Turning the analysis of obesity-mortality associations upside down: Modeling years of life lost through conditional distributions

Objective: We demonstrate the utility of parametric survival analysis. The analysis of longevity as a function of risk factors such as body mass index (BMI; kg/m²), activity levels, and dietary factors is a mainstay of obesity research. Modeling survival through hazard functions, relative risks, or odds of dying with methods such as Cox proportional hazards or logistic regression are the most common approaches and have many advantages. However, they also have disadvantages in terms of the ease of interpretability, especially for non-statisticians; the need for additional data to convert parameter estimates to estimates of years of life lost (YLL); debates about the appropriate time scale in the model; and an inability to estimate median survival time when the censoring rate is too high. Design and Methods: We will conduct parametric survival analyses with multiple distributions, including distributions that are known to be poor fits (Gaussian), as well as a newly discovered ''Compressed Gaussian'' distribution. Results: Parametric survival analysis models were able to accurately estimate median survival times in a population-based data set of 15,703 individuals, even for distributions that were not good fits and the censoring rate was high, due to the central limit theorem. Conclusions: Parametric survival models are able to provide more direct answers, and in our analysis of an obesity-related data set, gave consistent YLL estimates regardless of the distribution used. We recommend increased consideration of parametric survival models in chronic disease and risk factor epidemiology.