gamma-Gompertz). RESULTS: Despite notable differences in model fit across the six distributions, the estimated rate differences, corresponding NNTs, and their confidence intervals were remarkably similar. The linear hazard rate and Gompertz models, which provided the best fit according to the BIC, yielded a rate difference of -8.8 per 1,000 person-years, with an NNT of 114. These models also demonstrated increasing hazards, aligning with expectations for all-cause mortality. The estimated modes of the distributions from the best-fitting models (10.4 and 13.0 years) were more plausible than those from simpler models. CONCLUSIONS: The class of parametric additive hazard models offers a valuable tool for calculating time-constant absolute effect measures for time-to-event outcomes. This approach effectively addresses the issues of time-dependence and limited distribution flexibility, providing a single, interpretable absolute effect size. Future work could explore more general distributions and further derivation of absolute effect measures on the time scale.